RAM PRESSURE CORRELATIONS FOR

ASPIRATED CYLINDERS

by

ZACHARY JAMES SCHOLZ, B.S.M.E.

A THESIS

IN

MECHANICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

MECHANICAL ENGINEERING

Approved

Chairperson of the Conraiittee

Accepted

• j - y .1 - . 1 I I . • • • • . — • - — I I M >i

Dean of the Graduate School

May, 2004

ACKNOWLEDGEMENTS

I would like to take this opportunity to thanl< the people that have been influential

in my life and aided me in this publication. To Dr. Walt Oler, who is a valuable asset to

the Engineering program at Texas Tech, thank you for believing in me and allowing me

to pursue this project with your expert guidance.

To my committee members, Dr. Siva Parameswaran, and Dr. Timothy Maxwell,

for your classes and extraordinary leadership are a testament to the engineering reputation

of this university.

To Ford Motor Company for your generous fmancial support, without which, I

would not have been able to pursue this advanced degree.

Last but not least, to my fiancé, and both of our families, for your support in this

venture speaks volumes about your commitment to those you love.

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ii

ABSTRACT iv

LISTOFTABLES vi

LIST OF FIGURES vii

NOMENCLATURE ix

CHAPTER

I. INTRODUCTION 1

IL LITERATURE REVIEW 3

m. TECHNICAL APPROACH 15

3.1 Ram Coefficients for Individual Openings 15

3.2 Ram Coefficients for Combined Openings 21

IV. EXPERIMENTAL SETUP 25

4.1 WindTunnel 26 4.2 Model Parameters 26

4.3 Data Acquisition 29

V. RESULTS AND DISCUSSION 33

5.1 Zero FIow Rate Measurement 33 5.2 Ram Coefficients for Individual Openings 37

5.3 Ram Coefficients for Multiple Openings 46

VI. CONCLUSIONS AND RECOMMENDATIONS 57

6.1 Conclusions 57

6.2 Recommendations 58

REFERENCES 60

APPENDIX

A. LABVIEW VI SCREENSHOTS 61

B. RAM COEFFICIENTS FOR SINGLE OPENINGS TABULAR DATA 64

C. RAM COEFFICIENTS FOR MULTIPLE OPENINGS TABULAR DATA.. 71

ni

ABSTRACT

Design of automobile cooling systems involves tradeoffs in the sizing of grille

openings to provide adequate cooling airflow and the tendency to reduce grille opening

size to decrease vehicle cooling drag and produce aesthetically pleasing designs. Air that

enters the cooling system of an automobile is driven by two major sources, the freestream

dynamic pressure resulting from the forward motion of the vehicle and the intemal

vacuum created by the underhood fan. The flow fields associated with both sources must

be considered when assessing the cooling performance of a new automobile design. The

current investigation focuses on characterizing the external or dynamic pressure induced

flow through a parameter known as the ram coefficient.

The investigation utilized an aspirated cylinder in cross-flow as an idealized

representation of an automobile front end with grille openings. The pressure distribution

on the upstream side of the cylinder model includes a stagnation point and a significant

surface pressure gradient similar to those of an actual automobile front end fascia.

Various sized openings machined into the side of the cylinder model simulated the grille

openings in an automobile. A flexible hose connecting one end of the cylinder to a shop

vacuum provided a simulation of the cooling air flow induced by a radiator fan. The

primary advantage of the cylinder model is a dramatic reduction in the number of

experimental influences on the ram coefficient. The elimination of the various under-

hood components simplifies the investigation process down to the most basic

components, yielding accurate, repeatable results.

IV

Primary results are that the cylinder does provide a useful representation of

automobile front end. These results verify the general trends seen in previous full scale

model tests. Additionally, it was found that ram coefficients for single openings are

determined by opening size and location relative to the external surface pressure

distribution. It was also found that ram coefficients for combinations of openings can be

predicted from knowledge of the performance characteristics of the individual openings.

LIST OF TABLES

5.1: Cp,Q and k^ at Various Values of Cp 44

5.2: Model Test Itinerary 47

B.l: TabuIarData-SingIeOpening-Cp= 1.0 65

B.2: Tabular Data- Single Opening- Cp= 0.7 67

B.3: TabuIarData-SingIeOpening-C;,= 0.4 69

C.l: TabuIarData-MuItiple Openings- 19.05 {Cp= 1.0) and 8.73 (10 deg. Offset).... 72

C.2: Tabular Data - Multiple Openings - 19.05 {Cp = 1.0) and 8.73 (20 deg. Offset).... 74

C.3: Tabular Data- Multiple Openings - 19.05 (Cp= 1.0) and 7.14 (10 deg. Offset).... 76

C.4: Tabular Data- Multiple Openings - 19.05 {Cp= 1.0) and 7.14 (20 deg. Offset).... 78

C.5: Tabular Data- Multiple Openings - 8.73 {Cp= 1.0) and 19.05 (10 deg. Offset).... 80

C.6: Tabular Data- Multiple Openings - 8.73 {Cp= 1.0) and 19.05 (20 deg. Offset).... 82

C.7: TabuIarData-MultipIeOpenings-8.73 {Cp= 1.0) and 7.14 (10 deg. Offset) 84

C.8: TabuIarData-MuItipIeOpenings-8.73 {Cp= 1.0) and 7.14 (20 deg. Offset) 86

C.9: Tabular Data-Multiple Openings-7.14 {Cp= 1.0) and 19.05 (10 deg. Offset).... 88

C.IO: Tabular Data- Multiple Openings - 7.14 {Cp= 1.0) and 19.05 (20 deg. Offset).. 90

C.I I: Tabular Data - Multiple Openings - 7.14 (C;,= 1.0) and 8.73 (10 deg. Offset).... 92

C.12: Tabular Data- Multiple Openings - 7.14 (C;,= 1.0) and 8.73 (20 deg. Offset).... 94

C.13: TabuIarData-MuItipIeOpenings-8.73 {Cp= 1.0) and 8.73 (lOdeg. Offset)....96

C.14: Tabular Data- Multiple Openings - 7.14 {Cp= 1.0) and 7.14 (10 deg. Offset).... 98

VI

LIST OF FIGURES

2.1: Streamtube comparison (Schaub and Charles, 1980) 4

2.2: Screenshot of ttu_CooI® 6

3.1: Pressure changes from Freestream to Underbody 17

4.1: Wind Tunnel Schematic 25

4.2: Specimen Vacuum Connection 27

4.3: Model Schematic 28

4.4: shop'vac® 2.0 peak HP Wet/Dry Vacuum 28

4.5: Generic Ball Valve 29

4.6: TSI4000 Series FIow Meter 30

4.7: Top View of Model in the Test Section 32

5.1: Cylinder Pressure Curve 35

5.2: Cp,i versus qr/qO at C^ = 1.0 39

5.3: Complete Cp,, versus ^/go at Cp = 1.0 40

5.4: Cp, versus q/qodiXCp^ 1.0 42

5.5: Cp,, versus qj/qo at Cp = 0.7 43

5.6: Cp,i versus qt/qo at Cp = 0.4 44

5.8: Combined 19.05 {Cp= 1.0) and 8.73 (10 Deg. Offset) C ,, Coefficients 50

5.9: Combined 19.05 {Cp = 1.0) and 8.73 (20 Deg. Offset) Cpj Coefficients 50

5.10: Combined 19.05 {Cp= 1.0) and 7.14 (10 Deg. Offset) Cp,, Coefficients 51

5.11: Combined 19.05 (Cp= 1.0) and 7.14 (20 Deg. Offset) Cp,, Coefficients 51

vu

5.12: Combined 8.73 (C,,= 1.0) and 19.05 (10 Deg. Offset) C ,, Coefficients 52

5.13: Combined8.73(Cp=I.0)and 19.05 (20 Deg. Offset) C ,, Coeffícients 52

5.14: Combined 8.73 (Cp= 1.0) and 7.14 (10 Deg. Offset) Cpj Coefficients 53

5.15: Combined 8.73 {Cp= 1.0) and 7.14 (20 Deg. Offset) Cp,, Coefficients 53

5.16: Combined 7.14 {Cp = 1.0) and 19.05 (10 Deg. Offset) Cpj Coefficients 54

5.17: Combined 7.14 {Cp= 1.0) and 19.05 (20 Deg. Offset) Cpj Coefficients 54

5.18: Combined 7.14 {Cp = I.O) and 8.73 (10 Deg. Offset) Cpj Coefficients 55

5.19: Combined 7.14 {Cp= 1.0) and 8.73 (20 Deg. Offset) Cpj Coefficients 55

5.20: Combined 8.73 {Cp = 1.0) and 8.73 (10 Deg. Offset) Cpj Coefficients 56

5.21: Combined 7.14 {Cp = I.O) and 7.14 (10 Deg. Offset) C ,, Coefficients 56

A.l: LabVIEW Virtual Instrument (vi) Written for Data Acquisition (Front End) 62

A.2: LabVIEW Virtual Instrument (vi) Written for Data Acquisition (Diagram) 63

vui

NOMENCLATURE

AP^ Contraction pressure drop

p„ Freestream air density

Aj Inlet area

A^ Internal area

Cp Coefficient of pressure

k^ Experimentally determined coefficient - proportionality constant between

the ram coeffícient and inlet area ratio

K^ Wind tunnel contraction calibration coefficient

Kg Grille coefficient

^ram Rãm coefficient

K,^ Underbody coefficient

m Mass flow rate

P^ Freestream pressure

P, Inlet pressure

P^ Intemal pressure

Pj. Total pressure

Pj.^^^ Ram pressure

q^ Freestream dynamic pressure

q^ Inlet dynamic pressure

IX

q^ Internal dynamic pressure

V„ Freestream velocity

V- Volumetric flow rate

CHAPTERI

INTRODUCTION

Design of automobile cooling systems involves tradeoffs in the sizing of grille

openings to provide adequate cooling airflow and the tendency to reduce grille opening

size to decrease vehicle cooling drag and produce aesthetically pleasing designs. Air that

enters the cooling system of an automobile is driven by two major sources, the freestream

dynamic pressure resulting from the forward motion of the vehicle, and the intemal

vacuum created by the underhood fan. The flow fields associated with both sources must

be considered when assessing the cooling performance of a new automobile design. The

current investigation focuses on characterizing the extemal or dynamic pressure induced

flow through a parameter knowoi as the ram coefficient.

The ram coefficient has proven to be a meaningful way of characterizing the

influence of grille openings on cooling system performance, as seen in wind tunnel

research by Roseberry (1990), Crafton (1992), and Nguy (1992). Because the ram

coefficient is simply a fiinction of intemal static pressure normalized by freestream

dynamic pressure, it can be helpful in determining whether a new cooling design meets

the desired criteria, or whether further modifications should be made.

The investigation utilized an aspirated cylinder in cross-flow as an idealized

representation of an automobile front end with grille openings. The pressure distribution

on the upstream side of the cylinder model includes a stagnation point and a signifícant

surface pressure gradient similar to those of an actual automobile front end fascia.

Various sized openings machined into the side of the cylinder model simulated the grille

1

openings in an automobile. A flexible hose connecting one end of the cylinder to a shop

vacuum provided a simulation of the cooling air flow induced by a radiator fan. Because

the cylinder model is considerably smaller than the previous automobile models, it can be

tested inexpensively in a small wind tunnel. The elimination of the various under-hood

components simplifies the investigation process down to the most basic components,

yielding accurate, repeatable results.

Primary results are that the cylinder does provide a useful representation of the

idealized automobile front end. These results verify the general trends seen in previous

fiill scale model tests. Additionally, it was found that ram coefficients for single

openings are determined by opening size and location relative to the extemal surface

pressure distribution. It was also found that ram coefficients for combinations of

openings can be predicted from knowledge of the performance characteristics of the

individual openings.

CHAPTER II

LITERATURE REVIEW

The first major step in research that replaced the trial and error method for cooling

system design was taken in the mid-1970s. Olson (1976) attempted to quantify the total

grille airflow by performing full-scale wind tunnel tests. By traversing a system of

anemometers mounted behind the radiator, Olson was able to measure the cooling air

flow and to identify some of the effects of various grille opening confígurations. This

process, however, proved to be somewhat inaccurate because of the poor flow

measurement techniques used in processing.

Hawes (1976) argued that configuration of intemal cooling system components,

and not size of the openings alone determined the best method of engine cooling. He

argued that overly large frontal intake areas only increased drag coefficients, and power

requirements, which reduced overall vehicle efficiency.

Schaub and Charles (1980) focused their study on the interaction between the

intemal and extemal airflows. They noted that the upstream capture area for a

streamtube containing the cooling airflow is infínitely large when the vehicle is not

moving with the radiator fan running. However, this capture area can decrease to less

than one square foot in cases where the vehicle is moving at rapid rates (Figure 2.1). The

extreme variation in extemal flows associated with ram or freestream dynamic pressure

driven flow or fan induced flow was used as an explanation for the widely variable

pressure drop for the flow through the grille openings. Schaub and Charles used a

method similar to Olson in collecting data. Using a system of traversing anemometers

mounted behind the radiator, they measured internal velocities on both fuU-scale wind

tunnel tests and road tests. Schaub and Charles were also able to investigate the effect of

the radiator fan on the cooling system performance. This investigation was important

because it was the first technique that allowed for griUe pressure drop measurements over

a range of fan induced vacuum rates and freestream velocities.

WiUiams (1985) used the term grille open area when describing the amount of

grille area that can be projected onto the radiator. WiIIiams stated that the grille open

area was not a feature that could, alone, be used to accurately determine the performance

of an engine cooling system. After aerodynamic and environmental wind tunnel tests, it

was ascertained that other factors were involved in determining the cooling performance

of the system.

(a) Stationary Vehiole

(b) Moving Vehicle

Figure 2.1: Streamtube comparison (Schaub and Charles, 1980)

Renn and Gilhaus (1986) discussed the importance of providing a system that

ducts the incoming air through the cooling components, thereby increasing the

component effectiveness, and preventing backflow. This process controlled the airflow

over the radiator and condenser, which reduced hot air recirculation. They deduced that

aerodynamic improvements need not necessarily interfere with cooling requirements.

Automotive engineers commonly use Computational Fiuid Dynamics (CFD) in

the design of an engine cooling system for an automobile. Typical CFD results include

highly detailed distributions of velocity and pressure which are presented in the form of

intuitive graphical presentations superposed on the vehicle geometry. With adequate care

to assure the accuracy of the calculations, CFD predictions may, in many cases, be

substituted for traditional wind turmel experiments. However, this approach is not

without its disadvantages, as CFD modeling requires a great deal of time to formulate the

computational grid due to complicated external and internal geometries. Any time the

model is changed, the entire grid must be reformulated for alternate configurations.

Additionally, many of the design parameters that the CFD model requires may not be

available during the early stages of the design process.

In an altemate approach to predicting overall cooling system performance, a

multiple streamtube concept was used to create a computational cooling system model,

ttu_Cool® at Texas Tech University (Oler and Jordan 1988). ttu_CooI® was later

expanded to predict heat rejection parameters by Dr. Walt Oler and Dr. Duane Jordan

(1990), with ftanding from Ford Motor Company. This model uses basic thermodynamic

principles in an iterative process to predict the overall cooling performance under specifíc

operating conditions (Figure 2.2).

Vehicle Speed

Road Grade

AmbîentTemp

Ambicnt Prcs í

-Jjcat Rejcctían-

jÊngine Power

Engínc Hcat

Trans Heat

Radiator Hcat

Coolant nowrate

CondcnscrHeat

Refrigerant Flowrate

Trans Cooicr Heat f

Trans Oii Rowrale

*9B.G :

L\../ .' 20.0

íêm/h

%

C

0.59

"! m . kW

kW

" " " k W

kg/s

kV/

kW

k9/&

-System Performance

Rad.MaGsriow 1.295 íg/f

Rad. ExitVol. Fiow

Top-V/ater Terrip.

AírExitTcmp.

AC Head nres.

64.65 ACMM

^n.íj c

20.'i c

kPa »„,

jFan Parameters,-

(rpml

Fan»1

Fan S2

Fan 83

1800.0

«Powcr'

^^atts)

236.72

- '„/^'/„„

Figure 2.2: Screenshiot of ttu_Cool°

With the current investigation, research at Texas Tech University into the

aerodynamics associated with the air flow through an automobile cooling system has

come full circle. Utilizing a small scale, highly abstracted representation of a vehicle

front end, Roseberry (1990) evaluated the efficiency of a grille configuration in terms of

a grille coefficient and revealed the basic relationships describing its variation with

vehicle speed, flow rate, and grille opening size. Crafton (1992), Nguy (1992), and

Vemer (2000) utilized slightly altered full-scale vehicles to demonstrate that the same

concepts applied to the much more complicated geometries and processes. In the present

investigation, another highly abstracted representation of a vehicle front-end, a simple

cylinder in cross flow, is applied to further reveal the fundamental physics associated

with the induction of air through the cooling system of an automotive vehicle.

Roseberry (1990) measured the change in total pressure for the flow through grille

and bottom openings on an idealized one fifth-scale automobile front-end. The front of

the box shaped model was fitted with a rounded fiberglass shell that included a grille

opening on the front and a bottom opening ahead of an underbody air dam. The size of

both the grille and bottom openings could be adjusted or closed completely. The rear of

the box was connected by a flexible hose to the inlet of a blower which simulated the

effect of a fan and provided a controlled flow rate through the model. A laminar flow

element mounted at the blower exhaust was used for flow rate measurement. The

presence of a radiator was simulated by honeycomb and screen mesh flow straighteners

placed across the model interior a short distance behind the grille and bottom openings.

An average static pressure was sensed with a manifold of static pressure taps just aft of

the honeycomb and screen. The incremental static pressure losses due to the honeycomb

and screen mesh were eliminated during the data reduction process to obtain the desired

static pressure ahead of the radiator (simulated by the honeycomb and screen) and behind

the inlets. With static pressure and flow rate measurements, it was possible to quantify

an interior total pressure based on the average velocity across the face of the honeycomb.

Roseberry defíned a grille loss coeffícient on the basis of the change in total

pressure across the grille opening,

^,„,=(p.+\pV:)-(Pr+^PV')

^ ^^,n„e ^ Pr.,.,.+-2PV'

'"'"• ^PV^ ^oV' 2 h"^ •X, 2 r'' X (1 \\

where the subscript /• indicates average conditions at the front face of the simulated

radiator. A corresponding grille coeffícient was based on the interior total pressure

behind the grille and underbody openings.

K _Pr.,a,.+\pV^ JpVl-^P^,,,

'"'"' \PV1 " {pV^

= ^-^ioss- (2.2)

The grille coeffícient represents the fraction of the freestream total pressure (relative to

the fi-eestream static pressure) delivered through the grille and underbody openings. As

defíned, the maximum value of the grille coefficient is one, corresponding to an interior

total pressure equal to the freestream total pressure. The ram coefficient may take on

negative values if the blower-aided flow rate is sufficiently high for the total pressure

drop through the grille to exceed the freestream dynamic pressure.

Roseberry's measurements demonstrated that, when tested individually, the grille

coeffícients for the grille and bottom openings are a unique ftinction of the ratio of

average velocity through the inlet F, to the freestream velocity,

^grille ~ ^gO + ^g\ 'v^

V , (2.3)

(AA 2

[yj

Alternatively, the ram recovery coeffícients may be expressed as a function of the ratio of

an average velocity at the face of the radiator to the freestream velocity and the ratío of

the radiator face area to the inlet area,

^grille ~ '^gO + . ^g l

(2.4)

Roseberry also found that the grille coefficient resulting from the combinatíon of

grille and bottom openings could be predicted by assuming that the relative flow rates

through the two openings must be such that both are operating at the same grille

coeffícient, i.e., producing the same total pressure within the model. For a given grille

coeffícient, the individual correlations for the grille and underbody openings were solved

for the corresponding inlet velocity ratios thereby leading to the flow rate through each

opening. Thus, the total flow rate for the combination of openings operating at a

particular grille coeffícient could be determined from the sum of the individual flow

rates.

After Roseberry's thesis, the question was whether a real automobile with the

geometric and physical complications of a bumper, griUe, radiator, and fan would exhibit

the same behavior. Crafton's (1992) wind tunnel test of a mid-size sedan (Ford Taurus)

andNguy's (1992) test of a light truck (Ford F150) demonstrated that, indeed, the same

physics apply to full-size vehicles. In both tests, the vehicle front ends were replaced

with a fiberglass fascia which had the same general shape as the actual vehicle.

Interchangeable panels with a variety of opening sizes could be placed on the fiberglass

front ends at the same relative locations of the grille and bottom openings on the actual

vehicles. The cavity behind the grille openings was fully sealed so that all air flow

through the grille and underbody openings was forced to pass through the radiator. Low

profíle pinwheel anemometers mounted on the back of the radiator were used to quantífy

the flow rate. Because of the strong turbulence expected immediately behind the

openings, the static pressure was sensed behind the radiator. The desired static pressure

ahead of the radiator was obtained by subtracting the radiator pressure drop which was

known from a separate flow stand test. GriIIe coefficients obtained by Crafton for the

sedan and Nguy for the light truck are qualitatively identical to those obtained by

Roseberry.

Crafton and Nguy both noted that the freestream dynamic pressure also affects the

cooling air flow rate through a reduction in the pressure beneath the vehicle and

effectively, a reduction in the back pressure on the cooling system. The underbody

pressure reduction is the result of a venturi effect on the air as it is channeled and

accelerated beneath the vehicle. The reduction in underbody pressure is characterized by

an underbody pressure coeffícient

j ^ _Px-Pu

'pVl IP'^ (2.5)

Noting that both the grille coeffícient and the underbody coefficient scale with the

freestream dynamic pressure, Crafton and Nguy introduced the ram coefficient parameter

to represent the combined effects of the freestream dynamic or ram pressure.

Í : _ =K+K... ram g (2.6)

10

^ram ' ^ r + ^r\ V^j

The underbody pressure required for the underbody pressure coefficient and ram

coeffícient calculations was inferred from the static pressure measurements on the back

of the radiator. By adding the pressure jump across the fan and assuming a negligible

pressure drop through the engine bay, the desired underbody pressure was obtained. The

fan pressure jtmip at a particular flow rate and fan speed was estimated from correlations

of data obtained in a flow stand test of the fan.

ft was found that variations of the ram coefficients for the Taurus and F150 with

flow rate, vehicle speed and opening size are similar to the grille coefficient and are well

correlated by

= K,.n + ,., — — Â V

V^/ ; \.''-'J (2.7)

As for the griUe coeffícient, the correlation coeffícients for the ram coeffícient are

dependent upon the location and combination of the grille openings for a particular front

end confíguration.

Vemer (2000) introduced a new procedure for experimentally determining the

ram pressure and ram coeffícient that is not reliant on the diffícult static pressure

measurements between the radiator and the fan. Working with Crafton's (1992) wind

ttrnnel data from the Taurus, she noted that the energy required to overcome the net

pressure drop for flow through the underhood cooling package (heat exchangers and fan)

must come from the freestream dynamic pressure. Based on a flow stand evaluation of

the cooling package pressure drop as a fiinction of fan speed and flow rate, the net ram

11

pressure on the cooling package could be determined from a flow rate measurement

alone.

K..^... = ram

_ ^ram _ ^P conJen.ur + ^P radiaior + ^P/a,

' \pvl \pv: ^^ " (2.8)

It is assumed that changes in the average dynamic pressure through the cooling package

are negligible so that the change in total pressure is equivalent to the change in statíc

pressure. The revised procedure yielded a much higher degree of correlatíon in the ram

coefficient measurements and more clearly discernable trends in the results.

Vemer also provided a simple theoretícal explanatíon for the grille losses

associated with a single grille opening. The flow through the grille openings was divided

into two processes. First, for the flow from the freestream to the plane of the inlet, it was

assumed that the process is reversible so that pressure and velocity changes are easily

related by BemouUi's equation. Second, it was assumed that all of the grille losses occur

between the grille opening and the first heat exchanger and are a result of having zero

static pressure recovery associated with the deceleration and expansion of the flow

between the inlet and heat exchangers. With this representation of the grille losses and

approximation of the engine bay and underbody pressure changes with simple pressure

coefficients, the overall ram pressure coeffícient for a vehicle with a single grille opening

should follow an expression of the form

/ A \

^ram ~ .'^O + ^A fv^

A + ^bay

'v^ V.j (2.9)

12

The correlation coeffícients KQ and KA are unique to a particular opening style and

location but relatively insensitive to the size of the opening. By contrast, the engine bay

pressure drop coeffícient Kbay is characteristic of the underhood confíguration for the

vehicle and should not be dependent on the layout of the grille openings or underbody air

dam. Verner applied a unifíed least squares curve fítting procedure in which the KQ and

KA coefficients for an individual above bumper opening, bumper opening, below bumper

or chin opening, and bottom opening were determined simultaneously along with a single

characteristic engine bay coeffícient Kbay.

For configurations with multiple openings, Vemer applied the same concept as

Roseberry (1990), Crafton (1992), and Nguy (1992). It was assumed that the flow rates

through the individual openings are such that each opening is operating at the same grille

coefficient. On the basis of the simple model of the griUe loss mechanism, this implies

that wãth zero static pressure recovery dovmstream of the openings, the average static

pressures at the inlet planes of the particular combination of openings are equal. In this

way, the ram coefficient for any combination of the sizes and locatíons of the grille

openings may be predicted.

The data reductíon and correlation procedures developed by Verner (2000), may

be applied to predict the ram coefficient for any combination of grille and underbody

openings on a mid-sized sedan that is geometrically similar to the 1991 Ford Taurus. For

dissimilar geometries, an equivalent series of wind tunnel tests is required to determine

the base set of inlet and engine bay correlation coefficients. Unfortunately, the cost and

time associated with this effort is prohibitive in a typical production vehicle design cycle.

13

It would be very useful if the required correlatíon coeffícients could be estímated on the

basis of the measured or CFD determined pressure distribution on an unbroken, i.e.,

without grille openings, front fascia of a new vehicle.

The primai-y goal of the current research is to establish a relatíonship between the

pressure distribution on the generic front fascia shape of a new vehicle and the

corresponding grille correlatíon coeffícients. For this purpose, an aspirated cylinder in

cross flow was taken as an idealized representation of a vehicle front end. Intermediate

objectives for the research were to evaluate the realism of the cylinder model, determine

grille coeffícient correlations for grille openings (holes in the cylinder wall) of various

size and location with respect to the base surface pressure distribution, and to fiirther

evaluate the procedure first outlined by Roseberry (1990) for predicting the grille

coeffícient for combinations of openings based on correlations obtained for individual

openings.

14

CHAPTER III

TECHNICAL APPROACH

3.1 Ram Coeffícients for Individual Openings

Consider a sfreamtube that originates in the freestream far upstream of a single

grille opening of an automobile. As the streamtube enters the automobile, it passes

through the grille opening, condenser, radiator, and radiator fan untíl it reaches the

underbody. This study focuses on the freestream total pressure and the total pressure loss

through the grille opening, and does not consider the other streamtube pressure drops and

rises that occur between the front face of the first heat exchanger and the underbody.

Air passing through the inlets of an automobile grille expands from the inlet area

to the frontal area of the heat exchangers. If it is assumed that the flow is approximately

uniform over the exchanger area, this area may be taken as an intemal reference area A^.

With this definition for the reference area, a corresponding average velocity Vr and

dynamic pressure q^ may be calculated. For the cylinder model of a vehicle grille, the

intemal reference area is defíned to be the intemal flow area or simply the intemal cross-

sectional area of the cylinder. This area is used for the calculation of average intemal

velocity and dynamic pressures.

ft is also reasonable to assume that the static pressure disttibution over the heat

exchanger face area is approximately uniform and will be denoted as Pr- Similarly, it is

assumed that the intemal pressure on the cylinder model is uniform and will be taken as

the intemal reference static pressure.

15

In the development of a simple theoretical model of the loss mechanism

associated with flow through a grille opening, Verner (2000) assumed that there are no

losses in the freestream flow to the inlet openings. As shown below, this assumption is

only true in the case where the opening is located at what would be the stagnation point

on a front-end fascia without openings. At all other opening locations, losses occurring

in the exterior flow from the freestream to the inlet should be included. Verner also

assumed that because the change from inlet area to the heat exchanger flow area is

abrupt, there is no significant static pressure recovery associated with change in velocity

from the inlet at F, to the final internal velocity V^. That assumption is also applied for

the current study.

Developing a relationship for the ram pressure coefficient requires consideration

of the changes in the exterior and interior flow. Total pressure at the cylinder interior is

analogous to the ram pressure behind the grille openings on a real vehicle. As described

earlier, these intemal reference conditions are analogous to the average pressure and

velocity across the radiator area in an automobile. For the cylinder, it is assumed that the

static pressure is uniform and the average velocity and dynamic pressure may be found

from the cross-sectional area.

The ram pressure or total pressure behind the grille openings is expressed in terms

of the freestream total pressure and the total pressure loss associated with flow through

the grille opening

P - P -AP (•^•^'' ^Tr - ^T«= ^Tgrille •

16

The grille total pressure drop is divided into components which occur upstream and

downstream of the grille inlet

P , , = P , „ - [ A P , „ , + A P , , J . (3.2)

Consider, first, the exterior loss in total pressure. The pressure and velocity

change associated with the change in streamtube area from the freestream to the inlet can

be seen in Figure 3.1. Relative to the freestream static pressure, the freestream total

pressure is

^TX — Q<X, 5

while the total pressure at the plane of an inlet is,

PTi=Pi.g+^r

(3.3)

(3.4)

A^

PT^ = E

p<. ãD CD

_- --- ''~'"'~^^ —

. ^ " ^

PTt=P.,+^t

Tes Pipe

— ''j^

A.,

Pjr = Pj^ — ^Tiriik

Pr f-:

Figure 3.1: Pressure clianges from Freestream to Underbody

The change in total pressure from the freestream to the inlet may be written as

^T.e.=PT.-PTi=q.-(P,g+(l,)

^T.e.=PTx-PTi=-P,,g+^x-^i- (3-5)

17

The static pressure at the cylinder inlet can be written in terms of an inlet pressure

coefficient, Cpj,

P:,=^Sp., (3.6)

where

P -P P C ., = ^ ^ = - ^ . (3.7)

When the flow rate is zero, the inlet pressure coefficient is approximately equal to the

surface pressure coefficient on an unbroken fascia at the same relative location as the

opening. As the fiow rate increases, it is assumed that the inlet pressure P^g decreases as

a function of the ratio of inlet to freestream dynamic pressures. This dependence on the

ratio of dynamic pressures can be seen by considering an opening located at the

stagnation point. For isentropic flow through the opening,

C = ^ = i-l^. (3.8)

Equation (3.8) is generalized for an arbitrary opening location by expressing the inlet

pressure coefficient as

r -^''^ -C -k ^ (3-9)

where

C 0 = zero flow rate pressure coefficient

k^ = experimentally determined proportionality constant.

18

Rewriting Equation (3.6) in terms of the zero flow rate pressure coeffícient and the

experimentally determined proportionality constant.

P..g = 9»

/ \ C -k ^

\ 9«y (3.10)

Substituting this expression for the static pressure at the inlet into the equation for

the loss in external total pressure yields

/ ^T.e.,=PTx-Pn=-CI.

\

AP, T.e.xl — ^m (l-C,,o) + /

r -k -í^ V ^ o o y

UA-A

+ qx-q.

(3.11)

Arranging AP,^, in this way illustrates the effects of Cpo and k^ on the extemal pressure

losses. When the inlet opening is located at the stagnation point on an unbroken fascia,

the value of Cp,o is equal to one, k^ is equal to one, and there are no extemal losses. At all

other inlet opening locations, the zero flow rate pressure coefficient is less than one,

indicating that the inlet pressure is less than the stagnation pressure at zero flow rate and

that there are fínite exteraal losses. The expression for the change in external total

pressure will be used later in the defínition of the intemal total pressure or ram pressure.

It should be emphasized that the defínition of external total pressure loss is

specifícally for conditions within the grille inlet opening. In the limit as the flow rate

goes to zero, the dynamic pressure there goes to zero. However, in the exterior flow

immediately above the inlet, the pressure and velocity at zero flow rate are as they would

be for an unbroken fascia and are related to the freestteam conditions approximately by

19

assuming zero losses and simply applying BernouIIi's equation. The derivation here is

for conditions within the inlet rather than the flow just above the inlet.

Consider the interior loss in total pressure. Defíning the interior loss as the

change in total pressure from the inlet to the interior of the cylinder,

^TM=PTi-PTr ={P,+q,)-(Pr+qr)- (3-12)

Because the change in area from the inlet to the internal flow area is abmpt, it is assumed

that there is negligible static pressure recovery associated with the change in dynamic

pressure. Thus, P^ = P,., and the change in dynamic pressure has no direct effect on P^.

^T.in\=PT,-PTr=q,-qr- (3-13)

Substituting the expressions for external and intemal total pressure losses,

Equations (3.11) and Equation (3.13), respectively, Equation (3.1) can be written as,

PTr=q^-[qÁ^-Cp.o)+{kA-'^)q,+qi-qr]^ (3-i4)

or

PTr=qSp.o-kAq,+qr- (3^i5)

Normalizing the interior total pressure by the freestream dynamic pressure yields

the ram coefficient.

V -£iL-r -k -^ ^ram ~ ~ ^p,0 '^A

q^ V .q^J

Recalling Equation (3.9), the ram coefficient may be written as

^ram = ^ p^, +9,-

+ q,. (3.16)

(3.17)

20

With the assumption of zero interior static pressure recovery, there is no

interaction between the internal dynamic pressure and static pressure. Instead, the

intemal static pressure is determined entirely by conditions at the inlet. Therefore, in the

experimental results presented in Chapter V, the primary focus will be on the inlet

pressure coefficient and its variations with respect to size and location of an inlet and the

ratio of inlet to freestream dynamic pressures. As suggested by Equation 3.17, it is

expected that these variations in the inlet pressure coefficient Cpj may be correlated in

terms of an inlet zero fiow rate pressure coefficient Cp,o and an inlet loss coefficient k^.

3.2 Ram Coeffícients for Combined Openings

FoIIowing the approach introduced by Roseberry (1990), it is possible to make

predictions for the ram coeffîcients of multiple openings based on correlations for the

individual inlet openings. The key assumption required for the predictions is that the

combined fiow from the inlets mixes to a uniform interior pressure and velocity. Again

assuming negligible interior static pressure recovery, it follows that each of the openings

must be operating at the same inlet pressure coefficient. This does not imply, however,

that the inlet velocities are equal. The openings will have unique zero flow rate pressure

coeíficients and inlet loss coeffícients, thereby leading to different ratios of the inlet and

freestream dynamic pressures for a specifíc inlet pressure coeffícient.

Consider two openings Aa and Ab, from Equation (3.15), the unique ram pressure

correlation for the openings can be written as

^ram.a = ^ M ^ p O . o " " '^^,0^1,0 + ^r

21

^™„,,ft =qSpo.h -i^A.hq,,i,+qr- (3-i8)

Using the assumption that both openings are producing the same ram pressure, it follows

that

qSp0.a-kA.aq,.a = ^SpO.h ^ ^,1,^i.b- (3-19)

Dividing through by the freestream dynamic pressure, Equation (3.19) can be rewritten as

q^ q^

Applying conservation of mass,

ArVr-A/,+A,V,. (3.21)

Dividing through by A^Vr,

l = M± + (3.22) ArVr A,V,

Defining

^ = a, then ^ = l - a (3-23) 4n ^rVr

where a is the fraction of the total flow passing through opening a, and (1 - a) is the

fraction passing through the opening h.

It follows that

Ay, , qr,a qr J ' V =a—^—^ and = — «

A, q^ q^ \Aa J

(3.24)

Similarly,

22

A,. V,={l-a)^ and ^ = l ^ ( i _ a ) ^

' q. q. ^

( A \

\Ah j

(3.25)

Substituting Equation (3.24) and Equation (3.25) into Equation (3.20) yields

C -k ^a'-^pO,a I^A.a " A.. q«, \^a J

Rearranging and collecting terms

Cpo.h-kA,^{l-ay q^

'A.^

\Ah j

0 = aa^ +ba + c

where

a = U.^'

A.b \Ab J

-k U.-^'

A.a \^h J

b = -2k,,^ í A \

^-^h J

( A \

^ — ^pO.a ^p0.h + '^A.b A

q^ A.j

The solution for a is then

a -b±^b^ -Aac

2a

(3.26)

(3.27)

(3.28)

(3.29)

(3.30)

(3.31)

It is important to note than when a equals one, the left side of Equation (3.26)

equals C^Q^ . For the prediction to be valid, it is necessary to fulfill the assumption that

both openings must be operating at the same ram pressure (Equation 3.19). This

condition cannot be satisfied in the limit as the flow rate goes to zero; therefore, a

23

minimum value of q, /q,^ must be established. Assuming for demonstration purposes that

opening a is the dominant opening, the minimum internal dynamic pressure ratio where

both openings are operating at the same ram pressure can be defined as

_ y-^pO.a -^pO.hj 'q,'

Vq 00 J

A.a

pO.I

\Aa J

(3.32)

In summary, consider a pair of inlet openings which have been individually tested

to determine their respective values of Cp,o and k^. For a specific total flow rate at a

particular freestream velocity, the corresponding ratio q,. fq^ is applied to Equations

(3.28) to (3.30) to obtain a solution to Equation (3.27). The inlet pressure coefficients for

the openings are equal and may be found from

C. qr „2 'A.-^' - ^pO.a '^A.a '^ .

oo yAj

= Cp,,-k,,^{l-ay q^

( A \

\Ah j (3.33)

24

CHAPTER IV

EXPERIMENTAL SETUP

The aerodynamics laboratory at Texas Tech University contains two wind

tunnels, the smaller of which was used for this experiment. This closed-circuit wind

tunnel has a top speed of approximately 25 m/sec with an overall length of 7.62 meters

and test section dimensions of 0.40 meters wide by 0.30 meters high by 1.06 meters long.

The model was placed in the test section, just downstream of the wind tunnel contraction.

The flow through the model was generated by a shop»vac and regulated with a generic

ball valve and a TSI hot fílm flow meter. This setup is illustrated in Figure 4.1.

E cctric Fan

WindTimiid ContractioD

TSI2 4000 Scries Flow Meter

Generic BaU \'évc

Figure 4.1: Wind Tunnel Scliematic

shop*vac©

25

4.1 WindTunnel

The freestream dynamic pressure was derived from pressure taps on the inlet and

exit of the wind tunnel contraction. At the upstream pressure tap, the cross-sectional area

of the contraction is large and the static pressure is approximately equal to the stagnation

pressure. At the exit of the contraction, the cross-sectional area is equal to the test section

area so that the pressure is equal to the test section static pressure. The pressure

differential between tiie contraction inlet and exit is approximately equal to the

freesfream dynamic pressure. Because the upstream pressure taps do not sense the tme

stagnation pressure, a calibration constant was introduced to determine the actual

freestieam dynamic pressure,

q.=K,AP,. (4.1)

Equation (4.1) contains the wind tunnel contraction calibration coeffícient, Kc, and the

contraction pressure drop, AP^..

4.2 Model Parameters

In this study, a cylindrical model was used to simulate the front end fascia and

grille openings of an automobile. The test cylinder has an easily evaluated and repeatable

characteristic surface pressure distribution thereby facilitating the evaluation of the effect

of opening locations with respect to the pressure distribution.

The cylindrical model, shown in Figure 4.2, was constmcted from steel pipe with

an outside diameter of 53.34 mm and a 1.27 mm wall thickness. Circular openings with

diameters of 19.05 mm, 8.73 mm, 7.14 mm, and 6.35 mm were machined into the side of

26

tiie cylinder model to simulate the griUe openings in an automobile. The openings were

spaced such tiiat they could be closed with vinyl tape so that openings could be tested

individually or in pairs without interference caused by the other openings. The effect of

changing the location of the openings was accomplished simply by rotating the model.

This confíguration is shown in Figure 4.3. As illustrated, five holes of different

diameters were evenly spaced along the length of the cylinder with approximately 10

degree arc length separations. The opposite side contains two evenly spaced openings

separated by 20 degree arc length separations. This arrangement allowed a wide variety

of two opening combinations for testing.

The model was closed at both ends with caps that fit into bushings in the floor and

ceiling of the tuimel test section. A pressure tap in the top cap was used to sense the

intemal pressure. A fitting in the lower cap allowed attachment of a 25 mm diameter

flexible hose. The hose connected the cylinder model to a filter, a TSI hot film flow

meter, a ball valve, and a conventional shop vacuum. The flow induced through the

cylinder sidewall openings by the shop vacuum provided a simulation of the flow

induction provided by an automobile radiator fan.

27

-*7 .14n

Figure4.3; Model Schematic

Figure 4.4: shop'vac"'2.0 pealc HP Wet/Dry Vacuum

28

Figure 4.5: Generic Ball Valve

4.3 Data Acquisition

For data acquisition, several components were needed to obtain useftil results.

Two pressure tiansducers were needed to evaluate the pressure differential across the

wind tunnel contraction and the cylinder intemal pressure. A hot film flow meter was

used to quantify the flow rate through the cylinder, and a computer was used to collect all

of this data.

Data acquisition was performed with a Dell Optiplex GXl computer running

National Instruments LabVIEW 6.0. A National Instruments CB-68LP data acquisition

(DAQ) board was installed in the computer to sample the voltage outputs from the

pressure transducers. A serial interface was used to link LabVIEW with the flow meter.

A LabVIEW Virttial Instrument (vi) was written to acquire 1000 data points over fíve

29

seconds from each data source and output the corresponding numerical averages. Front

end screenshots as well as diagram views of the LabVIEW vi can be seen in Appendix A.

Figure 4.6: TSI4000 Series Flow Meter

An Omega differential pressure transducer (Model Number - 9948482) was

cormected between the pressure taps mounted at the inlet and exit of the wind tunnel

contraction. This transducer has an input range of ± 2.48 kPa with a corresponding

output voltage of ± 1.00 V. The differential pressures resulting from wind tunnel test

speeds of 20 to 25 m/s were approximately 120 to 230 Pa. As described earlier, the

pressure differential across the contraction is only approximately equal to the freestream

dynamic pressure. It is easily shown that if Reynolds number effects are neglected, the

required correction is a function of only the contraction ratio or a constant, i.e..

^ . A P . (4.2)

30

The dynamic pressure correction was determined by taking the average of the

ratio of the dynamic pressure obtained from a conventional pitot-static probe and the

confraction pressure differential over the range of velocities which were utilized in the

tests. The result value found was K,. = 1.04.

A second Omega differential pressure transducer (Model Number - 9948482) was

connected between the cylinder internal pressure tap and the static ports at the end of the

contraction. This arrangement yields the cylinder internal gage pressure.

The mass flow rate through the cylinder model was obtained in standard liters per

minute with a by a TSI® 4000 Series flow meter with a digital display (Figure 4.6) and

serial interface to the data acquisitions system. Ambient temperature and pressure were

obtained manually from a standard thermometer and barometer, respectively. Data taken

from the flow meter allowed for the computation of the average dynamic pressure

through the inlets and in the interior of the cylinder.

1 , , 2 1 qr=-pVr =-p

( • \ ^ 1 / _ . . \ ^

m \PArJ Ip

m \Ar J

(4.3)

where

p = —. (4.4) RT

The expression for the ram pressure coeffícient in Equation (3.16) can be

characterized by the values of Æ and Cp,o found for the different confígurations. These

values can be determined from a least squares curve fít of all opening sizes, flow rates,

and freestream velocities at a fíxed orientation. Orientation will be selected based on

zero flow rate values of Cp. Controlling the direction of the cylinder with respect to Cp

31

instead of angle will effectively remove any error that may have occurred in creating the

test sample. As \he samples were not created using high precision machinery, there could

be slight discrepancies in the exact location of the opening. Since Cp is sensitive to

orientation, testing at a specifíc value of Cp is the most accurate way of determining the

orientation of the sample. Additionally, selecting orientation based on Cp will provide a

prediction on where the '-intercept will lie. Noting that Cpj at zero flow rate is, by

defmition, Cp,o, provides a clear representation of the j/-intercept value for the Cpj

Coefficient plots shown in Chapter V.

Different values of Cp correspond to different angles, thus rotating the model to

specific angles was an important aspect of the test procedure. This was accomplished by

placing a protractor below the Plexiglas test section. By marking the center of the

openings on the bottom end cap, placement of the pipe with respect to the freestream can

be recorded in the LabVIEW vi developed for this experiment. A top view of the model

in the test section can be seen in Figure 4.7.

Figure 4.7: Top View of Model in the Test Section

32

CHAPTER V

RESULTS AND DISCUSSION

The goals of this experiment were to determine generalized ram pressure

correlations for single openings and combinations of openings in a cylinder model which

could serve as a guide for analogous correlations for automobile grille openings. The

correlations should also provide a better understanding of the effects of several grille

related variables influencing cooling system performance. These variables include the

size and location of the grille openings, as well as the vehicle speed and the vacuum

produced by the underhood radiator fan. This experiment differs from prior studies in

that the ram pressure correlations were evaluated with a circular cylinder model instead

of an automobile model.

This chapter contains the evaluations of ram coefficients for both individual and

combined cylinder openings. The individual opening data is used to form general

correlations of the effects of grille inlet position and size, freestream velocity, and

intemal flow rate on the ram pressure coefficients. The results for individual openings

are used as the basis for predicting the ram pressure coeffícient behavior of combined

openings. Measured ram pressure coefficients for combined openings data are used for

comparison with the predicted data in order to show the validity of the method used.

5.1 Zero FIow Rate Measurement

A basic objective for the current investigation was to establish the relationship

between the ram pressure coeffícient for a single grille opening and the pressure

33

distribution on the unbroken front end fascia of an automobile. It is suspected that

knowledge of the pressure distribution can be useful in guiding the selection of locations

for grille openings. This is particularly appealing in that determination of the pressure

disfribution on the unbroken fascia is a relatively straightforward and accurate CFD

calculation.

For the ctirrent investigation, utilizing a cylinder in cross-flow, the pressure

disfribution was determined by evaluating the cylinder internal pressure with zero flow

rate as a single opening was rotated to various positions on the front half of the cylinder.

With the location of the stagnation point defíned as the zero angular position, each

opening was tested from -90 degrees through 90 degrees, at 5 degree increments.

Normalizing the cylinder intemal pressure taken at each position by the freestream

dynamic pressure yields the surface pressure coeffícient,

C , = ^ . (5.1)

The Cp distributions produced with the various opening sizes are presented in

Figure 5.1. The impact of opening size on the surface pressure coefficient Cp can be seen

on this graph. It is noted that the results from the 6.35, 7.14, and 8.73 mm openings are

essentially equivalent. In contrast, the pressure distiibution obtained with the 19.05 mm

opening is inconsistent with the others. A pressure coefficient approximately equal to

one, indicating stagnation pressure, is obtained for a signifícantly broader range of

angular positions near zero for the 19.05 mm opening than the others. At angular

34

positions greater tiian ± 15 degrees, the pressure coefficient for the 19.05 mm opening is

consistently higher than the others.

Q .

o

1.5

1,0

0.5

0.0

-0.5

-1.0

-1.5

-2.0

• d = 19.05 mm

• d = 8.73 mm

A d = 7.14 mm

X d = 6.35 mm . 3á

.u*'^'*'

• ^

• *

• ^

V

• ^ 'K • n

X

í • •

^ •

•

• • •

-90 30 60 -60 -30 0

Degrees away from the location of the stagnation point if the cylinder fascia was unbroken

90

Figure 5.1: Cylinder Pressure Curve

Two possible explanations for the discrepancy between the surface pressure

results obtained with the 19.05 mm opening and those obtained with the smaller openings

are suggested.

For the first, it is noted that the pressure variation on the cylinder is relatively

large over the area spanned by the 19.05 mm opening. The opening covers

approximately 42% of the total circumference of the 53.34 mm diameter cylinder or an

35

arc of 12°. Taking the distributions obtained from the smaller openings as a guide, for

angular positions between 18° to 30°, the actual surface pressure coeffícient distribution

varies from 0.6 to 0.25 or equivalently, there is a pressure variation of 35% of the

freesfream dynamic pressure. Although it might be intuitively suspected that for a

specific opening, the internal pressure is equal to an average or approximately equal to

the surface pressure at the center of the opening, it appears that the internal pressure is

actually determined by the maximum surface pressure over the area spanned by the

opening.

A second explanation for the discrepancy between the internal pressure

coefficients obtained with 19.05 mm opening and the other smaller openings is also

related to the size of the opening relative to the diameter of the cylinder. The large

opening creates a significant change in the surface contour and should be expected to

cause a signifícant variation in the fíow streamlines over the opening. Furthermore, it is

possible that although the flow rate through the cylinder is zero, the flow over the

opening could induce an intemal circulatory flow which interacts with the extemal flow

in a manner similar to the classic case of flow over a cavity.

Regardless of the explanation for the discrepancy between pressure coeffícients

obtained with the 19.05 mm opening and the other smaller openings, it is apparent that

the flow over the large opening is signifícantly different. As will be illusttated in the

following section, it is not surprising that the effects of opening size on the ram

coefficient for the largest opening do not correlate well with the results obtained for the

smaller openings.

36

5.2 Ram Coefficients for Individual Openings

Measurement and correlation results for the ram coeffícients for individual

openings are presented in the current section. It is desired that the correlations include

the effects of variations of opening size and location plus the variable effects due to flow

rate and freesfream velocity or dynamic pressure. Recalling from Equation (3.16), the

simple theory suggests that the ram coeffícient may be correlated with an expression of

the form.

K =^ = C -k ^' ^^ram pO "^ A

q^

+ qr- (ref3.16) q^j

With the ram pressure coeffícient given by

Cp.i=^ = C^,-k,^, (ref3.9) q^ q^

the ram coefficient may be written as

Kram=C,,+qr. (rcf 3.17)

AIso recalling that with the assumption of negligible intemal static pressure

recovery, there is no coupling between the ram pressure coefficient Cpj and the intemal

dynamic pressure q^. Furthermore, the internal dynamic pressure is determined simply by

the flow rate and the choice of intemal reference area and is small compared to the

freestream dynamic pressure. Consequently, only the measurement results obtained for

the ram pressure coefficient Cp,j are presented herein.

As indicated in Equation (3.19), the ram pressure coeffícient is expected to be

linear with respect to the ratio of inlet to freestream dynamic pressures with an intercept

37

nominally equal to the surface pressure coefficient Cp. Cleariy, by definition, the ram

pressure coeffícient at a zero dynamic pressure ratio is equal to the surface pressure

coefficient. However, due to the effects of least squares curve fitting over the entire

specfrum of measured dynamic pressure ratios, the actual intercept obtained may be

different from the surface pressure coefficient and is designated with Cp. as the zero flow

rate or zero dynamic pressure ratio, pressure coefficient. Rather than specifying the

position of the openings in terms of angular position, the locations will be defined in

terms of the corresponding surface pressure coeffícients. This section describes the data

taken at all opening sizes and at Cp= 1.0, Cp= 0.7, and Cp= 0.4. The correlation results

are displayed in graphical format in this section and are discussed below. Tabular results

can be found in Appendix B.

The variation of ram pressure coefficient with the ratio of internal to freestream

dynamic pressures for an opening at the stagnation point or Cp= 1.0 is illustrated in

Figure 5.2. For these measurements, the freestream velocity was set at approximately 20

and 25 m/s. At each freestream velocity, the flow rate was varied from zero to the

maximum achievable with the throttling valve wide open. This gave a range of

maximum flow rates of 1.93E-03 kg/s for the 6.34 mm opening to 3.0E-03 kg/s for the

19.05 mm opening.

In Figure 5.2, it is observed that the effects of variations in freestream velocity

and flow rate on the ram pressure for each opening are well correlated by plotting the ram

pressure coeffícient against the ratio of internal to freestream dynamic pressures. It is

ftirther noted that the variation in opening size results in a distinctly unique curve for

38

4.0 .

2.0

0.0

O.COÔ\\ " ^ 0 . 0 0 1 0. 2

-2.0 -

-4.0

-6.0

-8.0 . -

-10.0

-12.0

-14.0

-16 0 .

-18.0

- - • % • -

\ \ \ \ \ \

O.

^

\ \ . : A \

i \

\ \ \ \

\>^x

03 o.q 04 o.Qos o.c 0.C07 0.008 0.(

• 19.05 mm Opening

• 8.73 mm Opening

A 7.14 mm Opening

X 6.35 mm Opening

Cp,i = 0.9879-85.11 (qr/qO)

Cp,i = 1.1675-2601.5 (qr/qO)

Cp,i = 0.8541 - 4223.6 (qr/qO)

Cp,i = 0.4276 - 5335.6 (qr/qO)

09

qr/qO

Figure 5.2: Cp,, versus qr/qO at C^ = 1.0

each opening. Stated differently, the effects of opening size are not correlated by

transforming the ram pressure data to the form of pressure coefficient as a function of

intemal to freestream dynamic pressure ratio.

In Figure 5.3, the ram pressure data is presented as the ram pressure coefficient

versus the inlet to freestream dynamic pressure ratio. Here, it is noted that the effects of

variations in opening size, flow rate, and freestream velocity on the ram pressure are

normalized such that all data collapse to essentially a single curve. This result

substantially verifies the assumption of negligible static pressure recovery within the

39

cylinder or behind the grille openings of an automobile. The ram pressure is determined

by conditions at the inlet and not by processes behind the opening. Furthermore, the

basic functional fomi of the ram pressure coefficient correlation given by Equation (3.16)

is seen to be appropriate for the data presented in Figure 5.3.

0

-2.0 .

-6 .0 .

-8.0 •

-10.0 -

-12.0 -

-1/1 n .

V 0 < 1 | 0 2

A • ^ X

•

0 3

A

4

1 0 4

• • - X • >

0 5

A

0 6l0

* 19.05 mm Opening

• 8.73 mm Opening

A 7 . 1 4 mm Opening

X6.35 mm Opening

é.

A X

7

>«<

X

0 8 0

qi/qO

Figure 5.3: Complete Q,,, versus q/qo at Cp - 1.0

Because this study focuses primarily on ram pressure coefficients for use in

automotive cooling system applications, data corresponding to flows that are primarily

ram dominated are of interest. The conditions automotive designers are interested in for

grille inlet design occur when Cpj is positive. The physical representation is an

40

automobile at high velocity with relatively low velocity through the heat exchangers.

Only the data obtained at test conditions where the cooling flow is primarily ram

dominated are presented in the remainder of the chapter. An example of this restricted

sample of the data in Figure 5.3 is shown in Figure 5.4.

Figures 5.4, 5.5, and 5.6 illustrate ram pressure coefficient results for openings at

locations corresponding to surface pressure coefficients Cp = 1.0, 0.7, and 0.4. From

these figures, it is noted that the ram pressure coefficients obtained with the 19.05 mm

opening are consistent with the smaller openings at C^ = 1.0 but are significantly different

at Cp = 0.7 and 04. From the surface pressure coefficient variation presented in Figure

5.1, the pressures across each of the openings are approximately uniform and equal for

the zero degree or stagnation point location. At other angular positions, it was noted that

the pressure varied significantly across the surface covered by the 19.05 mm opening and

that the variation of interior pressure coefficient was significantly different relative to the

smaller openings. Consequently, it is not surprising that the ram pressure coefficient

curve for the 19.05 mm opening is similar to the others at Cp = \ .0 but significantly

different at Cp = 0.7 and 0.4. Consequently, data from the large opening was excluded

from the curve fits at Cp = 0.7 and 0.4.

41

0.8 .

0.6 .

0.4 .

0.2 -

' 0.0 . O

0

-0.2 .

-0 4 .

-0 6 -

-0 8 H

-1.0 -

0

X ^ X

> < A

I 0,2 0]4

• 19.05 mm Opening

• 8.73 mm Opening

A 7 14 mm Opening

X 6.35 mm Opening

Cp,l = 0.9993 -1,7146 (qi/qO)

0 1

\ s ^ A

•

•

8 1

\ -

•

0

ql/qO

Figure 5.4: Cpj versus q/qo at Cp = 1.0

42

qi/qO

Figure 5.5: C„/ versus ^/^o at C^ = 0.7

43

1.0

0.8

0.6

• 19.05 mm Openlng

• 8.73 mm Opening

A 7.14 mm Opening

X 6.35 mm Opening

Cp,i = 0.3245 - 3.231 5 (qi/qO)

qi/qO

Figure 5.6: Cp., versus q/qo at Cp = 0.4

A least squares fit of the ram pressure coefficients Cpj yield curve fit coeffícients

which are the zero flow rate pressure coeffícient, Cp,o, and inlet loss proportionality

constant, k^. A summary of the values found for Cp,o and k^ are presented in Table 5.1.

Table 5.1: Cpo and k^ at Various Values of Cp

Cp= 1.0

Cp = 0.7

Cp = 0.4

Co.O

0.9993

0.6137

0.3245

kA

1.7146

2.7092

3.2315

i^A.corrected

1.71

2.39

2.42

44

As expected, the zero flow rate pressure coefficients are approximately equal to

the stu:face pressure coeffícients on the unbroken cylinder surface at points corresponding

to the opening locations. Generalizing the results for application to full scale vehicle

design, for inlets near the stagnation point of an unbroken fascia, selecting Cp,o equal to

Cp is a very good approximation. For inlets located away from the stagnation point, it is

remains reasonable to select Cp,o equal to Cp with the understanding that the resulting ram

pressure and ram coefficients will be somewhat overestimated.

The values of k^ vary as well when Cp decreases from 1.0. The general trend of

kA shows an increase in negative slope as Cp decreases. Crafton (1992) and Nguy (1992)

have suggested that inlet area effects may be more accurately correlated if the frontally

projected area of the openings is considered rather than the opening area itself This

effect on the current measurements may be evaluated by considering the influence of the

change in frontally projected area on the average inlet velocity and dynamic pressure.

The ram pressure coeffícient was given previously as

r -r -k -^ ' l o o

^"^'•"'''k (5.2)

where

y^A_ (5.3)

' pAi •

Assuming that a more appropriate average inlet velocity should be based on projected

area.

45

V =_A_-Ji / .corivcfcíl pA^cosO cos6

K = ÍVc™,vcVn/COS^. ( 5 . 4 )

substituting

Cpj = Cpo -k^^ cos e—— . (5.5)

Taking 6= 0, 20°, 30° at Cp = 1.0, 0.7, 0.4 yields the adjusted values for the inlet loss

coefficient k^ shovm in Table 5.1. Although not perfect, the consistency of the

coefficients appears to be improved by utilizing the frontally projected area concept. Due

to the significant difference in the details of the inlets on the simple cylinder compared to

a full scale vehicle, it is not expected that the values for k^ reported herein are directly

applicable to vehicle design. Results from equivalent full scale tests should be applied.

5.3 Ram Coeffícients for Multiple Openings

In order to add some practicality to this study, it is important to investigate the

impact multiple openings has on the ram coeffícient, as most common passenger vehicles

have multiple griUe openings. The equations used to predict the behavior of multiple

openings are Equation (3.18) through Equafion (3.32). These equafions were included in

the data reduction of the raw data taken, and solved to display the predicted values. The

experimental data taken with multiple openings was used only for comparison with the

predicted values. The results of this study are presented in graphical format and are

46

m discussed below. A tabular presentation of the data shown in this section is included i

Appendix C.

Table 5.2 shows the multiple opening combinations which were tested. In each

case, one opening was positioned at the zero degree or stagnation point location. The

second opening was positioned with a 10 or 20 degree offset with respect to the

stagnafion point location. The variations in offset and opening sizes provided ample

range of test confígurations to draw meaningful conclusions with respect to the accuracy

of the prediction method.

Table5.2: Model Test Itinerary

Stagnation Opening

19.05 (mm) 19.05 (mm) 19.05 (mm) 19.05 (mm) 8.73 (mm) 8.73 (mm) 8.73 (mm) 8.73 (mm) 7.14 (mm) 7.14 (mm) 7.14 (mm) 7.14 (mm) 8.73 (mm) 7.14 (mm)

Offset Opening

8,73 (mm) 8.73 (mm) 7.14 (mm) 7.14 (mm) 19.05 (mm) 19.05 (mm) 7.14 (mm) 7.14 (mm) 19.05 (mm) 19.05 (mm) 8.73 (mm) 8.73 (mm) 8.73 (mm) 7.14 (mm)

Degree Offset

10 20 10 20 10 20 10 20 10 20 10 20 10 10

When testing multiple openings, it is necessary to identify which opening

dominates the intemal flow. In all cases, with the exception of when the 19.05 mm

opening is involved, the opening that faces the stagnation point remained dominant. In

the case of the 19.05 mm opening, it remained the dominant opening when it was at the

47

10 degree offset position. At the 20 degree offset position, the opening that faces the

stagnation point maintained dominance.

For all of the fígures shown in this section, the measured and predicted ram

pressure coeffícients are plotted versus the dynamic pressure ratio based on the average

velocity for the total inlet area of the combinafions of openings (Figures 5.8-5.21). The

plots reveal that the method used to predict the ram pressure coeffícients for multiple

openings is relafively accurate. It is diffícuh to determine how well the predictíon

method worked for openings involving the 19.05 mm opening, as there is only a slight

overlap of data that can be used as a comparison. The range of measured data was

limited by the maximum flow rate which could be quantified by the TSI hot film

anemometer. For combinations of openings with similar size openings, it is easy to see

that the prediction method is valid.

It is important to note that the ram pressure coefficient for a combination of

opening always lies between the coefficients for the two individual openings at the same

dynamic pressure ratio. The combined opening ram pressure coefficient values serve as a

weighted average of sorts for the two individual openings tested.

The predictions of the smaller openings seem to be better than those involving the

19.05 mm openings. Figure 5.15 is an example of this. The individual opening data

predicts almost exactly what the combined openings will do. This prediction method,

however, is not without errors. When the 19.05 mm opening is offset to 20 degrees, there

seems to be a breakdown in the theory. Again, this could be due to the exposed frontal

area of the opening, which is signifícantly decreased at the 20 degree posifion.

48

A possible physical effect that has been left out of the theory could be the

influence of the surface roughness on the streamtube entering the openings. As the

openings are turned away from the stagnation point, air must pass over a sectíon of the

cylinder before reaching the opening. Surface roughness effects have not been taken into

account for this experiment, so without further testing, it is impossible to say whether

making the cylinder very smooth or very rough would increase or decrease the ram

coefficients.

Automobile grille openings are also more like nozzles in the respect that they ease

the change from the freestream air flow to the inlet air flow before they open into an

underhood plenum. This is unlike the testing in this experiment. The openings in the

models are sharp edged, and perhaps with the addition of more sophisticated nozzle inlets

on the cylinders even more accurate results can be obtained.

49

-1.0 qi/qO

Figure 5.8: Combined 19.05 {Cp= 1.0) and 8.73 (10 Deg. Offset) C ,, Coefficients

0.8

0.6

0.4

0.2

§ 0.0 C

-0.2

-0.4

-0.6

-0.8

-1.0

V^^^

v ^^^-^^\.

• ^

0 0

->* >v

2 \ . 0

•

, 1

>»

• 19.05 mm Opening Only

• 8.73 mm Opening Only

A Combined Openings

Predicted Values

Linear (1 9.05 mm Opening Only)

Linear{8.73 mm Opening Only)

>.

4 ^l>

^ \ B

> \

^ 0

>*. >*

" ^ - . .

\ . •

8 1

> k

>.

>.

0

•

qi/qO

Figure 5.9: Combined 19.05 {Cp = 1.0) and 8.73 (20 Deg. Offset) C ,, Coefficients

50

1,0

qi/qO

Figure 5.10: Combined 19.05 {Cp= 1.0) and 7.14 (10 Deg. Offset) Cp,, Coeffícients

1.0

qi/qO

Figure 5.11: Combined 19.05 {Cp = 1.0) and 7.14 (20 Deg. Offset) Cp, Coefficients

51

qi/qO

Figure 5.12: Combined 8.73 (Cp= 1.0) and 19.05 (10 Deg. Offset) Cp., Coefficients

a o

1.0 '

0.8 -í

0.6 -

0.4 -

0.2 -

0.0 -

0

-0.2 -

-0.4 -

-0.6 -

-0.8

-1.0

\ \ \ \ \ ^ L \ \ \ \ \

\ \ \ \

• \ A \

0 \ \ 0

-\ -—- — \ \ \ \ \ \ \ ^

" \ \ \ \ \ \ \ :

\ A ^

J 1

- A — \ l \ \

2 0

1

^ " ^ . •

•

4 0

8.73 mm Opening Only

19.05 mm Opening Only

Combined Open

— Predicted Values

— Linear(8.73 mm — Linear(19.05 mr

6 ^ \ ^ ^ 0

•

ngs

Opening Only)

n Opening Only)

8 1 (

• ^ ^

qi/qO

Figure 5.13: Combined 8.73 (C , . 1.0) and 19.05 (20 Deg. Offset) C„ Coefficients

52

8 73 mm Opening Only

7,14 mm Opening Only

Combined Openings

- Predicted \/alues

-L inear (8.73 mm Openmg Only)

-L lnear (7.14 mm Openlng Only)

-1.0 qi/qO

Figure 5.14: Combined 8.73 (Cp= 1.0) and 7.14 (10 Deg. Offset) Cp, Coefficients

qi/qO

Figure 5.15: Combined 8.73 {Cp= 1.0) and 7.14 (20 Deg. Offset) Cp, Coefficients

53

0 8

0.6

0.4

0.2

g 0.0

C

-0.2

-0.4 •

-0.6

-0.8

-1.0

T ^ ^ \ ^

0 0

\ N \ . N. N

\ N

^^ ^ \ N

\ N \ N

\ \ \ 2 0

^ v j i

N 4 ""N 0

N N^

N

N N

\

• 19,05 mm Openíng Only

• 7.14 m m Opening Only

A Combined Openings

Predicted Values

L lnear(7.14 m m Opening OnJy)

6 \ ^ 0

N

N

N N

N N

'V

N N

N \

m Opening Only)

—

— 8 1 0

\ ^

qi/qO

Figure 5.16: Combined 7.14 {Cp = 1.0) and 19.05 (10 Deg. Offset) Cp, Coefficients

-0.2

-1.0 qi/qO

Figure 5.17: Combined 7.14 {Cp= 1.0) and 19.05 (20 Deg. Offset) Cp, Coeffícients

54

-1.0

qi/qO

Figure 5.18: Combined 7.14 {Cp = 1.0) and 8.73 (10 Deg. Offset) Cp, Coefficients

Æ 0.0

-1.0

0

' • ^ • ^

•^ ^ *

X "V

\ , " '&v • \ "N

• \ . ^

0 0

S. N,

' \ ^ ^^>.

2 \ . 0

í .__.._ _. ...J ._ „..._ • 7,14 mm Opening Only

• 8.73 mm Opening Only

A Combined Openings

L inear(8.73 mm C

N

4 ^ X ^ 0

•N N.

\ - \ ^ N__

\ , •

6 ^ ^ ^ 0

^ N ^ ^

Dpening Only)

8 1

• ^

^ ^ A

0

ql/qO

Figure 5.19: Combined 7.14 {Cp = 1.0) and 8.73 (20 Deg. Offset) C^, Coefficients

55

1.0 -fr

-1.0

qi/qO

Figure 5.20: Combined 8.73 {Cp = 1.0) and 8.73 (10 Deg. Offset) Cp,, Coefficients

1.0 s-

-1.0 qi/qO

Figure 5.21: Combined 7.14 {Cp = 1.0) and 7.14 (10 Deg. Offset) Cp,, Coefficients

56

CHAPTER VI

CONCLUSIONS AND RECOMMENDATIONS

Air entering the cooling system of an automobile stems from two major sources,

the air forced inside from the forward motion of the vehicle, and air pulled in by the

intemal vacuum of the radiator fan. The interaction between these two flow fields occurs

at the griUe inlets, and is closely related to the determination of the ram pressure

coefficient. Both of these systems must be considered when assessing the cooling

requirements of a new automobile design.

The scope of this study is to simulate these systems by fmding analogous ram

pressure coefficients for aspirated cylinders. The single opening test results yield a set of

correlation equations that describe the variations of the ram pressure coefficient with

respect to size of the opening, location, freestream velocity, and intemal flow rate. The

multiple opening test results show how varied openings behave in the determination of

ram pressure coefficients. Findings from this study confirmed a prediction method that

modeled this interaction. Both correlations can be related to the automotive industry, and

these results can be incorporated into ttuCooI® for further use.

6.1 Conclusions

The ram pressure correlations for all opening sizes were evaluated directly from

the raw data per Equation 3.9, and fit to a linear curve fit described in Equation 3.16. The

resulting values of the curve fít yielded Cp,o and kx values that fit the data to 96% or

better. This does not include data from the 19.05 mm opening for Cp values other than

57

1.0. This exclusion was necessary as it was observed that the fundamental flow behavior

for the large opening was different from the smaller openings. The results of the various

curve fits can be seen in Table 5.1. The effects of the various positions were reflected in

the variations on intercept, Cp and slope, k^. These correlations can be applied over a

wdde range of areas for each location.

The general correlations for the multiple openings were developed from the

individual openings with a method described in Section 3.1, and tested accordingly. In

general, this method yielded accurate results. The only significant discrepancies

occurred with the 19.05 mm opening in combination with other smaller openings.

6.2 Reconmiendations

Further research is necessary to reveal the effects of large opening sizes on ram

pressure coefficients. It appears that variation of the surface pressure coefficient over the

area covered by an opening has a significant effect on the ram coefficient correlation,

particularly on the value oík^. This effect requires further exploration

Studies involving the interaction of three or more openings can be made to further

increase the practicality of this study. As automobile designs continue to improve the

aerodynamics of the overall vehicle, front end grille openings will invariably change.

Investigations of this type will certainly benefit automobile cooling system designers in

their quest to keep up with the changing front end layouts of new automobiles.

58

Finally, incorporation of these results into ttu_CooI® would prove to be useful in

the evaluation of multiple grille openings, as this study confirmed a reliable system of

equations to model this phenomena.

59

REFERENCES

Hawes, S.P. "Improved Passenger Car Cooling Systems." SAE Paper 760114 Febmarv 1976 - '

Oler, J.W. and J.W. Crafton. "GriIIe Coefficient Measurements for a Ford Taurus." TechnicaIReportTR-FMC-92-3. September, 1992.

Oler, J.W., Roseberry, C.M., Jordan, D.P. and T.T. Maxwell. "Ram Recovery Coefficient Correlafions." Technical Report TR-FMC-90-1. December, 1991.

Olson, M.E. "Aerodynamic Effects of Front-end Design on Automobile Engine Cooling Systems." SAE Paper 760188. February, 1976.

Renn, V. and A. Gilhaus. "Aerodynamics of Vehicle Cooling Systems." Journal of WindEngineenng andIndustrial Aerodynamics. Vol. 22:339-346. 1986.

Schaub, U.W. and H.N. Charles. "Ram Air Effects on the Air Side Cooling System Performance of a Typical North American Passenger Car." SAE Paper 800032. Febmary, 1980.

Vemer, D. "General Ram Correlations for Automobiles." Master's Thesis, Texas Tech University. May, 2000.

Williams, J. "An Automotive Front-End Design Approach for Improved Aerodynamics andCooIing." SAEPaper 850281. 1985.

60

APPENDIX A

LABVIEW VI SCREENSHOTS

61

Ble £dit Qperate Tools Browse Window He^

|<>|<g>| | i r | I 13pl Appkaton Font ' l o '

Transduær Calibration Slope

CMflidenb. ; i i 2 . 0 i 2 r Intercept

i)|.6.9174

Atnnapherjc Pressure Atmosphehc Temp Kc Correction Factor

/årí.ão , 1129.99

Degree Angle

í.lj .O

Hole Sre On)

; Í 0 . 3 ^ 3 8

Average Conlraction V - AJT Vekxity

Pressure Drop Cm. H20) i " ^

lO.OOOO

,_)11.0^78

Inputjnlteratlons

tiO - Free Stream Dynamic Pressure

!o.oo

ZeroFlowCp

jo.oooo

Average Pipe Static qt - Pipc Dynamíc Pressure Pr^ure&i .H20) (, ^

lo.oooo

Cllck to A o H ^ Data

<Thfi lo.oooo

Current Iteralion

Save D rectory

]C:V)oajments snd Settíngs\zachPesktDp\

mJBseconds/samplel Gas| Gas|

> ComPortl

1 Sli 1

FigureA.l: LabVIEW Virtual Instrument (vi) Written for Data Acquisition (Front End)

62

Figure A.2: LabVIEW Virtual Instrument (vi) Written for Data Acquisition (Diagram)

63

APPENDIX B

RAM COEFFICIENTS FOR SINGLE OPENINGS TABULAR DATA

64

Tambs

Pamb =

rho amb =

di =

Al =

Ar =

L di =

Ai =

TableB. l :

72

29.93

1,196

F

.iHcL.,,,. „. kgím"3

0.75

0,01905

2.850E-04

2

o.oW 2 . 0 2 7 E - 0 3

0 .3438

6.0087325 5 . 9 8 9 E - 0 5

in

m

in

m

in

m

m-2

295.4

101354.4'

,,.

Tabular Data -

Pa

Raw Dd(íi

dPc

[in H2 '|

.4579_

0,458Í

0.4580

0.4584

0.4573

0,4577

0.4616

0.4596

0.4579

0.4583

0I553" 0 .8856

0 .8858

0 .8848

" o ! 8 8 3 3 '

0 ,8803

0 .8830

0 .8882

0 .8833

0 .8868

0 .8862

0.8813

0 .4537

0 .4540

0 .4578

0 .4583

0 .4569

0 .4599

0 .4596

0 ,4585

0 .4575

6.4555 0 .4579

O.syzã

0 .8825

0.8951

0 .8909

0 .8896

0.8910

0 .8942

0.8319

0 .8884

0 .8888

.8853

í in H2Û)

0 .4803

'0 .47 ' l9

0 .4575

0 .3930

0,3115

0 1 5 9 7

0,1639

0,3212

0.4106

0.4612

0.4710

0.9238

0.9116

0 .8997

0,8461

0 ,7669

0 ,5962

0,6021

- "a75ÍT~ 0.8435

0,8950

0,9085

0,4850

0,4136

0,1530

l j , 7 4 8 5 ^

~ - '2 .7616'

-5 .7976

-5 .7995

-2 .3280

-1.0639

-0 ,0084

0 .4308

0.9333

0.S656

0 .4873

-0 .4493

-2.1558

-5.4157

-5.4014

-2 .4390

-0 .5769

0.4521

0.8521

Q J_SCFM1

0.000

17.388

35.358

78 .209

108.538

146 794

146.336

105.104

69 ,233

31.916

15,048

0,000

19.263

3 0 9 7 7

_ e 7 . 2 4 6

100!644

148,925

148 723

106.989

70 .257

36 ,723

17.120

Ô. OO

13.773

30 .684

56 .983

' 88.310

118.426

118.819

89.463

62 .384

37.Í51

12.239

0.005

12.694

35 .977

60 563

86.5S0

121013

120.676

90.913

62 .839

37.124

14.533

Single Opening - Cp=\.0

D.3U 'w'ith Cr.rreiMfd qO and

Unit Con'.'ersion

qO=dPi;

(P.E,)

119.71

119.74

119.73

119.83

119.55

119 65

120.66

120.13

119.70

113,80

119,02

231.50

231.56

231.30

230.90

230.11

230.62

232.20

230.91

231.81

231.63

230 38

120.18

118.67

119.67

119.82

119.44

120.22

120.13

119Ã

119.53

119,06

119.69

233.40

230.69

233.98

232.89

232.56

232.92

233,75

233,15

232.24

232.33

Pr.g

(P i )

119.29

117.20

ii3,ei 97,60

'77.3'6

39.66

40.69

79.77

101,96

114,54

116,97

229.42

226.40

223 .44

ZÚ9JÍZ

148.06

ns 53

186.57

209,47

222,27

225,62

120.45

102.71

38,01

"-i ' ss -685.81

•1439.79

-1440.25

-727.13

-264,22

-2.09

106,98

231,78

214.96

121,q2_

-'ií sg'" -535.38

-1344.95

-1341,38

-605.71

-143.26

112.27

231.44 1 211.62

0. ÍKgh]

O.OO E«O

3.550E-04

7.219E-04

1.597E-03

2.2ieE-03

2.997E- 3

2.939E-03

2.146E-03

1.414E-03

6.516E-04

3.072E- 4

O. 0OE»OO

Î.333E-04

e.324E- 4

^ 1.373E-03

" 2.055E- 3

3.041E- 3

3. 36E-03

2.184E-03

1.434E-03

7.438E-04

3 495E- 4

0 OE» O

2,813E- 4

6.2e5E- 4

1.ie4E- 3

1.8 3E-03

2.41SE-03

2.426E-03

1.827E-03

1.274E- 3

7.585E-04

2.511E- 4

1.021E-07

2.592E- 4

7.345E-04

1,23eE-03

1,768E-03

2 471E-03

2.4e4E-03

l.'35eE-03

1.2S3E-03

7.580E- 4

2.9e7E-04

1 i -'- i' — -

^

Da'a fí

qi (Pa)

0.000

0.649

2.683

13.125

25.279

46.233

45.988

23.704

10,285

2,186

0.486

.OO

0.796

2.058

9.703

21.736

47.591

47.462

24.562

10.532

2.894

0.629

O.OO

3.227

45.756

157.832

378.994

681.563

686.034

388.955

189.132

67,074

7,351

0.000

7.831

62.900

178.249

364.290

711.666

707.708

401.665

191.898

66.978

10.265

edu tion Results

qiíqO

0.0000

0.0054

. 224

0.1Û95

0.2114

0.3864

0.3812

0.1973

0,0859

0.0182

0.0041

0.0000

0.0034

0.0089

0.0420

0.0945

0^2062

0.2044

0.1064

0.0457

0,0125

0.0027

O. OO

0.0777

0.3823

1,3173

1.5815

0,5634

0,0614

0,0000

0,2688

0.7654

1.5664^

1.7227

0.8263

0.2883

0.0444

K'r

1,0

i,o 0,9

0.8

0,6

0.3

0.3

0.7

0,9

1,0

1,0

1,0

1,0

1,0

0,9

0.8

0.6

0.6

0.8

0.9

1.0

1.0

1.0

0,9

0.3

-1,6

-2,2 _

0,0 "

0,9

1.0

0.5

-0.5 •2,3

-26

•0.6

0.5

0.9

65

Table B. 1: Tabular Data - Single Opening - C, = 1.0 continued

Tambs Pamb =

——._,,

72

J 29.93

di =

Ai =

F ! ?9Kd

.[•intia. . l . .J i35+ '' ltgím"3

0.0071374 m

di = 0.25

Ai =

0.00635

3.167E-05

in

m m-2

i

^K

Pí

Râw Dâta

dPc

(in H201

0 4564

0,4528

0.4599

0,4582

0.4570

0.4573

0.4572

0 4582

0,4550

0.4541

0.8802

0,8860

" 6!887e 0,8S34

0,8849

0.8865

0,8342

0,8894

0,8899

0,8870

0,8813

0,4577

0,4560

0,4585

0,4588

0.4586

0,4591

0.4571

0,4585

0,4567

0,4578

0.4563

0,8366

0,8914

0.8912

0,8359

0,8972

0,8356

0,9002

0,8879

0.8324

0.8913

0,8949

Pr.g (in H2 1

0.4841

0 3991

0,1390

-0.6808 -3,6232

-6.9842

-6 9842

•4.2806

•0.1422

0.2413

0.9231

0.6340

-0,1249

-1,3372

-3,8351

„„-6-9,842

-6,9840

-3.1829

-1.0488

0.2950

0,8230

0.4831

0.3513'

0.0950

""•13650

-5.0498

-6,3842

_-6,3841_ ... _-~ ^ —

., • . • ' •393Z.

""-'o':79'Í3

0.2229

0.3242

0.8274

-0,0353

-2.8023

-5,5644

-6.9838

-6,9842

-5,8222

-13363

-0.0888

0.7741

Q (SCFMl

0 000

10.824

22.052

39.508

71.293

103.040

103.171

74.515

55.702

29.447

13.649

0,007

18,930

3S.469

54.526

77,675

104.696

104.631

70.674

51.615

23.903

f2.t66

0,000

10.938

19.013

40.375

66.095

_91,555

J93.293 "62.902

40.509

'33.694

15.558

0.003

3.512

30.530

56.197

_71550

"ãi'e^e 94.314

72.658

' 49.778

30.266

12.083

• •

Data '';/itli Correijtftd qO and

Unit Con'.iersions

qO--dP.;

(P^a)

119.31

118.36

119.11

120.24

119.77

119.47

119.54

113.51

119.77

113.95

118.70

250.10

231.61

232.02

230.94

231.33

231.73

231.14

232.51

232.62

231,88

230,39

119,65

119.20

119.86

119.94

119 83

120.01

119.49

113.87

119.33

119.67

119.27

231.76

233.01

232.36

231.53

234 55

234.12

235.32

23211 "

232.39

233.94

Pr.g

(^•3)

120.23

99.13

34.52

-169.07

-899.80

-1734.48

-1734.47

-1063.06

-486.63

-35.3n

59.93

229,25

163,37

-31,03

-332,08

-352,41

-1734:47

-1734.42

-790.44

-260.47

J3.27

204.33

119.96

87.39

23.59

-338.33

-1254.09

-1734.47

•1734.46

-1113.21

-346.11

-196.52

55.35

229.52

205.49

-23 8'"'

-636.06

-13S1.8S

-1734.37

-17,34.46

-1445.91

-480.36

-22.06

192.24

Q

íi:.qí )

O.OOOE.OO

2.210E-04

4.502E-04

8.066E-04

1456E- 3

2.1 4E-03

2.106E-03

1.521E-03

1.137E-03

6ni2E-04

3.808E-04

1.429E-07

3.865E-04

7.854E- 4

1.113E- 3

1.5S6E-03

2.133E- 3

2.137E-03

1.443E-03

1.054E-03

e.10eE-04

2.4S4E- 4

0.000E>00

2.233E-04

3 SS2E- 4

8.243E-04

1.349E-03

1.8e9E-03

1.305E-03

1.284E-03

8.271E-04

6.879E-04

3.176E-04

6.125E-0S

1.942E-04

6.233E-04

1.147E- 3

1.461E-n3

1.932E-03

1.32eE-03

1.4S3E-03

I.OieE-03

6.179E-04

2.467E- 4

1 1 r 1 — — . — —

Datâ Reduction Results

qi iPa)

0.000

12 758

52.355

169.973

1156 171

1159.115

604.641

337.368

94.426

37 372

0 000

161.151

323.756

657.011

m'i.f/sz 1193..518

543.909

290.110

97.404

16.118

0 nno

20.795

62.831

283.335

759.299

1456,333

1512,773

687 709

285.219

' 197.324

42.071

0.000

15.726

162.005

543.911

839.305

1556.299

1546.065

917.577

430.676

159.216

25.378

qiíqO

0.0000

0.1078

0.4446

1,4137

0,7938

0 3191

oono 0 1685

0.6945

1.4019

1.2471

0.4201

0.0700

0.0000

0.1744

0.5242

1.6489"

0.3527

0 0000

0.0675

0,6954

1.8463

0.6834

0.1085

K'r

1.0

0.8

J),3 " " : Í , 4 '

-0.3 '

0,5

1.0

0.7

-01

•1,4

-1.1

0 3

0.3

1.0 0.7

0.2

" '-'í.'6 0.5

1.0

0.9

-0.1

"•2,1

•0,1

0,8

66

Table B.2: Tabular Data- Single Opening- C„= 0.7

Tâmb =

Pamb =

rho amb =

• •

. , „

di =

J2_ 2~ 9.93

1,196

t 0.75

;, 0.01905 Ai =

di =

1 2.850E.04

0.343S

F

l„i,n,Hg kgím-3

in

m

m~2

in

r o , 687325' m

Ai= 5.989E.05 m-2

1 295,4

101364,4 Pâ

Râw Dât-a

dPo

(in H20)

0,4436

0,4475

0,'4476

0,4479

0,4465

0,4474

0,4448

qMes " 0"4482

0.4464

0.4432

0.8838

0 8871

0,8810

0,8783

0.8781

0.8726

0.8776

0,8753

0,8774

0.8882

0.8812

0.4673

0.4682

0.4665

0.4708

0.4633

0.4713

' 0.4725

0.4703

0.4682

0.4:646

0.4656

0.3125

0.3087

0,3132

0,3123

" 0,3135

0,9071

0.9161

0.9107

0.3131

0.9124

0.9118

Pr.g

(in H2 )

0.3325

0.2572

0.0838

•0.3097

•0.7617

•1.4115

-1,4083

•"•^^si

•02486

0.1272

0.2954

0.6595

0.6105

0.3470

-0,2382

•0,3413

•1,3631

•1,8699

-0,9833

-0,3490

0,4370

0.6019

0.3336

0,0588

-0,2622

-1,3772

-3,6864

-5,3882

-5.3316

-3.6363

.:1-5059

-6.2662

0.1144

0.6613

0.4710

0.0334

-1,2830

-3,4066

-6.0622

-6.0673

-2.3718

-1.2857

-0.0828

0.3250

0

(SCFM)

0.005

17.326

38.218

68.411

93.280

133.863

139,033

37,067

eí^s'í'" 33.940

13.363

0.000

13.S11

36.433

71.389

101 481

139682

139.193

103.671

75.330

29,360

14.872

0.008

18.432

30.644

57.553

92.497

118.068

118.201

32,314

59.677

30.665

15.790

.OOO

12.134

2S.143

57 .339

83 .565

117.456

117.278

84.531

58 .020

31.795

18.611

D-iU ''í.''itfi Correi-. i ted qO ând

Unit Coni.'ersi n

qO=dPc

(Pa)

117.52

116.99

117.00

117.10

116.72

116.95

116,27

117,26

117.16

116.70

117.42

231.04

231.91

230.31

229.59

229.55

228.11

229,41

223,97

229,37

232.19

230.35

122.17

122 39

121.96

123.07

122.42

123.36

123.52

123,08

122 J g '

121.45

121.72

23S.54

237.54

238.71

238.48

238.79

237.13

239,49

238,07

238.71

238.52

233.36

Pr.g

fPa)

82.57

63 33 . _ _ „ .

-76,92

-139,17

-350.53

-349.83

•186.03

-61.73

31.53

73.37

163.77

151.62

36.18

-53,15

-233.83

-464.13

-464.37

-244.19

-86.63

' 108.52'""

149.47

S2.35

14.59

-6512

-342.02

-915.48

-1487.12

-1487.37

-315.62

-373.38

-66,11

28,40

ie4,'22

116,36

3.79

-318.62

-845.99

-150549

-1506.78

-738.02

-319.29

-20.57

80.72

Q

(^.qís)

1 21E-07

3 f;eOE-n4

7.803E-04

1.397E-03

2.007E-03

2.835E-03

2.S39E^03

1.9S2E^03

1.319E-03

6.929E-04

2.728E-04

O.OO0E»OO

2.820E- 4

7.43SE-04

1 458E-03

2. 72E-03

2.852E- 3

2.S42E-03

2.117E- 3

1.538E-03

6.117E-04

3.03eE- 4

1.e33E-07

3.773E-04

6.256E-04

1.175E- 3

1.8S8E-03

2.411E-03

2.413E-03

1.8S5E-03

1.21SE-03

6.261E- 4

3,224E-04

O.O OE.

2.477E^04

5.746E-04

1.1S4E-03

1.823E-03

2.33SE-03

2.394E-03

1.72SE-03

1.185E-03

6.431E-04

3.80 E-04

: Dâta Reduction Results

qi ÍPa]

0 000

0.690

3:i34

10.043

20.726

41.330

41,479

20,218

8,951

2,472

0.333

0,000

0.403

2.84S

10.336

22.098

41.867

41.575

23,062

' " l 2 " l 77 " " '

1,926

0,475

0,000

16,600

45.636

160.971

415 7S4

677.449

673.377

414.144

173.072

45,698

12,116

0.000

7.155

38 .430

163.475

389 .842

670 .444

ees.414

347.251

163.594

49.128

16.833

qiíqO

0.0000

0.0059

0 0268

0.0858

0.1776

0.3533

0.3567

0,1724

0.0764

00212

0.0033

0.0000

. 018

0.0124

0.0476

0.0963

0.1835

0.1812

0.1007

' 0:0531

0.0033

0.0021

0.0000

0.1356

0.3742

1.3030

1.4140

0,3763

0,0395

0.0000

0.0301

0.1612

0.6855

i :6326

1.4536

0.6853

0 2 0 6 0

0 0706

K'r

0.7

05

02

-0.7

-1.6

-3.0

•3.0

•1,6

-0.5

0.3

0.6

0.7

0.7

04

-0.3

-1.0

-2.0

-2.0

-1.1

-0,4

0,5_

'o'e" 0,7

0^1

_ - 0 ^ 5

" " " - 2 , 3 " " '

-3,1

-0,5

0,2

0.7

0.5

0.0

•1.3

•3.5

•3.1

•0.1

0.3

67

Table B.2: Tabular Data - Single Opening - C„= 0.7 continued

Tamb =

Pamb =

rho amb =

dl =

Ai =

di =

Ai =

72

29.93

1.136

' 6 281

0,0071374

4.0 1E.Û5

0,25

F

.LnHg . kgilm*3

m m'2

in 0,00635 m

3,167E-05 m'2

295.4

101354.4

dPc

íin H201

0.4566

0,4518

0,4543

0,4530

0,4552

0.4555

0.4570

0.4533

0.4434

0,4531

0.3871

0.8812

0.8852

0,8841

0,3347

0,3332

0.8796

0,3861

'0.8826

6.8813

0.3730

0.4532

0.4540

0.4543

0,4572

0,4537

0.4590

0.4600

0.4566

0.4575

0.4573

0.4547

0.8820

0,8843

0,8354

0.8866

_ 0,8350

'"ô.'ss'^'i 0.8307

'"6.3881

0,3335

0.8813

0.8787

K

Pa

Râw Data

Pr.g

(in H20)

-0,0598

-0.3333

-2.3685

•5 4359

•6 9S41

-6.9842

-4.7896

-25964

-0,4208

0,1426

0.6491

0.3711

-0.4322

-2,2643

-4,3648

-6.9838

-6.3841

-5.3243

-2.0250

-0.2255

0.1783

0.3551

-0.0590

-0.9130

-2,1978

-5,7830

-6.9840

-6.9841

-5,0356

-3.1282

-0.8233

-0.0884

0.6613

_ 0.4111

'-'0.2399

-2.2165

-5.0523

-6.3840

-6.3840

"•;6,9842_

' -4 .5624"

-1.1931

0.1020

Q CSCFM)

0.010

16.445 35.032

52.613

80.022

100.765

100.885

73.129

55.000

24.61S

9,851

0,000

11,239

28,577

__52.110_

697753"

Í01,087

101.066

73.789

49.695

24.780

16.463

0.006

15.383

29.696

43,633

68,282

32.739

92.565

64.137

51,743

23.456

16.023

" 0.000

9.371

22.664

44.743

64.427

93.454

93.479

. . ^.^•'Sl

"61,223

35.240

17.443

Dat.=i 'v.'ith Corr' cted qO and

Unit Con'.'6'rsions

qOrdPc

(Pa)

118,78

119,37 118.11

118.75

118.41

119.01

119.06

119.46

118.63

117.49

118.46

231.88

230.35

231.40

23111

231.27

230.88

223.34

231.65

230.56

230 38

229.73

118.47

118.68

118.83

119,51

120,18

119,99

120,25

119,36

119.58

119,55

118,37

230.56

231.32

23145

231.76

231.35

231.12

232.84

232.15_

232.52

230.39

229.69

Pr.g

(Pa)

8161

-14,86 -246.63

-588.21

•1364,87

•1734.44

•1734.46

•1183.47

•644.81

•104 50

35.42

16120

32.16

"""167.33 '

•562.33

•1083.96

-1734.36

-1734.45

-1322.37

-502.90

-56.00

44.29

83.20

-14.65

-22673

-545,31

-1439,88

-1734,43

-1734,45

-1250,54

-776.87

-205,71

-21,95

164,22

102.0S

-59.59

-550.46

-1254.81

-1734.42

-1734.43

-1734.47

-1118.13

-296.23

—i2±:—1.

0 íy.gls)

2.042E-07

3.358E-04

7.152E-04

1.074E-03

1.634E-03

2 057E- 3

2.060E-03

1.493E- 3

1.123E-03

5. 2eE-04

2.ni1E-04

O.OOOE-00

2,235E- 4

5834E^04

1064E^03

1.424E-03

2. 64E-03

2.n63E-03

1.e03E- 3

1 015E- 3

5.059E- 4

3.361E-04

1.225E-07

3.141E-04

e 063E-04

8.320E^ 4

1.394E^03

1.S33E-03

1.890E-03

1.30SE-03

1.056E- 3

5.810E-04

3.271E^ 4

.OOOE.O

2. 36E-04

4.627E^ 4

9.13eE^04

1315E-03

1.908E-03

1.3n3E-03

J.575E-03

"1250E-03

7.195E-04

3.561E-04

Data Rsduction Results

V (Pa)

0.000

23 450

133 641

301.437

697.315

1105.681

1108.316

582.3.56

329.409

65 936

10.567

0,000

13.755

88.929

295701

523.905

1112.751

1112.296

67S.992

268.928

66.867

29.515

0.000

41130

153.275

331762

810,373

1494.856

1489.255

714.978

465355

140.742

44.623

0.000

17.280

89.282

343.047

721.453

1517.993

1518.311

1034.570

651.613

215.848

52.383

qiíq

0,0000

0 2467

0.5617

0.0832

.O OO

0.0597

0.3843

12795

11664 '

0,2903

0,1285

0.0000

0.3466

1.2333

1.1772

0.3754

0.0000

0,0747

0.3857

1.5018

0.3363

0.2302

K'r

0.7

-0.3

0 3

0.7

0.4

-0.5

-2.4

-2,2

-0.2

0.2

0.7

-01

-1.3

-17 -0.2

" 0 7

0,4

•0.3

•2.4

•13

6.1

68

Table B.3: Tabular Data - Single Opening - C„ = 0.4

Tamb =

Pamb =

rho amb =

di =

Ai =

_,_„., _... . ..

di =

Al =

72

29.93

1196

0.75

0.01905

2.350E-04

o.sí's's'

F

.b.Hfl kgím*3

in m m-2

in 0.0087325 m

5.989E-05 m-2

1 295.4

101354,4

K

Pa

Raw Data

dPc

(in H201

0 4451

0,4501

0.4479

0,4468

0.4453

0.4458

0.4474

0,4457

0,4459

0.4454

0,4536

0,8740

0.8735

0:'87'5'5""

0.3616

0.8627

0.S682

0,8665

0,8634

0.8660

0:'8'765

0.3713

0.4652

0.4613

0.4622

0.4665

0.4670

0.4636

0.4677

0.4654

0,4660

0,4678

0.4631

0.9033

0.8334

0.8387

0.3022

0.3010

0.8385

0.8335

0,3001

0,8388

0,S956

0,9011

Pr.g

(in H2 1

0.1770

0.1030

_ - ,J830_ -"6 8864 " -1,4847

-2.5532

•2.5656

-1,5661

-0,8076

•0 2277

0,0306

0.3796

0:3204

... " •0842

~ -0.7323

-1.sn;31

-3,2346

-3,2238

-2.0278

:p,8355

- ^6050 0,2689

0.2049

•0.0196

-0.6032

-1,4398

-3,8275

-6,2553

-6.2563

-3,5693

"^2.'66e5 -0.5122

-0.0525

0.4179

0.1032

-0.6882

-21605

-4.5574

-6.5275

-6.5286

-3.7507

-1.83S5

-0.7719

-0.0031 1

Q

(SCFM)

0.031

14.087

40,471

76,321

98 284

136.436

136.750

101.880

72,515

43,179

17,915

0.000

12.034

28.716

67.375

'39,145

134.883

135.147

105033

70,330

34.152

15.235

0.Û 1

13.386

34.021

52,827'

89.251

115.449

"1Í5:483 86,297

6"3.25Í

31.407

15.575

0.004

15.416

36,301

63,183

35,430

115.171

114.619

85.942

5S.450

33.813

19.132

Datã Vnh CorrectS'd qO and

Unit Conuersions

qO=dPc

ÍP^a)

1ie,.34

117 66

117.09

116.81

116.42

116.53

116.94

116.52

116.55

116.43

113.58

223.47

22S 33

228.87

225.24

225.52

226.36

226.52

225.63

226.37

229.12

227.90

121.60

120.72

120.81

121.34

122.07

122.75

122.27

121.66

12181

122.23

122.63

236.14

234.S4

234.92

235.33

235.52

234.37

235 13

2353

234.95

234.12

235.57

Pr.g

(Pa)

43.97

26 83

;4545^

'"ãi Tí'" -368,72

-635.56 -637.14

-388.32

-200.57

-5R54

20.01

94.28

73.58

20.90

-196.75

-443.02

J03.30 -302.10"

-503.53

-222.33

-124

66.78

50.88

-4.S8

•143.73

-357.51

•950.53

-1553.61

•1553.71

_J36.4

""-"5T3.I9

-127.20

•13.05

103.79

25.64

•170.91

•536.55

•1131S0

-162105

-1621 31

-33146

-456.57

-191.70

-0.76

Q í>:-gís)

6.329E- 7

S.263E-04

1,55SE-03

2 007E-03

2.786E-03

2.792E-03

2.030E-03

1.481E-03

8.816E-04

3.658E-04

O.OOOE.OO

2.457E-04

5.863E-04

1 37eE- 3

2.024E- 3

2.754E-03

2 753E-n3

2.146E-03

1449E-03

e.973E- 4

3.110E- 4

2.042E-08

2.S55E-04

6.34eE-04

1.079E-03

1.322E-03

2.357E-03

2.35SE-03

1 762E- 3

1.291E-03

6.412E-04

3.180E^04

8.ie7E-08 "

3.147E-04

7.514E- 4

1,290E-03

1,348E-03

2.351E-03

2.340E- 3

1.755E-03

1193E- 3

7.324E-04

3.916E-04 1

Datã Reduction Results

. .V (Pa)

0.000

3.515

12.499

20.728

39.944

40.128

22:272

11284

4.001

0.689

O. O

0.311

17R9

9.741

21.033

39.040

39 193

23.702

10.811

2.503

0.498

0.000

9.506

66.248

135.620

337.113

647.728

643.109

361.912

194.423

47.936

11.789

0.000

11.549

65.816

134,005

442570

644.613

638.448

353.941

166.028

73.209

17.881

qiíqO

O.O OO

0.0300

0 1070

0.1780

0 3428

0 3431

0.1311"

0.0963

0 0344

0 0058

0.0000

0.0014

0 0077

0.0432

0.0935

0.1720

0.1730

0.1050

0.047S

0.0109

0.0022

0 nnoo 0.0787

0.4656

11122

1.5961

0.3920

00961

0.0000

0.0492

0,2302

0,8226

18791

1,5255

0.7067

0.3127

0.0759

K'r

04

-0.4

-1.9

-3.2

-5.5

-5 4

ZJ:Í?Z -l'f""" -0.5

02

0.4'

03

0.1

-0.9

-20

-3.5

-3.5

-2.2

-10

0.0

0.3

0.4 n.

-1.2

-2.9

-4.2

-1.0

-0.1

0.4

0.1

-0,7

-2,3

-4,3

-4,0

-1.9

-0.8

0.0

69

Table B.3: Tabular Data - Single Opening Cp= 0.4 continued

Tamb =

Pambs

fho amb =

di =

Ai =

72 29.33

1.196

0.28V

0,0071374

F 295.4

inHq 101354.4

kqím'~3

K Pa

in m

4.001E- 5 .m-2

;

di = 0.25 in ' 0.00635'm

Ai= ' 3.ie7E-05 m-2

1

dPc

(in H2 )

0.4552

0.4543

0.4555

0.4536

0.4523

0.4595

0.4577

0.4565

0.4575

.4561

0.4519

0.8787

0.8768

0,8816

'"'6:87"82 0.3774

0.3850

0.8811

0.8792

0.8761

0.8763

0.8833

0.4602

0.4572

0.4559

0,4624

0,4656

0,4633

0,4623

0.4655

0.4624

0,4627

0,4621

0,8313

0,8885

0.8337

0.8362

0.3382

0.3964

0.8973

0.8950

0.8933

0.8940

0.88S1

Raw Dat-a

Pr.g

(inH20)

0,1990

-0,3576

-1,0625

-2,5384

-5.2134

-6 9340

-6.9S41

-5.5207

-2.7330

-0.6434

-0.1129

0.4000

-0.2317

-1.0339

-2.6950

-5,7278

-6.9340

-6.3340

-5.3432

-2.6014

-0,9036

-0.2571

0.1327

- .126S

-0.6442

-2.9043

-6.9844

-6.9841

-6.3840

_-6.3842

"" -'3'l'779

-0.3851

-0.4216

0.3877

-0.0410

-0 6362

-2.5555

-6.9833

•6.9839

•6.9840

•6.9341

•4.1978

•0 5767

•0.0534

Q (SCFMl

0.000

18,644

31.699

50 280

73.112

99.673

99.243

74.7"31

52.948

24.331

12.429

0,002

17,953

31,466

50,631

76.317

99.148

98.760

72.365

43,313

29,393

18,500

0.000

11.111

21.146

46.077

74.769

92.020

91.351

75.495

4S:589

26.321

17,465

0,012

11.367

22.566

42.780

71.420

31.333

31,526'

71.663

54.968

20.990

12.222

Dâtâ''í/ ithCorrect

Unit Con'.'&rs

qOrdPc

(Pa)

118,98

118,76

119,08

118.59

118.23

120.12

119 66

113.35

119.59

119.23

118.12

229.70

229.22

230.46

223.58

229 35

23134

230,32

229,33

"223.6 " 229.q7_

"'"'2'3Í.'03

120.29

113.53

113.18

120 S7

121.71

121.12

120.84

121.68

120.37

120.95

120.79

232.93

232.27

233.62

234.28

234.79

234.34

234.56

233.35

233.67

233.71

232.17

Pr.g

ÍPa)

43,42

-88,81

•263,36

•630.39

•1234,70

•1734.43

•1734.45

•1371.02

•691.15

-159.78

99.34

-57,54 '

-256,75

•669.29

•1422,45

-1734.43

-1734.43

-1326.34

-646,04

-224,39

"'-es.'sí" 47.S6

-3148

-159.38

-721.25

-1734.51

-1734.44

-1734.41

-1734.46

-789.19

-244.65

-104.71

96:27

-10.17

-172.90

•634 64

•1734.40

-1734.40

'"-Í734.'42"

-1734.44

•1042.50

•143.23

•13.27

"•• ™ ™ "

?d qO and

ons

Q (kgís)

O.OOOE.OO

3.806E^04

6.472E-04

1.027E^03

1.493E^03

2.035E^03

2.026E^03

1.52eE-03

1.0S1E-03

4.3eSE-04

2 53SE^04

3.403E-08

3.6e5E-04

e424E-04

1.035E-03

1.558E-03

2.024E-03

2,016E-03

l,477E-03

1019E-03

6,001E-04

3,777E-04

O.OOOE. O

2.2eSE-04

4.317E-04

3.4n7E-04

1.527E- 3

1.873E-03

1.875E-03

1.541E-03

9.920E-04

5.374E-04

3.56eE-04

2.45 E-07

2.443E-04

4.607E-04

3.734E- 4

1.45SE- 3

iseeE^os 1869E^03

1.463E-03

1.122E- 3

4.285E- 4

2.495E-n4

1

,. Dai:a Rs'duction Results

qi íPa)

0.000

37.852

103.421

275.297

582.087

1081846

1072.532

608.152

305.288

64.466

16 822

0.000

35.038

107.313

279.816

634.239

1070.479

1062.117

570.253

271.2"96

94.082

37.270

0.000

21.458

77.720

363.010

971.670

1471770

1466.369

990.631

410.347

120.416

5'3":6Í7' O. OO

24.891

88.508

318.095

886.575

1451658

1456.011

332.613

525.160

76.577

25.963

qiíqO

0.0000

0.3187

0.3189

0.5407

0.1424

0.0000

0.1531

0.4678

1,2138"

1,1846

0.4107

0.1613

O. OO

01795

0.6521

0.3356

0.4383

0.0000

0.1072

0 3788

13578

0.3277_

0.ÍÍ18

K'r

0.4

-0.7

-2.2

-1.3

-0.2

0,4

•0.3

•1.1

-2.9

-2.3

-1.0

-0.3

0.4

-0.3

-13

-2,0

-0,9

0,4

' "ã'o"~ " -0.7

:2.7

-0,6

-0.1

70

APPENDIX C

RAM COEFFICIENTS FOR MULTIPLE OPENINGS TABULAR DATA

71

Table C.l: Tabular Data - Multiple Openings - 19.05 {Cp= 1.0) and 8.73 (10 deg. Offset)

Tambs

Pamb = tho amb =

q^oorreodon =

71

30.04 1.202

F

inHq

kgím~3

1,053

i Openinq 1

d1 =

-Al =

kAl =

CpU

kAriArí A i r2 =

C d2 =

A2 = kA2 = Cp2 =

kA2'(Arí A2)"2 =

0.75) in 0.01905

2.850E-04

1.5473

0.967

m

m'"2

2.27

(10 deg sep)

Dpenin'3 2

0,3438 in

0.00373252: m

i 5.989E-05 1.6804

0.3565

1 55.73

m-2

1

.

1

284,8

101726.9

K

Pa

Raw Dsií

dPc

in H2 1

0.4744 0.4736 0.4761 0.4733 0.4769 04741 04713 0.4736 0.4760 0,4744 0,4755 0,9198 0.9173 0.9154 0.9138 0.9129 0.9204 0.9142 03187 09155 0.3158 0.9132

0.4511

0,4518

0.4547

0.4553

0.4497

0.4511

04512

0.4510

0.4490

0.4487

0.4503

0.8901

0.8304

0.3302

0.8948

0,8326

0.8.934

0.8340

0.3936

0.3350

0.8834

0.8327

Pr.g [inH2i:i|

0.4855 0.4749 0.4567 0.4100 0,3431 0,1311 0,1388 0.3483 0.4151 0.4611 0.4783 03463 0.3356 0,9135 0.8611 0.7691 0.6337 0.6283 0.7796 0.3615 0.9136 0.3332

0.4211

03943

0.2710

0.1542

-0.0277

-0.2787

•0,6760

-0,3256

-1.1764

-0.3335

-0.7394

0.8549

0,8231

0.7773

0.6886

0.4591

0.2136

•0.0743

-0.4481

-0.3179

-1.2497

-2.2006

Q (SCFMl

OOÛ 19.459 43.372 73.418 102.762 148.010 148.479 101.498 71.137 38.135 18.373 0.002 14.740 33.153 70.871 109.603 151.032 150.966 107.823 71.157 33.283 13.930

0.000 5,757 19 322 26,932 35,842 45.693 58.280 64.267 72.011 64,632 60.907 0,000 6.379 11.052 18.804 31.478 41.433 51,267 61.432 71.993 81.117 97.617

Eiat.3 Virh Corrected qO and Unit Con';er£Íons

q =dPc

iPaJ

124 07

123.32

124.50

123.89

124.70

123.97

123 39 123 85

124.47 124.06 124.35

240 53

239 88

233.33 233.36

233.72 240 70 233.06

240.24 233 33

233.48

238.81

117.96 113.14 118.90 113.03 117.53 117.96

113.00

117.93

117.42

117.33 117.91

232 76

232.35

232.79

234.00

233.42

23.3.61

233.63

234 05

232.57 233.44

Prg

iPâJ

120 57

117.35

113.41 101.82

85 20

47.46 46,90

36.50 103.09

114.50

11378 235 16

232.35

228.11 213.85

191.00 167 37 156.17

193.62 213.95

226.39

231.74

104.59 98,08

67 30

38.30

-6 83 -63.20

-167.38 -223.37 -23214

-233.33 -136.05 212.30

204.40

133.04

17102

114.02

54.29

-18.45

-11128 -203.12

-310.35

-546.50

IJ

(kg/5|

0 O OE. O

3.373E-04 8.855E-04

1499E-0J

2. 98E-03

3. 22E- 3

3.0JtE- 3 2. 72E-03 1454E- 3 7,736E- 4 3.751E-04

4. 83E- 8

3. 3E-04

6.769E-04 1 447E-03

2.238E-03 3. 84E-03 3. 82E-03

2.201E-03 1 453E-03

7.S16E-04

2.844E- 4

O.O OE.OO 1175E-04

3.345E-04 5.499E-04

7 318E- 4 3.329E- 4

1.13 E-03 1.312E-03 1.470E-03

1.320E-03 1.244E-03 O.OOOE.

1221E-04

2 25eE-04

3.833E-04

6.427E-04

8 459E- 4

1.047E- 3

1.254E-03

1.470E-03 1656E-03

1.933E-05

„ . ^ . _

— - 4 '

DatãRedijctionRe;ijlt

qi (Pa|

0 000 0.808 4 014

11502

22.534

46.748

47 045 21.363 10 317 3.103 0.720

0 000

0.464

2.345

10 718 25 637 48.676 43.633

24.311 10.305

3.123 0.414

O. O

1.602

18.043

35.054

62,035

100.904

164 150

199.608

250.610

201.831

179.232

O. OO

1.728

5.303

17.088

47.387

32 965

127 021

182.337

250.485

317.338

460.521

qi(q

OO

0.0065

.0322

0.0328

0.1807

0.3771

0 3813

01775

0.0363

.0250'

0.0053

.OO

0.0013

0.0098

0.0449

0 1074

0.2022

0.2034

0.1033

0.0451

0.0131

0.0017

O.O

0.0136

0.1518

0.2344

0.5280

0.8554

1,3911

1.6926

2.1344

1.7207

1.5204

.O O

0.0074

0.0254

0.0730

0.2051

0.3551

0.5433

0 7305

1.0702_

1.3G73

1.3728

Cp.i

1.0 1.0 0.9 08 0.7 0.4 0.4

0.7 03 0.3

10 10 10 1.0

0.3 03 0.7 0 7 0.8 OJi 0.3

1.0

0.3 0.3 0.6

0.3

-0,1

-0,1 _,

0.9

0.3

0.3

0.7

0.5

02

•0.1

-05

.-...J>í.ZI.

72

Table C.l: Tabular Data - Multiple Openings - 19.05 (C, = I.O) and 8.73 (10 deg. Offset) continued

Tamb»

Pamb =

tho amb =

71

30,04

1.202

F 234.8 K

'"^^a i _ l 1726,9 Pa kgím"3 j

1

! 1 Combined Ogenings

à r r j 3.443E-04 [qr'íq )min = i Ô.Ô4S766632

*?.:M. dia. (]nj

2.036E-0;

0.825044508

m-2

Raw Data

dPc

^inH2 l

0.4674 0.4636 0.472 0.4639 0.4667 0.4632 0.4652 0.4664 0.4715 0.4691 0.4693 0.9125 0.3074 0.9103 0.9106 0.9007 09105 0.3058 0.9010 0.9105 0.3043 0.3073

Pr.g

(inH2 l

0.4303 0.4756 0.4634 0.4163 0.3631 0.2455 0.2436 0.3533 0.4263 0.4607 0.4745 0,3375 0,3226 0.3101 0.8744 0.7971 0.6927 0.6881 0.7359 08694 0.3038 0.9216

' P

qifq

0.043

0.244

0.433

0.634 0.823

1024

1.220

1415 1610 1.805

2000

a

2.61

13,04

23,47

33,30 44,34

54.77

65.20

75 63

86.07

36.50

Q (SCFM)

0.001 14.207 36,646 76,043 104.043 143.472 149.065 106.633 68.863 35.356 17.715 O. 16.577 36.913 66.533 104.203 150732 150.557 105.380 71.294 37.345 19.577

Eiala V/ith Correct Unit Con'jers

q =dPc (Pal

122.24

122 79

123.43 122.88 121.79

122.45

12165

121.97 123.31

122.66

122.86

233.62

237 23

238.05 238.13 235.53

23310

236 37

235.63 233 03

236.43 237 43

Pr.g

fPa)

119,27

11811

115.03 103.53

30.16

60.38 60.50

33.97 10537

11441

117.33

232.83 229.12

226.02 21715

137.96

172.02

170.88

197.66

215.90 224 44

228 67

ed qO and ons

Q

1.356E-03

2 901E-04

7 4S2E- 4

1.553E- 3

2.124E- 3 3031E-03 3 043E- 3

2178E-03 1406E- 3 7.341E-i:i4 3.617E-04 O.O OE.OO

3.384E-04 7.533E-04 1.360E-03

2.127E-03

3. 77E-03

3 074E-03

2.152E-03 1 456E-03

7 625E-04 3.397E-04

" í "

Data Reduction Re ult

qi (Pa)

0.000 0 294

1.957

8.426

15 774 32.122 32.373 16.538 6.310 1884 0.457 0,000 0,400

1.336 6.462 15 823

33.107

33.031

16,132 7.407 2 032 0Í558

. tídicted Ra

b

-5.44

-27,13

-43,33

-70,68 -'o'Ss •114.18

-135.93

-157.68

' -179.43

-201.18

-222.92

m Coeffície nt

0 alpha

2.83 i 1.000

13.70 ' i ' 0.85:3

24.58 j 0.844

35.45 i 0.840 46.33

57.20

63.08

78.95

0.833 0.837

0.836

0.836

89.32 i 0.335

100.70 \ 0.335

111.57 ' 0.835

Cp,í

0.857

0,564 0253

-0,047 -0,353

-0653

-0.965

-1 272

-1.578

-1834

•2.130

qi qO

0.0000

0 0024

0 0153 0 0686

0.1235 0.2623 0.2662

01360 0.0560

0 0154

0.0037 0.0000 0,0017

0.0033 0,0271 0.0672

0.1330

0 1394 0.0687 0.0311 0.0086 0.0024

Cp,i

10

10

0.3

0.3

0.7 0.5 0.5 0.7

'" 'o','3" " ' 0 9

1.0

10

1.0

0.9 0.9

0.8

0.7

0.7

08 0.3 0.3 10

1 í 1 i ' \

;

- I 1 1 1

í

73

Table C.2: Tabular Data- Multiple Openings - 19.05 (C,= 1.0) and 8.73 (20 deg. Offset)

Tamb =

Pamh=

rhoamb =

q (îotre'Ction =

71 30.04 inHg

1202 kgím-3

1.053

294.81 K 101726.9iPa

Openingl

0.75 in

A1 =

kAU

. Cp1 = kA r iA r í A1)"2 =

0 01905

2 S50E.04

1.5473

0.367

2.27

i

m

m~2

\

í

' (20 deg sep)

Openinq 2

d 2 = | 0.3433 iin

! 0.0037325 m

A2= : 5.3S3E. 5 m-2

kA2 =

Cp2 =

2.3053

0.5934

k.A2"(AríA2)~2 = i 76.46

}

i

—

• • • -

i i

í

Raw Data

,...„'JP'= (in H201

0.4744

0.4735

0.4761

0,4738

0,4769

0.4741

0.4713

0,4736

0.4760

0.4744

0.4755

0,3193

0,3173

0,3154

0,3138

0.3123

0,9204

0,9142

0.9187

0.9155

0.9158

0.3132

0.4546

0.4536

0.4570

0,4551

0.4437

0.4554

0.4525

0.4518

0.4528

0,4530

0,4546

0,3074

0.9013

0.3358

0,3343

0.8383

0,3873

0,3363

0,8373

0,3350

0.3308

o.aai3

P'9 (in H20)

0.4855

0.4743

0.4567

0,4100

0,3431

01311

0,1338

0,3483

0,4161

0.4611

0.4783

0.3463

09356

0.3135

0.8611

0.7681

0.6337

0,6233

0.7796

0.8615

0.9136

0.9332

(5CFM)

0.3162

0.2081

0,0650

-0,1805

-0.4296

-0,3172

-1.1151

-1.4551

-0.3795

-0.5913

-0.2737

0.6533

0.5416

0.4040

0.0620

•0.3552

-06383

-1.1738

-1.5310

-1.8663

•25632

-3.0381

0.000

13.459

43,372

73,413

102.762

143.010

143.479

101493

71137

33.135

18.373

0002

14.740

33.153

70.371

103.609

151.032

150.966

107.328

71.157

33.233

13.330

Data With Corrected qO and IJnit Con'jersi n s

'qO=dPo

(Pa)

0,001

11.719

20.935

31997

41.160

53.387

61.261

69.221

55.182

46,436

35,960

0,000

10.340

18,163

31.234

43.568

51373

63.812

71.563

73.256

31.230

93.493

124,07

123.32

124.50

123.39

124.70

123 97

123.39

123.85

124.47

124.06

124.35

240.53

239.38

233.33

238.36

233.72

240,70

239,06

240,24

233,39

239,48

238,81

Pr.g

(Pa)

118.83

' 118 62

119.50

119.01

117.59

119.03

118.33

113.15

118.42

118.47

113.37

237.29

235.85

234.26

233 87

235 06

232.18

234.38

234.65

234.04

'232.95'

233.20

120.57

117.95

113.41

10182

35.20

47.46

46.90

86.50

103.03

114.50

113.73

235.15

232.35

228.11

213.85

191 00

157 37

15617

193 62

213.95

0

226,33

23174

78.62

51.68

16.14

•44.33

•106.69

•202.94

-276.93

-361.36

-213.41

-146.33

-63.22

163 62

134.51

100.33

15.33

-83 20

-171.07

-23151

-392.64

-463.47

-636.54

-754.50

O.OOOE.OO 3.373E-04 8.855E-04 1.439E-03 2.093E-03 3 022E-03 3.031E-03 2 072E-03 1454E-03 7,786E-04 3,751E-04

4 083E-03

3,0 3E-04

6.763E-04

1.447E-03

2.238E-03

3.084E^ 3

3.082E^03

2.201E-03

1.453E-03

X8ÍeE- 4 "

2,844E-04

Data Reduction Results

qi

EåL 0,000

0,803

4,014

11,502

22,534

46 748

47,045

21.383

10.817

J.103

qí/qO

2,042E-03

2 393E- 4

4,236E^ 4

6 533E^04

8 404E-04

1,030E^03

1251E-03

1 413E-03

1.127E-03

3,481E- 4^

7.342Í-04

.OOOE.OO

J.111E-04

"3'7Í0E-04

6 339E-04

8395E-04

1.061E-03

1.3 3E-03

1461E-03

1 613E-03

1.8e4E-03

2.031E-03

0,000

0.464

2.346

10 713

25.637

43.676

48.633

24.311

JÍ0.8 5

0,414

0,000 6,637 21303' 49,473

81,875

137 744

131372

231,567

147,162

_ 1 4,2J2

62,4?r 0^000

——^ 47 329

91,735

130,546

196,791

247.543

303.575

402.673

478.443

0.0000

0.0065

0.0322

0.0328

0 1307

0 3771

0.3813

0.1775

0.0369

0.0250^

] M58 "o.oooo' 0,0013

0,0038

0,0443

0.1074

0.2022

02034

0.1033

0,0451

"0T0I31"

Cp,i

0,0017

0,0000

0.0560

6,1783 0,4158

0.6963

1,Í567

15328

1.9600

12427

0.3736

0.5257

0,0000

I0JID213

'o.ôi'oT 0.2024

0.3903

0.5623 0.3396;

1.0549

12371

1.7236

2.0516

' • . 0 .

10 0.3 0,8 0 7 04 0,4 0,7 0,3 0,9

w . - . ,

1,0

1,0

0,3

08

0 7

0,7

0.8

0,3 J|,3 'i'. " ' 0.7

0.4

; 0.1

'-04

-0.3

01

0.6 ""0.4

0.1

-0.4

"-0,7"

74

Table C.2: Tabular Data - Multiple Openings - 19.05 {Cp= 1,0) and 8.73 (20 deg. Offset) continued

Tamb =

Pâmb=L

tho âmb =

q^oorrection =

71 30,04

1.202

1.053

Comblned Openings

. ^ r= i 3,449E-04'

(qr>qO)min = ^ 0,162232,

....

nHg It'g7m'3

m"2

j

i-

234,8

101726,9

K Pa " t

Raw Data

dPc

i;in H201

0.4765

0.4733

0.4318

0,4741

0,4697

0.4746

0.4715

0.4713

0.4765

0.4788

0.4778

0,3343

0,3234

0,9256

0.3324

0.3282

0.3135

0,9306

0,9262

0,9274

0.9265

0.9304

qiíqO

^•162..,

0,346

0,530

0 714

0.337

1.081

1.265

1.449

1632

1,816

" " " " 2 , 0 0 0

Fr.g (in H201

0,4730

0,4686

0,4567

0,3982

0,3318

0,2353

0,2260

0,3334

0,4004

0.4550

0,4702

0.3419

0,3211

0.3390

0.8473

0,7714

0.6423

0.6534

0.7723

0.3233

0,8957

0,9229

F

a 1204

25.67

3931 52 34

66 5"

80 21

93 34 107 48 12111

134 75

148,38

Q (SCFM)

0,000

16,356

32,478

72,977

105.357

148.541

143.346

105,711

70.739

31.116

15,492

0.000

13.506

38.732

66,823

103,574

150.507

150,653

101878

75,443

34,267

14,823

I

i

' Dâta Vith Corrected qO and

Uriit Con\;ei ions

qO=dPc

(Pa)

124,60

125,07

125,99

123,98

122,82

124,11

123,31

123,25

124,61

125,21

124,95

244,32

242,73

242.04

243.83

242.73

240.46

243.36

242.21

242.53

242.23

243.31

Pr.g

(Pa)

113.70

116.37

113.41

98.90

82.40

58.44

56,13

82,73 33,44

113,00

116,73

233.91 223.74

220.77

210.57

131.57

15352

162.26

191.30

206.08

222.44

229.20

=redicted R

b

-24.81

1 -52^91

' -3101

l d l l

r r . i 11-' c

.43 6..

277 72

1 -305,83

0

(Kgís)

O.OOOE-O

3.339E- 4

6.631E-04

1.43 E- 3

2.163E-03

3. 33E-Û3

3.023E-03

2.158E-03

1.444E-03

e.353E-04

3.163E-04

0 0 E»00

2.757E-04

7.918E-04

1 364E-03

2.115E-03

3 073E- 3

3.076E-03

2.0S0E-03

1540E-03

6.99eE-04

3.028E-04

am Coefficient |

c alpha

12 77 I.OUO

26.32 0.900

40.87 0.382 54 32 ' 0.874 63 37 0.869 33.03 0.367

111.13 0.863

125.13 0 362

133.23 i 0.361

i 153 28 1 0.860

Cp.i

0.593

0.333

0.034

•0 263

-0.570

-0,873

-1175

•1,478

-1.781

•2,034

•2,387

DataF

qi (Pa)

0.000

0.390

1637

7 760

16.360

32.152

32,063

16.234

7.232

1.411

0.350

0 000

0 266

1 2 . 1 3 2 _

5,503 1 15.'632

33 003

33.075

15124

8.295

_ 1,711

0,320

• " !

eduction Result

qiíq

0.0000

0.0031

0.0122

0.0626

0.1332

0.2531

0.2601

0.1321

0.0585

0.0113

0.0028 . OO

0 0011

0.0031

0.0267

0,0644

0.1373

0.1353

0.0624

0.0342

0,0071

0.0013

Cp.i

1.0

0.9

0.9

0.7

05

0.5

07

0,9

0^3

1,0

0,9

0,9

0,3 0,8

' ' 7

0,7

0 3

0.3

0.9

0.9

1

75

Table C.3: Tabular Data - Multiple Openings - 19.05 (C, = 1.0) and 7.14 (10 deg. Offset)

Tamb =

Pambí

ihoamb =

q^cottection =

30.04 IF

1202 kgiim-3

1 1.053 J

í j

-~~~ ™ ^.. _ .

1

Openinql

d1 =

Al =

ltA1 =

Cp1 =

0.75|in

2.â50E-L"i4 1.5473

0.967

^ i.Ul ;, ^ „ ..„

j _

i (10 deg sep)

m"2

Opening 2

d2 = 1 0.281

1 0.0071374

in

m

A2 = ' 4.001E.05 !T,'2

ltA2 =

Cp2 =

15433

0.8235

fcA2'(AríA2JJ = ! 101.89

1

1 294je|K

1

dPc

(in H201

0.4744

0.4735

0.4761

0.4738

0.4763

0.4741

0.4713

0.4736

04760

0.4744

0.4755

03198

0.3173

0.3154

0.3138

0.3129

0.3204

0.9142

0.3187

0.3155

0.3158

0.9132

0.4555

0.4516

0.4534

0.4513

0.4537

0.4561

0.4536

0.4514

0.4549

0.4538

0.4530

0.3368

0.8340

0.8327

0.8328

0.8937

0,8935

0.8373

0.3875

0,8325

0.8388

0.8325

1 1 1

„„„

Raw Data

Pr.g

(in H20)

0.4855

0,4743

0,4567

0.4100

0.3431

0.1311

0.1838

0.3483

0,4151

0,4611

0,4783

0.3463

0.9356

0.3185

0,8611

0,7631

0.6337

0.6233

0.7736

0.8615

0,9136

0.9332

0.4124

0,3655

0,3115

0.1752

•0.1214

-0.4372

-0.7536

-1.0493

-0.7737

-0,3638

-0,2091

0,3230

0,7802

0,6864

0,5131

0,1433

-0,3633

-1,0432

-1,5216

-1,9905

-1.6133

-11551

Q

(SCFM)

0.000

19.459

43.372

73.413

102.762

148.010

143.473

101438

71137

38.135

13,373

0,002

14.740

33.153

70.371

103.609

151032

150.366

107.328

71.167

33.283

13.330

0.000

5.533

10.202

17.243

27.433

35.531

41.371

47,371

42.535

45.328

23.873

OOO

5,843

11,777

19,030

30.134

41436

52,674

59,043

64,390

60,058

54,304

1

— — • - - " .

f

Data With Corrected qO and UnitConversions

qO=dPc

(Pa)

124,07

123 82

12450

123,33

124,70

12397

123,33

123,35

124,47

124.06

124.35

24053

239.88

239.38

238.96

238.72

240.70

239.06

240.24

239.39

233.48 238 81

119.11

113,09

118,56

113.01

113.65

113.26

118.62

113,05

113,37

118,68

113,46 '

231,30

233,79

233,44

233,48

233 71

233.66

232.13

232.07

233.38

232.43

233.40

Pr,3

(Pal

120.57

117.35

113.41

101.82

35.20

47.46

46.90

86.50 103 i"i9

114.50

118.78

235.15

23235

223.11

213.35

131.00

157 37

156.17

133 62

213.35

226.33

23174

102.43

90.76

77Í36

43.51 •30.14

-108,57

-137,13

-260,59

-193,37

-233.36

" -51,92"

205.37

133.77

17046

123 66

36 35

-91.86

-260.31

-377.87

-494.32

-400.31

-286.36

Q

íkg's)

O.OOOE.OO

3.973E-04

3.865E- 4

1433E-03

2. 33E-03

3.022E-03

3.031E- 3

2.072E-03

1454E-03 7.786E-04

_ 3 75IE-04

4,083E-08

3.0 3E-04

6.7e9E- 4

1.447E-03

2.23SE-03

3 0S4E^03

3.032E^03

2.201E- 3

1.453E- 3

7.316E- 4

2.844E-04

O.OOOE-00

1.130E-04

2.083E-04

3.521E-04

5.611E-04

7.2e7E-04

8 563E-04

3.672E-04

S.684E^04 3.357E^04

6.099E^04

0 OO E-00

1.133E-04

2.404E-04

3 S9eE-04

6.152E-04

8.460E-04

1.076E-03

1205E-03

1.315E- 3

122eE-03

1.1 9E-03

Data

__..<1i

( P a )

. OO

0.308

4 014

11502

22534

46 748

47.045

21.333

10.317

3,103

0,720

0,000

0.464

2.346

10 718

48.676

43 633

24.811

10.805

3.128

0.414

.o o

3.315

11.271 32 193

81.795

137.177

130.765

243.010

195.326

227.437

36.640

0.000

3.697

15.020

39.424

33 336

185.332

300.464

377.617

443.390

390.608

319.347

^eduction Result

_ _qi'q

0.0000

0.0065

0.0322

0.0323

0.1.307

0 3771

0.3813

0.1775

0.0363

0.0250

0,0058 0,0000

0 0019

0,0093

0,0449

0,1074

0.2022

0.2034

0.1033

0.0451

0.0131

0.0017

0.0000

0.0281

0.0951

0.2723

0.6334

1.1502

1.6082

2.0536

1.6463

1.3164

0,8158

0.0000

0.0153

0.0643

0.1683

O4208

0.7353

1.2941

16267

1.9233

1.6805

1.3633

Cp.i

10

10

0,9

0.3

0 7

0.4

0.4

0.7

0.3

1.0

1.0

1.0

1.0

0.9

0,8

0.7

0.7

03

0.3

03

1.0

03

0.3

07 04

-0.3

-0.3

-0.4

09

0,8

, ^ O J ' ~

0,6

0 2

-04

76

Table C.3: Tabular Data - Multiple Openings - 19.05 (C^ = /,0) and 7.14 (10 deg. Offset) continued

Tâtnb = i

Pamh =

ihoamb =

qoorrection= j

Combin

.Ar=!

(qrfqO)min =

71 i F

30 04 : inHg

1,202 i kgím'3

1,063 1

294,8| 1 1 ! 101726,9; Pâ i

>i Openings

3 25Ô -04im-2

0 0633333

Raw Eiata

dPc

(in H201

0,4701

0,4722

0,4721

0,4704

0,4703

0,4684

0,4698

0.4717

0.4707

0.4722

0.4708

0.3090

0.9082

0.3120

0.3166

0.9158

0.3126

0.9103

0.3103

0,3114

0,3125

0,9135

' : • • -

qiíqO

0,068

0,262

0.455

_ 0.643

0.841

1034

1227

1.421

1.614

1807

2.000

Pr.g

(in H201

0.4310

0.4713

0,4610

0,4158

0,3608

0.2383

0.2335

0.3625

0.4213

0.4608

0.4733

0.9328

0.9186

0.9036

0.8636

0.8109

0.6761

0.6743

0.7369

0.3595

0,9107

0,9252

F

a

6,33

26,12

45,41

64 70

34,00

103.23

122.53

141.8S

16117

180.46

133.76

Q (5CFM)

0.001

20.593

36.073

71743

103.108

148.407

143.260

102216

63.324

36.059

15.871

0.000

17,526

34,772

75,510

102.132

143.338

150.467

110.560

74.338

33.342

19,735

'redicted R-

b

-13,33

-53,23

-92,65

• 132 02

-171,33

-210,74

-250,11

-233,47

-328,84

-363,20

-407,56

i 1

r _t r "!

Data With Corrected qO and Unit Conuei ion

qO=dPc

[Pal

122.94

123.48

123,47

123,00

122.99

12249

122.35

123.36

123.09

123 43

123.11

237.71

237.43

233.49

239.71

239.43

233.65

233 13

238.17

238 34

233.63

238.89

mCoefdcie

Pr.g

(Pa)

113.44

117.19

114.49

103 27

83.59

59 34

53.24

90.03 10477

114.44

117.53

231 66

223.13

225.83

214.47

201,38

l'67'e6 '

167.58

' 135 42

213,44

226,16

223.76

nt

c aipha

710 1.000

26.78

46.46

0,837

0.368

66.15 0 834

35 33 .SS3

105.51 0.382

125.13 0.331

144.87 0.330

164.56 0.380

184 24 .S79

203.92 0.873

Q

Ms)

2.042E-08

4.205E- 4

7.3e6E- 4

1465E-03

2.105E-03

3 030E- 3

3.047E-03

2 0S7E-03

1335E-03

7.362E-04

3.240E-04

0 OOOE.OO

3 57SE-04

7.099E-04

1542E-03

'2.036E-03

3.062E-03

3 072E- 3

2 257E-03

152SE-03 6.8 7E-04

4.033E-04

Cp.i

0.823

0.544

0.246

•0.053 '

-0 351

•0.650

•0.943

-1.248 -1.546

-1845

-2.144

Data Reduction Reîults

qi ÍPa)

.OO

0.636

2.135

3.447

' 17.445

36.141

36 557

17.144

7 660

2.134

0.413

0 000

0.504

1.334

3.356

17.133

36.913

37.151

20.05S

3.130

1.324

0.642

qi(qO

0.0000

0.0066

0,0173

0,0687

01418

0.2350

0.2376

0.1390

0.0622

0.0173_

0/^034"'

0 0000

0.0021

0.0033

0.0330

0.0715"

0.1547

0.1560

0.0842

0 0386

0.0076

0.0027

--

c _,-J . -_ -

1

Cp,i

1.0

09

0,3

0.3

0.7

0 5

0,5

0,7

0 9

0.3 _ _ - , ; g - ~ -

1.0

1.0

0.3

0.3

0.8

0.7

0.8

0.9

0.9

1.0

:z£ |__ í

„_!_„ , „ , . .

, . ! J 1

77

Table C,4: Tabular Data- Multiple Openings - 19,05 (C^= 1.0) and 7.14 (20 deg. Offset)

Tímb = l 71 Pamb =' 30,04

tho amb = 1.202

.jJMirreotion = , 1.053

inHg

kgi'm'S

.-î enínq 1

0.76 in

Al: k..' 1 =

J.AJJAríA1]-2j

0,01905 m

2,850E-04 m'2

1,5473 0,967

2.01

(20 deg sepj

Qpeninq

d2 =

A2 =

kA2 =

j : p 2 j

kA2'(ArW2] '2 =

0,281 in

0 0071374 m

4. 01E-05 m-2

2.0724

0.5314

136,771

294,_8

Î 7269" Pa

Raw Data

dPc

(in H20)

0,4744

0.4735

0.4761

0,4733

04763

0,4741

0,4713

0,4736

0,4760

0.4744

0.4755

0 9133

0.9173

0,3164

0,3138

0,9123

0,9204

0,9142

0,9137

0.9155

0,3153

0.9132

0.4543

0.4552

0.4534

0.4661

0.4556

0.4559

0.4560

0,4538

0,4568

0.4576

0.4555

0.8364

0.3336

0.8962

0 8977

0.8977

P'-9 (inH201

0.4356

0,4743

0,4567

0.4100

0.3431

0.1311

0,1883

0,3483

0.4151

0.4611

0,4733

0.3463

0.9356

0.3185

0,8611

0.7691

0,6337

0,6239

0.7796

0.8615

0.9136

0.9332

Q (SCFMl

0.3146

0.0380

-0,6810

-1,7647

-1.1364

-1,2434

-0.5053

-0.2906

-0.1455

0.0168

0.1323

0.6537

0.5705

0.4032

0 0526

-0,7354

0.000

13.459

43.372

73.413

102.762

143.010

148,479

101,493

71,197

38,135

13,373

0,002

14,740

33,153

70,871

103609

151,032

150966

107.823

71157

33,283

13,930

0,000

13.454

34.508

52,037

42.668

44.523

30.563

25.213

21.233

16.132

11.432

0.000

5.44S

12,368

22,847

33,722

Dati Vi'ith Corrected qO and Unit Conyersions

qO=dPc

(Pal

124,07

123,32

124,60

123,39

124,70

123 97

123,39

123,35

124,47

124,06

124,35

240 53

239,88

239,33

233,36

238,72

240,70

233,06 240,24 233,33 _ 239,43'

233 81

Pr,g

(Pa)

113,80

113,04

118 67

113 26

11,9,14

119,22

11923

119 97

119,47

119,67

119,12

234,42 235,26 234,37 234,75 234,74

120,57

117 95

113 41

101,82

35 20

47,46

46,90

86,50

103,09

114,50

113,78

235,15

232,35

223,11

213 85

191,00

157,37

156 17

133,62

2Í3!35

226,89

231.74

73,12

21,85

-169,12

-435,77

-232^22

-303,80

J25,50

' -72.'16'

-36.13

,_4.J8

'~33.0'Ô"

162.35

141.63

101.63

13.07

-195 06

Q

0 OOOE.O

3,973E- 4

8,365E-04

1433E-03

2.Û38E-03

3 022E-03

3.031E- 3

2.072E-03

1.454E-03

7.736E-04

3.751E-n4 "

4 33E-03

Í.003E-04

6.769E-04

1,447E-03

2,23SE- 3

3,0S4E-03

3,032E-03

2,201E- 3

1453E-03_

"^SeE- i 2.344E-04

0.000E*00

2.747E-04

7 045E-04

1064E-03

S.711E-04

9.091E-04

e.240E-04

5.14SE-04

4.343E- 4

3.3 6E-04

Data Reduction Re ults

qi (Pa)

0.000

0.808

4.014

11.502

22,534

46 743

47.045

21983

10.817

3,103'

qiíqO

0,720

2,334E-04

O.OOOE.OO

1.112E-04

2.525E-04

4 665E- 4

8.110E- 4

0.000

0.464

2.345

10718

25 637

48.676

46.633

24.311

10.805

""ri28

0.0000

0 0066

0.0322

0.0328

0.1807

0.3771

0.3813

0.1775

0. S63

0,0260

Cp,i

0,0058

0,414

0.000

13.602

128.955

233.317

197.153

214.717

101.166

63.341

43127

28.333

14.153

0.000

3,214

16,565

56 527

170.863

0,0000

0,0013

0,0033

0,0443

0,1074

0,2022

0,2034

0,1033

0.0451

0,0131

0,0017

10 1,0

0,3

" 0 , 3 '

0 7

0 4

04

0,7

0,3

0,3

0,0000

0,1647

1,0876'

2,4645 16548" 1,8010

0,8434

0,5733 0,4112

0,2373

0,1188

0,0000

0,0137'

0,0707

0 2408

0 7273

JJ5_ " i'o

10

1,0

0,3

0,8

0 7 "

0,8

03

1,0 0,7

0,2

-0,6

-03

0.0

0.3 "

0.7

0,6

'0,4

0.1

-08

78

Table C.4: Tabular Data - Multiple Openings - 19.05 {Cp= 1.0) and 7.14 (20 deg. Offset) continued

Tâmb =

Pamb =

rhoamb =

qcorrection =

_ Combir

,Ai =

[gríqOJmin =

dia, (m)

dia. [inl

—-

-

71 IF 1 294,8! K 30.04 linHg [ 1ÔÍ726.9P3

1.202 k'3Ím-3 i

1.053

ed Openlnqi:

3 250E-04 m'2

0 1366619

2.034E-02

8009E-01

j j

i

1 1 i

Raw Data

dPc

(in H20)

0.4707

0,4726

0,4678

0.4671

0.4633

0.4653

0,4693

0,4633

0.4654

0.4670

0,4703

0.9164

0.9064

0,3433

0.3032

0.9083

0.9118

0.9124

0.9056

0.9101

0.9053

0.9077

Pr.g

(in H20)

0.4743

0.4660

0.4413

0,4042

0,3288

0,1336

0,1377

0,3274

0.3849

0.4446

0.4664

0.9285

0.9034

0.9283

0.8277

0 7527

0,6320

0,6329

0,7711

0.8551

0.3327

0,9103

qiíqO

0.137

0.368

0,543 0,731

0.312

1033

1,275

1,456

1637

1,313

2000

P

a

25,15

49,53

74,03

98,46

122,30

147.33

171.77

136,21

220.64

245.03

263,51

Q (SCFM)

0.000

16.473

37.503

64,688

107,272

147,310

147,440

105,776

77.070

33,701

12,522

0.000

18.734

33,322

73,664

108 437

143.809

149.645

99.779

58.423

35,917

13,452

redicted Ra

5

-6106

-looee -150,26

•199,86

-249,47

-299,07

-343,67

-393,27

-447,87

-497,48

-547,03

Dâta With Corrected qO and Unit Conveisions

q =dPc

ÍPa)

123,08

123 53

122,34

122.16

122.72

121.34

122.38

122.72

121.69

122.13

122.99

233.65

237.03

248.24

237.49

237.51 "

233.45

238.53

236.81

238.00

236.73

237.38

Pr.g

(Pa)

117.92

115.72

109.61

100.37

31.65

43.09

43.09

3131

95.60

110.41'

116.82

230.60

224.35

230.53

205.56

186.34

156.96

157.18

19143

21237

219,22

226,06

m Coefficient

c alpha

25.31

50.71

1000

0,928

75.51 0.315

100.31 0.3 S

125.11

149.91

0,905

0,303

174.71 0.301

133.51 0.900

224.31 .S99

243.11 0.898

273.91 0.333

Q

0, 0nE.00

3,3e3E- 4

7,668E-04

1,32'lE-03'

2,130E-03

3,Û20E-03

3. 10E-03

2.160E-03

1.574E-03

e.S81E-04

2.557E-04

O. O E- O

3.S35E-04

6.326E-04

1.604E- 3

2.215E-03

3. 63E-03

3.065E-03

2 037E-03

1193E-03

7.333E- 4

2.746E-04

j

Data

ÍPa)

0.000

0.445

2.309

6.866

1S.332

35.833

35.671

13.353

3.747

1864

0.257

0.000

0.573

1.S88

8.304

13.312

36.326

36.746

16.337

5.601

2.117

0.237

1 -

Cp,i

0.-531

o!323

_ 0,043 _

-0.536

-0.826

-1.115

-l'405

-1.635

-1.985

-2.276

1

t, ., . i !

1 ^eduction Result

qi(q

0.0000

0 0036

0.0189

0.0562

0.1539

02346

O2303

0,1496

0.0301

0.0153

0. 021

0.0000

0.0024

0.0076

0.0375

0.0S13

0,1544'

0,1540

0.0630

0.0235

0.0039

0.0013

Cp,i

1,0

0,9

0 3

0,3

0,7

0,4

0.4

0,7

0 3

0,3

Í9

1,0

0,9

0,3

0,9

0.3

0.7

0.7

0 8

0,3

0.9

1.0

..... -

79

Table C.5: Tabular Data - Multiple Openings - 8.73 (C,= 1.0) and 19.05 (10 deg. Offset)

Tamb = í 73 JF 1 295,9

q^correction =

0

1 1,063

(10 deg sep]

leninql

dl= 1 0.75

A1 =

l(..A1 =

..--... Cpl = KA1XAríAJ)"2 =

0.01905

in

m

2.860E-04 m-2

2,5548

0,9674

3,74

; (Upstream)

Opening 2

d2 =

A2 =

kA2 =

Cp2 =

kA2'(Arí A2]-2 =

0,3438 |in

0.0087325 m

5.389E-05 rTí-2

16369

1,0102 54.29

IUÍ:IÍUI',L>

j Pa

[

1 i

dPc

i;in H201

0.4543

0.4511

0.4556

0.4515

0.4574

0.4530

0.4543

0.4572

0.4551

0.4529

0.4552

0.3326

0.3902

0.8313

0.8370

0.3327

0.8346

0.8343

0.8324

0.8342

0.8830

0.8942

0.4741

0.4726

0.4727

0.4759

0.4713

0,4722

0,4701

0.4695

0.4722

0.4745

0.4735

0.9139

0,8157

0,9171

0.3151

0.9079

Rai,v' Data

Pr.g

(In H20)

0.4730

0.4593

0.4522

0,4229

0.3577

0.2401

0.0035

0.1337

0.3081

0.3334

0.4424

0.9234

0.3970

0.8694

0.7336

0.6556

0.3943

0.5787

0.7355

0.8040

0.8472

0.8325

0.4996

0,4861

0.4200

0.2211

0.0250

-0.3330

-0.6635

-1.0630

-1,3223

-0.8461

0.4506

0.3655

0.9294

0.8331

0.6600

0.3253

Q (SCFM)

0.000

16.990

26.372

42634

70.646

102.049

145.940

123.260

36.901

60.216

33.424

0.000

13312

37.437

70.127

104.183

147.738

120 31

86.231

66.158

47.333

26.353

0.000

5.334

16262

30.584

33.410

52.566

53,432

67,278

71,747

63,034

13,070

0002

10,142

21187

31946

45,377

! 1

Data Vlth Corrected qO and UnitCon'jersions

q =dPc

(Pa)

113.30

117.37

113.13

113.08

119.62

118 48

113 94

119.66

119 02

118.44

119 03

233.43

232.73

233.23

234.53

233.44

233.35

234.02

233 33

233.34

232.46

233 33

123.93

123.53

123.62

124.46

123 25

123.47

122.94

12277

123 47

124 03

123.S1

240.31

233.47

233^84

239.30

237.42

Pr.g

[Pí:]

118.70

114.06

112.30

105.03

88.83

53,63

2.35

33.20

76 51

95 21

109.83

223 32

222.75

215.31

137.08

162.81

97 31

143 72

182.66

133,67

210,40 22164

124.04

120.71

104.31

54.31

6.22

-35.10

-166.27

-265.24

-.328.53

-203.38

111,90

233.73

230.81

206.83

163.30

80.92

Q

(hq/s)

O.OOOE-00

3.4e9E-04

5 4S6E-04

8.717E- 4

1442E-03

2 0S4E-03

2.3S E-03

2.617E- 3

1774E- 3

1.223E-03

6.S24E-04

.OOOE.OO

4.045E-04

7.643E-04

1.432E-03

2127E-03

3. 1SE- 3

2.452E-03

1.761E-03

1.361E-03

3 f:75E-n4

6.380E- 4

0.000E»00 1212E-04 3 320E-04 6.244E- 4

3.046E-04

1.073E-03

1,213E-03

1,374E-03

1465E-03

1.237E-03

2668E- 4

4.083E-08

2.071E-04

4,326E- 4

e.622E-04

3.264E-04

Data

qi ÍPa)

0.000

0.613

1.633

3.871

10.533

22116

45.229

32.264

16.037

7.700

2.372

0.000

0.834

2.976

10.443

23.052

46.333

30 626

16.731

9.295

4.763

1475

0.000

1.694 12.713

44 386

74 637

132.391

169.876

217.690

247,671

191092

8,216

0.000

4.347

21.639

743.032 ' 93.023

T'"- • --

Heduct ion Resu l t s

qí/q

O. OO

0.0062

0.0123

0.0328

.osse 0.1867

0.3303

0.2633

0 1347

0 0660

0.0199

0.0000

0.0036

0.0128

0.0445

0.0338

0.1983

0.1303

0.0677

0.0337

0.0205

0.0063

0.0000

0.0137

0.1023

0.3615

0.6060

1.0763

1.3318'

17732

2.0050

1.5400

00664

0.0000

0.0207

0.0900

0.2051

0.4171

Cp,i

1.0

1.0

09

0.9

0 7

0.5

0.0

0,3

0.8

0.9

1.0

1.0

0.9

'ã's " 0.7

0.4

0.6

0.8

0.9

0,9

09

1.0

10

0.8

0.4

0.1

; .8

0.3

1.0

1.0

0.3

0.7

03

80

Table C.5: Tabular Data - Multiple Openings - 8.73 {Cp= 1.0) and 19.05 (10 deg. Offset) continued

1 amD 3 ; rs 11-Pamh = 1 30.3 1 inlHq

rho amb = 1.208 ' kg(m'3

qcorrection =

Combir

Ar =

(qríqOJmin =

dia. (m)

dia. (in)

1.053

i (10 deg sep)l

ed Openings

3.443E-04

-0.0114388

1 2.6'96E'-02

m-2

3250E-01

235.9 102607.3

dPc

[in H20)

0,4707

0,4726

0.4678

0.4671

0.4633

0.4659

0,4699

0,4693

0,4654

0,4670

0,4703

0.9164

0.9064

0,9433

0.3032

0.3083

0.3118

0.9124

0.9056

0.3101

0.3053

0.9077

K

Pa

Raw Data

Pr.g

(in H20)

0,4743

0.4660

0.4413

0.4042

0.3238

0.1336

0,1377

0.3274

0.3343

0.4446

0,4664

0.9235

0.3034

0.3283

0.3277

0 7527

0.6320

0.6323

0.7711

0.3551

0.8827

0.9103

qiíqO

-0.011

0.130

0,331

0.592

0.793

0,994

1,195

1397

1,593

'Í733

2.000

P

a

-0.58

3.59

19.76

29.92

40.03

50.26

60 43

70 59

30 76

90 93

10109

Q (SCFM)

0.000

16.473

37.509

64.683

107.272

147.910

147.440

105.776

77.070

33.701

12.622

0.000

13.734

33.822

73.664

103.437

143.809

143,645

93,773

58,423

35,917

13,452

Data V'ith Corrected qO and Unit Con^jersions

qO=dPc

(Pa)

123.08

125 59

122.34

122.16

122.72

121.84

122.38

12272

121.63

122.13

122.99

239.66

237.03

248.24

237.49

237.51

233.45

233.53

236.81

238.00

236.73

237.38

Pr.g

[P<y\

117.92

116.72

109,61

100^37

3165

48 03

43.03

31.31

95.60

110.41

Í16.82

230.60

224.35

230.53

205.56

13694

156.36

157.18

131,48 21237

21322

226.06

redicted Ra

h

1.24

-20.60

-42,44 1

•64,28 '

-86,12

-107.36

-129.80

-15164

-173.47

-135.31

-217 15

Ti Coefíicient

c alpha

-0.66 1.143

10.26 0.734

21.18 0.783

32.10 0 790

43 02

53.'94 ,

0.730

0.731

64,86 0,791

75.77 0.791

36.63 0 791

97.61 0.731

108.53 : 0.791

Q

(kgi's) O.O OE.OO

3,3e3E-04

7 653E04

132tE-03

2.130E-03

3.020E-03

3.01 E- 3

2.160E-03

1.674E-03

e.881E- 4

2.567E-04

OOOOE-00

3.S35E- 4

e.326E- 4

1.604E-03

2 2t5E-03

3.069E-03

3 055E- 3

2. 37E-03

1.193E-03

7.333E-04

2.746E-04

Cp,l

1024

0,531

0,059

-0,413

-0.385

-1.357

-1830

•2 302

-2.774 •3.246

•3.713

Data Reduction Results

(Pa)

0.000

0,394

2 040

6.063

16.637

31725

31.624

16.225

8.613

1647

0.227 '

0.000

0.512

1.669

7.863

17.067

32 545

32.474

14.437

4.350

1.871

0,262

" •• 1

1

qi/q

0.0000

0 0032

0 0167

0.0497

0.1360

0.2604

0.2565

0.1322

0.0703

0.0135

0.0018

0.0000

0.0022

0.0067

0.0331

0.0719

0.1365

0.1361

0.0610

0.0203

0.0079

0,0011

i

EZ 1 ' i

Cp,i

10

03

0 9

0.3

0.7

0.4

0.4

0.7

o.s 09

09

10

09

0.3

0.3

0.3

0,7

0,7

0.8

03

0,9

1.0

^

;

_, i i

81

Table C.6: Tabular Data - Multiple Openings - 8.73 {Cp= 1.0) and 19.05 (20 deg. Offset)

_ _Tâmb_=

Pâmbs rho âmb =

73

29 99

1196 '

q ootreotion = 1053

— ---

' (Upslream)

O p e n i n q l

d l =

Al = k,' 1 =

„C,pl„=_ kAr(Arí A r 2 =

£,.... 1 295.9

inHg : 101557.5

kg im"3

0,3438 | i n

0 ,0037325 m

5 333E-05

1,5676

1.0071

51.99

(20 deq sep

m'2

i Openinq2

d2 = 0,75 | i n

0,01906 m

A2= 2,S50E-04 m-2

k,A2 =

C p 2 =

20.015

0,7227

1

{

1

i

K

Pa

Rau' Data

dPc

(in H20)

0,4571

0.4603

0.4558

0.4575

0.4579

0.4605

0.4531

0.4576

0.4613

0.4532

0,4615

0.9003

0.9010

0.9062

0.9029

0.9035

0.3041

0.9031

0.8971

0.8973

0.8904

0.8907

0.4532

0.4464

0.4486

0.4513

0,4498

0,4460

0,4492

0,4432

0,4472

0.4482

0.4446

0.3820

0,8785

0,3751

0,8826

n fiftnn

Pr.g

(in H20)

0.4841

0.4791

0.4074

0,2926

0.1061

-0.2184

-0.4730

-0.3537

-1.3603

-1.0363

-0,7310

0,9430

0.9233

0.3322

0.7402

0.5632

0.3149

-0.1702

-0.5229

-1.1333

•1.7432

-1,9266

0,3733

0.3133

0.2036

-0.0271

-0.3250

-0.6317

-0.8077

-10335

-1.2731

-1.3645

-1,4364

0.7262

0.6042

0,3743

0,0459

.n djp.ri

Q (SCFM)

0,000

4.700

16.055

25,560

35,962

43,366

55,841

64,236

76,316

63.121

61,831

0.001

6.001

14,340

26,295

36,346

46,295

60,620

68,272

81,523

90,745

93,691

0,000

18,382

30.176

50.212

68.310

36.584

95,637

111,745

123.105

128,527

133285

0,003

20,734

37,242

52,154

70 459

' Data With Corrected qO and

Unit Convetsions

.qO=.JPc

iPa)

113 54

120.37

11313

113.63

113.75

120.41

113.30

119.66

120.78

119.83

120.63

235.44

235.61

236,36

236,12

236,26

236.43

236.13

234.60

234.64

232.34

232.32

118.51

116.73

117.31

118.02

117 62

116 63

117.47

117 20

116.95

117 21

116.27

230.64

229.74

228.84

230.81

23012

Pr.q (Pa)

120.23

113.33

101.18

72.67_

26.34 '

-54 24

-117.47

-212.00

-337.34

-257.35

-181.63

234.17

230.55

213.03

133 33

133.36

78.20

-42.26

-123 85

-231.56

-432.31

-473.46

92.33

73.43

^ '50.5'7

-6.73

-80.72 -156.37

-200.53

•271.56

-316.15

-333.35

-356.72

130,36

150.06

92.96

1140

-105 79

Q (Kqís)

O.OOOE.OO

9.53eE- 5

3.278E- 4

5.213E-04

7.342E-04

3 375E-04

1.14 E-03

1311E-03

155SE- 3

139tE-03

12e4E-03

2 042E-08

1.225E-04

3. 30E-04

5.3e3E- 4

7.421E-04 9.452E-04

1.233E- 3

1.394E-03

1.6e4E-03

1.853E-03

1.913E- 3

O.OOOE.OO

3.875E-04

6 t6tE-04

t. 25E-03

1.395E- 3

1.768E-03

1.354E-03

2.2S1E- 3

2513E-03

2.624E-03 2.S23E-03

1.833E-07

4233E-04

7.604E:04

1.065E- 3

l Data Reduction Results

qi (PaJ

0.000

1073

12.525

^ ' • ^ . . .

62.841

113.668

151.513

200.500

283.002

226 486

186.123

0.000

1.750

10.701

33.537

64.131

104.142

178.563

226.437

322.933

400.132

426.534

0.000

0.773

1,954

5,403

10.012

16.035

13.644

26.791

32516

35.443

41.029

0.000

0.322

2.976

5.336

10.651

qi(qO

0.0000

0.0033

0.1061

0.2654

0.5243

0.9440

12647

1.6756

2,3431

13817

15423

0 0000

0.0074

0.0462

0.1423

0.2717

0 4405

0.7561

0.3664

13763

17186

13313

0.0000

0,0066

0.0167

0,0458

0,0351

04373

0,1672

0.2236

0.27S0

0.3024_

0.3529"

O.O O

0.0040

0,0130

0.0263

Cp.i

1.0

1,0

0 3

0.6

0 2

-0.5

-1.0

1.0

10

0.9

0.6

06 0 3

-0,2

-0.6

03

0.7

0.4

-0.1

-0,7

0,8

0.7

0.4 O

-U.3 _

82

Table C.6: Tabular Data - Multiple Openings - 8.73 {Cp = 1.0) and 19.05 (20 deg. Offset) continued

_ ,_ . Tâmb = [ 73 JF 1 295,9|K | ! ! Pamh =

rhoamb =

q^cotrection =

29 99 inHg ' 101557.5''Pa

1196 kgiim-S 1053

(Upstream)

Combined Openings

Ar = ! 3.449E-Ô4

(qríqOjmin = 0.0054703 m'2

_ dia. (m) 2.096E-02

dia. [in) S,25 E-01

!

1 t

!

!

i

j

!

i

Raw Data

dPc

(in H201

0,4456

0,4450

0,4473

0,4446

0,4475

0,4483

0,4511

0,4444

04450

0,4487

0,4457

0,3880

0,8860

0,3851

0,8856

0,3765

0,8845

0,8800

0,8733

0,8788

0,3802

0,8802

Fr,3

(in H20)

0,3333

0,3614

0,2301

0.1263

-0,2722

-0,4282

-0,6544

-0,8810

-0,7797

-0,5406

-0,3592

0.7651

0.7136

0.6768

0.4613

-0,1505

-0,7032

-03917

-0,8622

-0.6732

-0.1588

0.0551

qi qO

0,005

0.205

0,404

0.604

0,303

1,003

1.202

1,402

1601

1801

2,000

Q (SCFM)

0.000

21.208

44.537

61.756

86.121

104.017

123.611

142162

133.358

114.586

35.330

0.002

23.210

40.283

63.450

92.316

116.663

143.307

131.062

114.309

93.163

36.397

T •

i Dâta Vith Corrected qO and

Unit Conwersions

qO=dPc

(Pa)

116.53

116.37

116.97

116.27

117 02

117 39

117.95

116.21

116.38

117.35

116.54

231.70

23147

23159

229.21

231.30

230.13

229.82

229.S1_

230J3^r 230.16"""

Pr.3

(Pa)

33.17

83.75

72,04

31,37

-67 53

-106.34

-162.51

-218.79

-193.63

-134.25

-S9.13

190.00

173 72

168.07

114.71

-37.37

-174.63

-246.23

•2Í4.12

-167.13

'"-'33'45

13,63

î

Q (kgi's)

0 OOOE.OO

4,330E-04

9,105E.04

1,261E- 3

1753E-03

2,124E-03

2,524E- 3

2,902E-03

2,723E-03

2,333E-03

1,ã46E-n3

4 OS3E-08

4,739E-04

S.224E-04

1.39SE- 3

1.897E-03

2.360E-03

2.926E- 3

2.676E-03

2344E-03

1.302E- 3

1.764E- 3

Dafa

(Pa)

0 000

0.653

2.314

5.588

10.867

15.852

22337

23.610

26.056

13.237

13.315

0.000

0.7S9

2.377

6.365

12.643

13.568

30.033

25. 67

' 13,312 '

12,716

10.336

Predicted Ram Coeííicient

a

-0.12

-4.65

" "-9.17""'

Ji§5_, •18.22

-22.74

-27,27

-3179

-36.31

"-40.84

-45.36

b

•0.32

-12.01

" -23,70

-35,40

-47.09

-58,73

-70,47

-32,17

-93,86

-105.55

-117.24

c alpha

0.44 1000

6.23 0447

12.14 0.438

17.38 i 0.435

23,83 ; 0,433

29.67 • 0.432

35.52 \ 0.432

41.37 : 0.431

47,21 ! 53.06

53.30

0,431

0 431

0,431

Cp.i

0.723

-1.117

-3.023

-4.930

-6,837

-8.743

-10,650

-12,557

-^•*64 -16,372 -18,273

Reduction Results

qííqO

0.0000

0.0057

0.0249

0.0481

0.0323

0.1350

0.1893

0.2548

0.2239

01639

0.1142

0.0000

0 0034

0.0103

0.0296

0.0552

0.0846

0.1307

0.1095

0. S40

0.0552

0.0475

Cp.i

0.9

0.8

0.6

0.3

-0.6

-0.3

-0.3 0.3

0 8

0.7

0.5

-0.2

-03

-0.9

-07

-0.2

0,1

" :

l 1

1 1

83

Table C.7: Tabular Data - Muitipie Openings - 8,73 (C^= 1.0) and 7.14 (10 deg. Offset)

„ .Ti!í ),'> = 73

Pamb = 30 3

F

inHq rhoâmb= 1,203 k,gím~3

qcorrection= 1,053

,

.,. ,. j. !

Openinq 1

d l = | 0,3433 lin

A l =

kAl =

cpi =

0.0037325 m

5.9S9E-n5 m-2

1,6369

1.0102 k.Ar(AríA1)~2 = 4,55

i

-

i 1 i

(lOdegsep)^

Opening 2

d 2 = | 0,281 !in

00071374 m

A2= 4.0 1E-05 ^ " 2

kA2 =

. -.^CP2.=-

1,8821

0.3163

kA2'(AríA2)-2 = : 1173;

! i

— 'i "

i \

i ;

1 :

295.3 102607.3

dPc

(in H20)

0.4741

0.4726

0.4727

0.4763

0.4713

0.4722

0.4701

0,4635

0,4722

0,4745

0,4735

0.3133

0,3157

0,3171

0,9151

0,3079

0 3116

03121

0.3140

0.3033

0.3179

0.9112

0.4610

0.4614

0.4640

0.4647

0.4670

0.4613

0.4634

0.4611

0.4613

0.4669

0.4614

0.9105

0.3133

0.3083

0.3133

n 915?

• ! <

Pa

Raw Data

Pr.g

(in H20)

0.4996

0.4361

0.4200

0,2211

0,0260

-0,3830

-0,6636

•1,0680

-13229

-08451

0,4506

0,3655

0,3294

0,8331

0,6600

0,3258

0.1195

-0.2291

-10431

-1.5441

-2.2009

•2,2350

0,4632

0,4023

0,2131

•0,0370

-0 6223

-14622

-1,0463

•0.6235

-0.3174

0,0452

0,2455

0,3170

0,3666

0,6322

0.2977

-fi-2'7«!-

0

(SCFM)

0.000

5,934

16.262

30,534

33.410

52.566

53.432

67,278

71747

63,034

13.070

0.002

10.142

21,187

31.346

45.377

52.054

60.838

73.767

86,335

34,853

96179

0.000

7.039

16,607

25,722

37.024

43,306

43,660

36.925

30.834

21334

15.262

0.000

5.288

16398

25.932

37,65»

!

Data With Correoted qO and Unit Con'versions

q =dPc

(Pa)

123.93

123.53

123.62

124.46

123.25

123.47

122.94

122.77

123.47

124.08

123.81

240.31

239.47

239.84

233.30

237.42

23S.,33

239,01

237,73

240.04

238.29

120.56

120.66

121.35

121.52

122.13

120.64

121.17

120.57

120.63

122.08

120,65

233,11

233,35

237,52

240.15

239 34

Pt'J (Pa)

124.04

120,71

104,31

54.31

6.22

-95 tO

-166.27

-26524

-328.53

-209.88

111.90

239.78

230.S1

206,33

163,30

80.32 " 29.67

-56.33

-259.04

-383.47

-546.57

-569.34

116.23

100.03

52.31

-24.09

-154.66

'-36343

-259.83

-154,85

-78^32

1123

60,96

227,72

216,22

157.00

73 94

-63.53

Q

(l<.q/s)

O.OO E.OO

1.212E-04

3.320E- 4

e.244E-04

S.IJ46E-04

1. 73E- 3

1.2t3E-03

1.374E-03

1.465E-Û3

1.2S7E-03

2 668E-04

4 S3E- 8

2.071E-04

4.32eE-04

e.522E-04

9.2e4E-04

1063E-03

1.242E-03

1.608E-03

1.7e3E-n3

).937E- 3

1.9e4E-03

O.OO E.OO

t.437E-04

3.331E-04

5.252E- 4

7,659E- 4

1.0 7E-03

8.3t4E- 4

7.533E-04

6.295E-04

4.4e8E-04

3.116E-04

O.OOOE.OO

1030E-04

3.34SE-04

5.234E- 4

7.689E- 4

1 i

( •

Data Reduction Results

qi

(Pa)

0.000

1.694

12.713

44.986

74 637

132.831

163.376

217.680

247 571

191.032

S.216

. O

4.947

21.539

49.032

33.023

130.317

178.003

298.338

353.431

432.753

444.89Ô '

0.000

5,340

23,722 71,302

147,726

261333

205.427

146.337

102.461

51,611

25,102

0,000

3,014

28,977

72.471

152.323

qiiiqO

aoooo 0.0137

0.1023

0.3615

0.6060

10763

1.3818

1.7732

2.0050

1.5400

. 664

0.0000

0.0207

0.0900

0.2051

04171

0.5467

0.7463

1.2484

1.5076

1.3023

0,0000

0,0443

0,24't3'

0.5367

1.2095

2.1717

16953

1.21S7

0.8434

0.4228

0.2081

0.0000

0.0126

0.1220

0.3013

06385

Cpj

1.0

1.0

o.s 0.4

o.t

-0.8

0.3

10

1.0

0.3

07

0.3

01

-0.2

10

_ 0.8

0.4

-0.2

-0.7

01

0.5

1.0

0.3

0.7

0 3'

-03

84

TabIeC.7: Tabular Data-Multiple Openings-8.73 (C^= I.O) and 7.14 (10 deg. Offset) co«/(«weí/

, _ _ _ Tambs

Pâmh =

rho amb = qcorrection =

73 !F

30,3 • inÍHg

1,203 kgím~3

„ .

Combir

Ar =

_(grígO)min =

ed Openings

9.99 E-05 m'2

^ 0.0206173/

295,9

102607,3

dPc

(in H201

0,4419

0,4435

0,4450

0,4472

0.4452

0,4464

0,4443

0,4466

0,4437

0,4460

0,4477

0,3774

0,8736

0,3731

0.8820

0,8763

0,3784

0,8736

0,8810

0.8730

0,8796

0,8813

1 1 Pâ ' i

!

Raw Data

Pr.g

(In H20)

0.4738

0.4420

0.3632

0.2653

0.0250

-0.3306

-0.5337

-0.9305

-1.1570

-1.4074

-1.9716

0.9306

03737

0,7774

0,5831

0,2635

0,0146

-02747

-0,4501

-0,7600

-1,0735

-1,5640

Q

(SCFM)

0.007

16.124

23.271

41526

60.111

84.525

32.921

106.023

113.350

121431

137,901

0.000

16.717

32.381

51.095

71.238

86.301

97.796

104.260

115.733

125.341

133,603

Data Vith Corrected qO and Unit Con'jersions

q =dPo

ÍPa)

115 66

117 23

116.37

116.94

11642

116 74

116.13

116.78

116 03

116 64

117.06

223 45

230.03

229.90

230.64

229.30

229.70

230.03

230.37

223 37

230.02

230.62

, F redictedRa m Coel^ficie

Pr ' ; (Pa)

118.90

103.77

90.20

66.02"

e.22

•37.01

-147.44

-231.07

-237.33

-343 52

-483.62

231 09

218.22

193.06

Î46.30

66.68

3 64

-63.22

-111.77

-138.73

-267.S4

-388.41

-it

i 1 f qlíqO

0.021

0.213

0.416

0.614

0.812

1,010

1.208

1.406

1604

1802

2.000

a

0.16

1,57

2.99

4,41

5.83

7.25

8.67

10.10

11,52 _ ,

1234

14,36

h

-0,43

-5,13

-9,77

-14,42

-19,06

-23,71 ^

-28.36

-33,00 j

-37,65 -42,23

-46,94

0 ; alpha

0.34 1000

2,66 í 0,646

4 33 ' 0 632

7 30 '

9 63

1195

14,27

16,59

18,32

0 627

o :4 U623

0.621

0.621

0.620

21,24 "• 0,620

23.56 l 0.613

0

(kgís)

1.361E-07

3.232E- 4

5 376E-04

S.478E-04

1.227E-03

t726E-03

1.397E-03

2.165E-03

2.314E-03

2.479E-03

2.815E-03

OOO E.OO

3.413E-04

6,611E- 4

l,043E-03

l,4.54E-03

r762E- 3

l,997E-03

2,129E- 3 2.3e3E-03

2.569E-03

2360E-03

1

Data Reduction Results

(Pa)

0,000

4.434

14.310

29,807

62.458

123 435

143.243

194.321

222.037

254.882

323,712 0 000

4.330

13.124

45.127

S7.721

128.740

165.313

187.335

231.547

273.732

336.905

qiíqO

0,0000

0,0333

0.1273

0.2543

0.5365

10573

1.2345

16640

1.9140

2.1352

2.3080 0.0000

0 0210

.07S3

0.1957

0.3326

0.5605

0 7187

.S156 10073

1.1900

1.4603

Cp.i

0.916

0.596

0,253

-0.083

-0 431

-0,773

-1,115

-1,457

-1,800 -2142

-2,434

í

L_. í

1 E

1

Cp.i

10

0 3

o.s û.e 01

-0.3

-1.3

-2.0

-2.5

•3.0

-4.2

1.0

0 3

0,8

0,6

0,3

0,0

-0,3

-05

-03

-1,2

•1,7

, , f ; ' 1 s

i '<

1

85

Table C,8: Tabular Data - Multiple Openings - 8,73 (C„= 1.0) and 7.14 (20 deg. Offset)

3 3

iho •amb =

q cotrection =

—~ __—

d1 =

A1 =

kA1 =

C,p1 =

lî,Ar(AriiA1)-2 =

73

29,9

1,192

Í.053

,..-..

F

inHg

kgím'3

1 0.3433! in

_l 0.0087325

5.9S3E-05

1.6592

10305

4.62

m

' "?

l^u aeg sepj Opening 2

d2 =

A2 =

kA2 =

Cp2 =

kA2'(AríA2)"2 =

0.28l! in

0 0071374 m 4.001E-05 m"2

23965

0.6435

14.94i

295,9 K

101252.8 Pa

dPc

(in H20)

0.4426

0.4485

0.4473

0,4463

0,4453

0.4480

0.4468

0,4464

0,4450

0.4441

0.4453

0.3832

0.8837

0.3824

0.8811

0.8833

0.8823

0,8739

0,8803

0,8764

0,87S4

0,8754

0,4494

0,4478

0,4486

0,4439

0.4473

0,4432

0,4474

0.4501

0.4503

0.4515

0,4520

0,3876

0.8344

0,3334

0,8353

08317

Raw Data

Pr.g

(in H20)

0.4736

0.4621

0.4039

0,2967

0.1125

-0.1267

-0,5381

-1.1863

-0.3216

-04495

-O0962

0.3375

0.3233

0,8707

0,7860

0,6234

0.4300

0.1218

-0.2319

-0.7643

-13106

-2.0791

03542

0,2902

0.1632

-o.otes -0,1348

-05775

-0.3663

-1,2323

-15301

-0,3280

-04027

0.7007

0.5332

0.4763

0.2807

0,1048

Q

(SCFM)

0,000

8,412

15,733

24.715

34.537

43.663

55.613

69.383

61.538

53.308

42,784

0,000

6,733

14,332

22,327

31.334

40.805

50,671

60,311

71,993

79,543

92,834

0,000

4,807

10,357

16.833

21223

23.648

36.416

40.692

45.212

35.371

26,220

0.000

5 961

10.661

16.328

mfeifl

Data Vith Cortec Unit Con'^er

'qO=dPc

ÍPa)

116,74

117.27

117.10

116.71

116 44

117.15

116.34

116.74

116,37

116.14

116 62

230.37

232.67

230.75

250.93

230 34

223.33

230.34

223.17

223.72

223 33

117.52

117.03

117 32

117 40

117.11

117.20

117.00

' l Í770

117.91

118.06

118.20

232.11

23127

2-3259

231.52 73319 1

Pr.'J

(Pa)

113.86

114.76

101.80

73!63

27.34

-31.45

-133.64

-294.61

-204.04 -111.62

•23.89

232.32

230.79

216.23

156.31

106.77

30.25

•70.00

-139.80

-325.48

-516.33

87.36

72,08

40,52

-4,18

-45,38

-143,41

;233.93

-306.04

-394.90

-230 45

-100.01

174.02

147,31

118,03

69,72 ?f; r\í.

led qO and 5Íons

Q

(kgí5)

O.OO E.OO

1.717E-04

3.224E-04

5.04eE-04

7 051E-04

8.916E-04

1.135E-03

l,417E-03

1,257E-03 1, S8E- 3

3 735E-04

0, 00E.O0

1375E- 4

3,06.9E-04

4 553E-04

6.532E-04 3.331E-04

1. 35E-03

1.244E-03

1.470E-03

1.624E-03

1.335E-03

. OOE.O

3814E-05

2.2t7E- 4

3 438E- 4

4 333E-04

6.053E-04

7.435E-04

3.3 SE-04

9.231E-04

7.324E-04

5.353E-04

0 OOOE.OO

1.2t7E-04

2177E-04

3 334E-04 i 'AílP.M 1

Data

qi

0,000

3.443

12.156

29,770

53134

32 342

150.733

234.623

134.366

138.500

83,213

o.O

2.203

10,340

24,235

43 883

81.150

125.137

130 324

252.606

303.367

420.028

O.O

2.624

12.873

30.363

49.190

95.937

144.826

180.334

223.233

140523

75,081

0,000

3,831

12412 29,116

ík í'.-r\ 1

-j

Reduction Results

qi/q

0.0000

0.0294

01038

0.2551

0.4993

0.7333

1.290Í

2.0093 1 58S6

1.1326

0.7650 0,0000

0,0095

0,0474

0,1054 0 2160 0 3516

0.5445

0,7850

11023

1,3424

18347

0,0000

0,0216

01097

0.2637

0.4200

0.3131

12373

15364

1.3933

11302

0,6352

0,0000

0,0168

0,0534 0,1253 n ^•5'3i

Cp.i

1.0

1.0

0.9

0.6

0,2

-0 3

-10

-0.2

1,0

1,0

0,3

^ • 3

0,7 115

0,1

-0,3

-0 3

07

0,6

03

0 0

-0,4

-0,3

0.1

0,6

0,5'

'oF_ n 1

86

TableC.8: Tabular Data-Multiple Openings-8.73 (C^= 1.0) and 7,14 (20 deg, Offset) co«//«Meí/

. Tâmb.=i 73 iF 1 295.9 Pâtrib:

iho amb =

q (îoitection =

^ 29,9 inHq < 101252.8 1192 |í.gím"3

1053

- , i í 1

CombinedOpeninqs

At =

(giíqOJmin =

9.990E-05

0.0S253 5

m"2

dPc

(in H201

0.4432

0.4478

0.4498

0.4517

0.4498

0.4513

0.4503

0.4438

0.4479

0.4491 0,4514 0.8346

0,8843

0,8322

0,8351

0.8365

0.8844

0,8346

0,8876

0,3813

0,3334

0.8839

K

Pa

Raw Data

Pr.g

(inH2 t

0.4435

0.4272

0.3381

02693

0.1353

0.0342

-00713

-0.2538

-05155

-06604

-1.4685

08762

0.8032

0.7302

0.6156

0.4255

0.1538

•0.0792

-0.3681

-0.6845

-0.9414

-1.7227

i-J (SCFM)

0,000

5.325

14.526

33.053

40,771

43.246

60.316

70.623

S4.610

90.853

118.602

0.000

12.771

23,709

38,076

53,406

63,318

82,205

34, S4

105,559

114,840

137,703

! Data Vith i:;orreoted qO and

Unit Con',/ersions

q =dPc

(Pa)

117,20

117 09

117.62

118.12

117.62

113.03

117.83

117.62

117.12

117.44

118.05

23134

231.24

230.71

23146

231.82

231,27"

231.32

232.10

230.47

231.03

231.13

• '•

i I

i

qiíqO

0,033

0,274

0,466 0,653

0 350

1,041

1.233 1425

1.617

1808

2,000

P

a

0.35

2.33

4,81

6,73

8,77

10,76

12,73

14.71

16.69 i

18,67 '

20,65 :

redicted Ra

b

-2,47

-3,20

-13,33

-13,66 "

-25,39

-31,12

-36,35

.42^8 !

-48,31 \ -54,04 i

-53,77

m Coefficíe

Pr,3

ÍPa)

111,64

106,03

36,33

67,02

43.66

23.39

-17 83

-64.51

-12801

-164 01

-362.21

217.60

139.47

13134

15233

105.67

38.21

-13.68

-3141

-163.38

-233.79

-427.32

Q

(k,qís)

O.O OE.OO

1.037E-04

2.966E-04

6.743E-04

8.324E-04

1005E- 3

1231E- 3

1,442E-03

1,727E-03

1855E-03

2.421E- 3

0 OOE.O

2 6 7E-04

4.841E-04

7.774E04

1.030E-03

1.407E- 3

1.673E- 3

1.321E- 3

2.165E-03

2.345E-03

2.S12E-03

1

; 1

Data Reduction Results

(Pa)

0,000

0,497

3.696

19.137

23.113

42 480

63.724

37.366

125.393

144 603

246.338

0.000

2.357

3.346

25336

49960

33.139

118.372

155.054

136.133

231.014

332.178

-it

c alpha

1.61

4,43 1

7.34 1

10,21 '

1.000

0.731

. . 0 ^ 3 + ^ 0.673

13,07 0.670

15.94 ,

18.80 •

0.665

0.662

21.67 ! 0,659

24,53 1 0.657

27,40 1 0,656

30,26 ! 0,654

Cp.i

0,650

0,353

-omA _ ^ ' -0,367

-0.731

-1036

-1.461

-1.826

-2.131

-2,557

-2,322

qi|iqO

0.0000

0.0042

0 0314

0.1620

0.2475

0 3539

0.5406

0.7428

1.0707

12313

2.0S72 0.0000

0.0124

0.0427

0.1097

0.2155

0.353S

0.5117

0.6680

0.3463

10000

1.4372

Cp,i

10

09

0.3

0.6

04

0 2

-0.2

-05

•1.1

-1.4

-3.1

0.9

0.9

0.3

0.7

0.5

0 2

-0.1

-0.4

-0.7

-1.0

-19

1" ' ,

87

TableC,9: Tabular Data-Multiple Openings-7.14 (C^= 1.0)and 19.05 (10 deg. Offset)

1 âmb = 1 73 Pamb = • 30 3

F 1 295,9 inHn in^ftn7 •!

rhoamb= 1206 kqiim'3 q^correotion = j 1053 i |

" 1 1 ••-" í ~

(10 deq sep)

Openinq 1

0,01905

kA1 =

Cpl =

kAr(AtíA1)-2 =

25543

0,3674

I„ in

m

m*2

, 1

lupstreamj • Openinq 2

d 2 = | 0,28l|in

1 0,0071374

A2 = : 4,001E-05

kA2 =

Cp2 =

16133

1.0213

m

m*2

kA2^(AríA2)-2 = ' 106,871

i • \

dPc

(in H20)

0,4543

04511

0,4555

0,4515

0,4574

0,4530

0,4543

0,4572

0,4551

0.4523

0.4552

0.8326

0.3302

0.3919

0,8370

0,8327

0,8346

0,8943

0.8924

0,8942

0,8890

0,8342

0.4513

O4510

0,4532

0,4541

0.4535

0,4626

0,4437

0,4532

0,4523

0,4434

0,4529

0.3935

0.8957

0,3922

0,8345

K

Pa

Raw Data

Prg

(inH2 )

0.4780

0.4593

0.4522

04229

0.3577

0.2401

00095

0.1337

0.3081

0,3834

0,4424

0.9234

0.8970

0.3634

0.7336

0.6,556

0,3943

0,5737

07355

0,8040

0,3472

0,8325

0,4848

0,4625

0,3631

0,2755

01516

-0.0172

-04165

-0.7424

•1.0911

-0,7296

-04757

0.3361

0.9177

0.7976

0.4970

Q

(SCFM)

0.000

16,990

26.872

42694

70.646

102049

146.940

123.260

86.301

60.216

33,424

0.000

13.812

37,437

70,127

104.183

147.738

120,031

86.231

66.158

47,389

26,353

0,000

5,656

13,756

17,941

22,279

27,135

36,846

41777

46,452

41.491

37,161

0,000

6,664

14,774

25,671 1

D a t a Vitt-i C o r r e o t e d qO and

Unit Conuers ion^s

'qO=dPc

(Pa)

113,80

117,97

11313

118,03

113,62

113 46

118,94

119,56

119,02

118 44

119 03

233 43

232,78

233.23

234.53

233.44

233.35

234.02

233.38

233.34

232.46

2.33.33

118.01

117.93

113.51

118.76

113.53

113.34

117.33

118.50

118.23

117.53

113.'>3

233!e5

234.24

233.32

233.31

Pr .g

(Pa)

118.70

114.06

112,30

105,03

83.33

53.63

2.35

33.20

7f: 51

36.21

103.38

229.32

222.75

215.91

197.08

162.81

97,91

143.72

182 65

133.67

210,40

22164

120.40

114.86

30.16

63.42

37.64

-4.26

-103.44

-184.37

-270,97

-18113

-118.13

232,43

227 31

198,06

123,43

Q

m%\ 0 O OE.OO

3,469E-04

5 486E-04

8 717E-04

1442E-03

2 034E-I.I3

2,930E-03

2,517E-03

1774E- 3

l ,229E-03

6,324E-04

, 0 0 E . 0 0

4,045E-04

7,e43E-04

1,432E-03

2,127E- 3

3 01SE-03

2,452E- 3

1.7eiE-03

1.351E-03

3.675E^04

5.3S0E-04

O.OOOE.O

1155E-04

2.S 9E-04

3 663E-04

4 549E- 4

5 652E-04

7.319E- 4

3.523E-04

3.434E-04

8 471E- 4

7.5S7E-04

O.OOOE.OO

1.156E-04

3.016E-04

5 241E- 4

Da ta

(Pa)

O.O

0.613

1 533

3.S71

10.538

22115

45.229

32.264

16 037

7 700

2372

0.000

0.834

2.376

10.443

23.052

46.3S3

30626

15.731

9.295

4.769

1.475

0.000

3.448

20393

34 638

53.491

73.702

138.475

183.090

232.639

185.523

148.821

0,000

3,457

23,523

71020

Reduction Reîults

qiíqO

0,0000

0.0052

0.0129

0.0323

0.0836

0.1867

.3S03

0.2699 0.1347

0 0650

0 0199 0.0000

0.0036

0.0123

0.0445" 0.0983

01333

0.1303

0.0677

0.0397

0,0205

0,0063

0,0000

0.0292

0.1721

0.2921

0.4510

0 6735

1.1302

15872

1.3653

1,5786

12566

0.0000

0.0148

0.1008

0,3036

Cp.i

1.0

10

0.3

0.3

07

0 5

0.0

0,3

0 6

0 8

0,3 1

10

1,0

0,3

~Ô.3 07

0 4

0,6

0,8

0,3

0,3

03

1,0

10

0,3

fie

0,3

0,0

-03

-1,0

10

10

0,3

05

88

TableC.9: Tabular Data-Multiple Openings-7.14 (C/,= 1.0) and 19.05 (lOdeg. Offset) continued

_.., ._ Tamb = l 73 :F Pamb = 30 3 ini-i.-'

rho amb = 1 208

q oorrection = i 1.053 I

—

kg/m'3

1

' (10 deq sep)

Combined Openlngs ,Ar =

[qríqOlmin = 3.250E-04

^-6,0162232 j . - - • • -

dia. (inj 80Û9E-01

{

m-2

295,9

dPc

(in H20)

0.4492

0.4514

0.4629

0.4509

0.4533

0.4512

0.4551

0.4543

0.4523

0.4542

0.4501

0.8903

0.8894

0.3393

0.3313

08831

0.8856

0.8361

0.3351

0.8363

0.8873

0.8901

í

K

Raw Data

Pr.g

(in H201

0.4746

0.4679

0.4540

0,4340

0,4034

0,3693

0,3470

0,3005

0,2486

0.2041

0,1234

0.9243

03141

0.3354

0.8749

0.3333

0.8090

0.7790

0.7128

0.6307

0.6239

0,5520

- \-^

Q (SCFM)

0.000

13.055

30,538

45,797

65,403

81.609

91499

105.373

119.437

130.416

146.332

0.000

12.424

28,709

45,444

66,103

78,854

89,724

110,133

113,002

130,513

147,296

i

Data V'ith Cotrect Unit Con'jers

'qO=dPc

ÍPa)

11747

118.03

113.43

117 32

iis.ee 117 93

113.01

113.34

118.43

118.78

117.71

232.81

232.58

232.56

233.07

232.50

23153^"

23172

231.47

231.33

232.17

232.75

Pr.g

(Pa)

117.86

116.20

112.74

107.78

100.13

31.72

86.16

74.62

6173

50.70

30.65 223.67

227.01

22J._36

217.27 "

206.35

200.90

193.47

177.03

169.06

156.44

137,03 j

ed qO and ons

Q (kq/s)

0 OOOE.O

2.665E,04

6 235E-04

9.350E-04

1.335E-03

1 66eE- 3

1868E-03

2.162E-03

2 439E-03

2.ee3E-03

2.999E-03

.OO E.OO

2.537E-04

5.861E-04

3.273E-04

1.350E-03

16t E- 3

1.332E- 3

2.250E-03

2 430E-03

2.665E- 3

3. 07E- 3

DataReductionRe ult

(Pa)

0.000

0.273

1523

3.425

6 985

10 876

13.671

18.304

23 294

27.774

35 235

0.000

0.252

1346

3.372

7.135

10,154

13146

19,825

23,125

27,815

35.429

qiíqO

0.0000

0.0024

0 0129

0.0230

0.0589

0 0922

0.1149

0.1533

0.1967

0.2338

0.2993 0.0000

0 0011

0.0058

0,0145

0.0307

0.0438

0,0567

0,0856

0.0997

0.1133

0.1522

Cp.i

1.0

10

1.0

0.3

0.3

0 3

0.7

0.6

0.5

0.4

0.3

10

10

1.0

0.3

0,9

0.9

0.3

08

0,7

0.7

0.6

89

Table C.IO: Tabular Data - Multiple Openings - 7,14 (Cp= 1.0) and 19.05 (20 deg. Offset)

,. Tamb = !

Pamb =

iho amb =

q eottection =

,. Of dl =

A1 =

kA l =

Cp1 =

kAl ' íArí A i r 2 =

73 F

29.9 inHg

1.192 kqím'3

1053

(Upstream)

eninq 1

0.2Sl|in

0.0071374 m

4.001E-05 m-2

15626

1.0157

103.12

1

! : (20 deq sep

Opening 2

d2 =

A2 =

kA2 =

Cp2 =

KA2'(AríA2)"2 =

0 75|in

0.01905 m

2.850E-04 ^ " 2

19 955

0.7227

25.95

• - ^ ;

i

295.9]

101252.8

K

Pa

Ra'.s' Data

dPc

i;in H20)

0.4677

0.4641

0.4671

0,4634

0.4677

0.4652

0.4666

0.4665

0.4672

0.4653

0.4644

0.9103

0.9063

0.9036

0.3105

0.9131

0.8992

0,9073

0.3062

0,3039

0,9037

0.9006

0.4532

0.4464

0.4436

0,4513

0.4438

0.4460

0.4492

0,4482

0.4472

0,4482

0,4446

0,8820

0,8785

0,8751

0,8326

n flRnri

Pi.g

(in H201

0,4990

0,4751

0,4236

0,2983

0.0953

-0.3426

•0.6728

-0.9393

-10730

-0.4308

0.0533

0.9631

0.9323

0.3886

0.7839

0.6412

0.4023

0.1749

-0.3276

-0.8270

-1,3921

-2.4360

0.373S

0.3193

0.2036

-0.0271

-O3250

-0,6317

-0,3077

-1,0935

-12731

-13645

-1,4364

0,7262

0,6042

0.3743

0.0453

.0 4?Rn

Q

(SCFM)

0.000

5.301

10.238

17.551

24.441

36.179

40,950

45,061

47.091

36.810

25.636

0.030

5.553

10.536

16.612

22.202

28.416

34.216

43.563

50,443

57,501

67.215

0.000

13.332

30.176

50.212

68.310

86.584

36,687

111,745

123,105

123,527

138,235

0.009

20.734

37.242

52,154

1 70,453

Datd V,'ith Coiieot IJnit Con'.'er

qO=dPc

ÍPa)

122.31

121.37

122.14

122^3''

122 30

121.65

122.03

121.93

122.16

12167

121.45

233.06

237.01

237.69

233.10

238.78

235.16

237.39

236.98

237.68

237.62

235.50

118.51

116.73

117.31

118.02

117 62

116.63

117.47

117.20

116.35

117.21

116.27

230.64

229 74

228.84

230.81

230.12

Pt.g

(Pa)

123.33

117.99

106.63

74.21" '

23,67

-85 08

-167,09

-233.42

-267,72

-106,39

13,40

239,13

23166

220,63

134,67

153,23

33,90

43,43

-31 33

-205,37

-345.71

"-e 4?96"

32.83

79,43

50,57

-6,73

•80.72

-156.37

-200.53

-271.56

-316,15

-333.85

-356,72

130,35

150 06

92.96

1140

"d qO and '3ns

Q (kgís)

O.OOOE.OO

1.0S2E-04

2.090E04

0.633E^ 4

4.990E- 4

7 182E-04

8.361E-04

3.200E-04

3614E-04

7!615E-04

5.234E- 4

6 125E-07

1.135E-04

2.161E-04

3.332E-04

4.533E-04

5.301E-04

6 3S6E-04

3.395E-04

1.030E-03

1.174E-03

1.372E- 3

O.O OE.OO

3.375E-04

6.ieiE-04

1.025E-03

1.335E-03

1.7e3E-03

1.954E- 3

2.231E-03

2513E-03

2.624E-03

2.S23E- 3

1.83SE-07

4 233E-04

7.604E-04

1066E-03

' • ;

Data Reduction Resuíls

qí (Pa)

0.000

3.063

11447

33.641 65.233

135.154

133.134

221.750

242.130

147,377

71,768

0 000

3,374

12,123

30,137

53,834

38,177

127.856

207,303

277,834

361,088

493..334

0.000

0.775

1.360

5.426

10.042

16J33

13.704

26.872

32613

35.549

41152

0.000

0.925

2.985 ' ' 5.854

qi/qO

0.0000

0.0253

0.0337

o'.^^^e 0 5334

1.1110

1.5003

1.3173

19324

1,2162

0,5909

0,0000

0.0142

0.0510

0.1266

0.2255

0.3750

0.5386

0.8743

11692

1.5196

2.0951

0.0000

0.0066

0 0167

0.0460

.085'(

0.1333

0.1677

0.2233

0.2783

0.3033

0.3539

O.O O

0.0040

0,0130

0,0254

0,0464

Cp.i

1,0

10

0 9

0,6

02

-0,7

-0,3

" 0,1

10

10

0,9

0,3

0,7

0.4 0,2

-0,3

-0,9

0,3

0,7

0,4

-0.1

-0.7

0.8

07

0.4

00

-05

90

Table C.IO: Tabular Data - Multiple Openings - 7.14 (C,,= 1.0) and 19.05 (20 deg. Offset) continued

Tâmb =

tho âmb =

q correotlon =

73 29.9

1.192 1.053

.F 1 295,9 JnHg • mÚ.ê

kqím"3

^[Ups(reâmj_

Comblned Openinqs

Al = 3.250E-04

(qríqO)min» 0.0028412

diâjmj^

dia. (in) 2.034É-02

8,009E-0t

m 2

i i 1

Pa

Raw Data

dPc

(in H201

0,4444

0,4463

0.4427

0.4463

0.4464

0.4468

0,4463

0,4457

0,4453

0,4428

0,4426

0.3784

0.3765

0,3750

0,8763

0.8821

0.8765

0.3761

0.8781

0.8763

03714

0.8767

qiíqO

0.003

0.203

0,402

0.602 0.802

1.001

1,201

1.401

1.601 1300

2,000

Pi.g

(in H20)

0.3303

0.3433

0.2501

0.0351

-0.2322

-05614

•0.7336

•0.8703

-10416

-0.4308

-0.6913

0.7646

0.7046

0.6250

0.4476

-0.3233

-0.3087

-11914

-1.4987

-1.3634

-1.0253

•0.5325

P

a

-0.22

-15.63

-31.05

-46.46

-61.87

-77.28

-92,70

-108,11 í

-123.52 i

-13334

-154 }5

Q ÍSCFM)

0.000

24.638

44.672

53.015

82.823

103.603

116.933

127.747

141227

37.673

114.210

0.000

24.836

44,267

58,580

85.184

104.532

121.237

140.772

130.302

112.093

90,687

lediotedRa

b

-015

-1051

-20,88 ^

-31,24

-4l,ê 1 -5137

-62,34

-72,71

-83,07

-93.44

-103,80 :

Data Vith Coirec

IJnit Con' je i :

qO=dP';

(Pa)

116.21

116 71

116.76

116 71

116.74

116.83

11646

116 56

116 45

115.S1

116.72

223 70

228.96

223.81

223.32

230.63

223.20

223.11

229.62

223.30

227^87

229.26

Pi.'q (Pâ)

97.03

86.74

62.10

23.62

•70.07

-139 42

-182.16

•216.14

-258.67

-12183

•171.63

183.33

174.37

155.22

11115

-3029

-225 66

•295 37

-372.20

-338.53

-254.75

-132.24

m Coeffioie

1 -|t

c ' alptiâ

0.37 1.000

5.55 î 0.343

10.73 i 0,341

5,31 l

21,10 i

26.28 '

31.46

36.65 ;

41.83 ;

47.01 ;

5219 ;

0.339

0.338

0,337

0,336

0,336

0,336

0.336

0335

ed qO and \oris

0

(Míî) 0 OOOE.OO

5 040E-04

3.121E-04

1.134E-03

1.691E-03

2 115E-03

2.337E-03

2,608E-03

2 883E-03

1.934E-03

2.332E-03

0 OO E.O

5.0S3E- 4

9033E-04

119eE-0J

1.733E-03

2.135E-03

2.475E-03

2.374E-03

2.e71E-03

2.2S3E- 3

1.852E-03

Cp.i

0.723

-1513

-3,810

-6,108

-8.406

-10,705

-13,003

-15,301

-17,600

-13,338

•22,136

!

Data Reduction Results

ÍPaj

0,000

1.003

3.302

5.570

11.353

17 762

22.627

27.005

33 005

15.787

21.585

0.000

1026

3.243

5.673

12.008

18,039

24.323

32.793

23.312

20 792

13.609

qiíq

0.0000

0.0036

0.0285

0.0477

0.0372

0.1520

01343

02317

0.2S34

0.1363

0.1865

0.0000

0.0045

0.0142

0,0243

0.0521

0,0730

0.1062

0.1428

0.1235

0.0312

0.0534

Cp,

03

0.7

0 5

02

' ã'e T2 -1.6

-19

-2 2

-11

-15

0 3

0.8

0.7

05

-0,3

-1,0 -13

-1.6

-1.5

•11

-0,6

'

91

Table C l l : Tabular Data- Multiple Openings - 7.14 (C„= 1.0) and 8.73 (10 dea. Offset)

Tambn Pamb =

iho amb =

SL SÍ I OSÍSSUILJ

73 1F 295,9 30.3

1203

1,053

inHq kgím"3

peninq 1

dl =

A1 = kM--Cp1 =

ltA1-(AríAir2'=

0,2Sl l ín

0 0071374 m

4 001E-05 m"2

16133

10213

1Û.1Û

(10 deg sep )

Qpenin'] 2

d2 =

A2 = kA2 =

Cp2 = kA2-(Ai(A2)-2 =

0,3438

0 00373252

in m

5,383E-05 m - 2

19591

0.913

5,45

102607,3 K Pa

Raw Data

dPc

(in H2 1

0 4513 0,4510 0.4532 0.4541 0.4535 0.4526 0.44S7 0 4532 0.4523 0.4494 0.4529 0.8935 0.8957 0,8922 0,8845 0,3940 0.3968 0.9005 0.8928 0.8863 0.3873 0.8339

0.4601 0.4607 0.4603 0,4575 0.4552 0.4583 0.4569 0.4594 0.4536 0.4600 0.4544 0.3394 0.9031 0.3002 08331 0,3333

Pi.q (in H201

0.4343 0.4626 0.3631 0.2765 0.1516 •0.0172 -0.4165 •0.7424 -1.0311

•0.7236 -0,4767 0.9361 0.9177 0.7976 0.4370 0.1163

-0.6002 -1.5433 -2.4415 -2,2527 -1,7114 -0,7018

0,4675 0,4433 0,3792 0,2327 0.1575 -0.0563 -0.2342 -0.6322 -0.3662 -12215 -13333 0.3040 0.8632 0.7778 0,5637 0,3132

Q ISCFM)

0.000 5.656 13.766 17.341 22.279 27.196 35.346 41.777 46.452 41491 37.161 0.000 5,664 14,774 25.671 34.313 46.631 53.120 65.884 64.512 53.353 48.084

0.000 5.022 12.301 13.387 26.754 36.470 44.530 55.636 61.736 67.000 72.284 0.001 6.856 14.684 26.571 37,225

Data With Corieoted q and Unit Con'jeisions

qO=dPc (Pa)

118 01

117 93

118 61

113.75

113.53

11334

117 33

113.50

118 23

117 53

118.43

233 65

234.24

233,32

233.31

233.73

234.52

236.49

233.48

231.78

233.75

120.32

120.43

120 37

11363 119.05 119.34 119.43 120 13 119.91

120.23

113.33

2 3 5 2 0

236.13

235.42

236.12

233.60

Pi.g iPa)

120.40

114.86 30.16 63.42

37 64 -4.26

-103.44 -13437 -270.97 -13119 -113.13 232 49 227.31 133.06 123 43 23 03

•143.06 -334.65 -606.32

-559.43 -425.01

•174.23

116.11 110.24 94 16 72.69 33.11

-13.33 -73.07 -169.41 -233.35 -303.34 •547.41 224.50

214.37 193.16 141.24 77.73

0 (kg/ )

OO OE. O l.t55E-04

2 S03E-04 3,663E-04

4.543E-04 5.552E- 4

7.313E-04 8 629E-04 9 484E-04 8 471E-04 7.5S7E-04

. OE. O 1.156E-04 3.016E- 4 5.241E-04 7.109E-04 9 533E- 4 1137E-03

1 345E-03 1.3t7E-03 1.212E-03

3.S17E-04

aoooE.oo 1.025E-04

2.6t4E-04

3,35SE-04

6,462E- 4

7,446E- 4

9,1 2E-04

1136E- 3

1,262E- 3

l ,363E-03

1476E-03

2 42E-DS

l,4 0E-04

2,3SSE-04

5,426E-04

7,eO E-04

Da ta Reduo t l o r

qi

IPaJ

0,000

3,448

20,333

•34,688

53,431

73,702

13S475

1SS 090

232,539

185,523

148,321

0,000

3,457

23,623

71.020

130.664

234.940

364 034

467.789

44S.512

379 643

249.163

0.000

1.213

7.831

13.076

34.426

63.363

35.581

14S.S64

183.653

215.335

251 291

0.000

2.261

10.370

33.356

66.644

qi/qO

0 0000

0 0292

01721

0 2321

0.4510

0.6736

1.1302

15872

1.9653

1 5736

1.2566

O. OO

0.0143

0.1003

0 3036

0.5533

1.001S

1.545S

2.0036

1.3351'

16362

1.0653

0.0000

0.0101

0.0655

0,1511

0.2892

0.5338

0.8000

1.2332

1.5316

1.7343

2.1143

.OOO

0.0036

0.0440^

0.1444

0.2S53'

:-í

Result

cp.i

1.0

1.0 0 8

0.6 0.3

0.0

-0.9

•10 1.0 10

0.3 05 01

-0.6

-0.7

1.0 03 0 3

0.6 0.3 -0,1

-0,6

10

0,3 0.8

0.6 0.3

92

Table C. 11; Tabular Data - Multiple Openings -7.14 (C',,= 1.0) and 8.73 (10 deg. Offset) continued

Tamb»

_ _ Pamb = rho amb =

___g.correction =

Comb Ar =

Jgríg Jrnln =

dla. (mj dla. (in)

73 30.3 1.208 1,053

IF

J,nHa.,. . kgím"3

Ined Openlngs

3,990E-05 m'2

0.010133009

1,128E-02

0.444626336

1 2959

102607.3

dPc

|in H201

0.4435

0.4437

0,4488

0,4475

0,4516

0,4491

0,4430

0,4477

0,4475

0,4466

0.4468

0.8344

0.3908

0,3893

0.3307

0.8863

0.3314

0.3877

08881

0.8860

0.3817

0,8863

' i

1 1

qiíqO

0,010

0,209

0,403

0,607

0,306

1.005 1,204

1,403

1,602

1,801

2,000

K

Pa '""'

Raw Data

Pi.'q tin H2Û)

0,4746

0.4465

0.3943

0.3233

0.2431

0.0923

-0.1264

-0.3337

-0.5541

-1.0631

-13032

09290

0.3322

08515

0.7607

0,6155

03123

01096

-0,1777

-0,4455

•0.6951

-14333

P

a

-0.05

-0,97

-1,90

-2,82

-3,74

-4767

-5,59 1

•6,52 ]

-7,44 J -8.37 1 -3,29 1

Q (SCFM)

0000

11,650

22,331

32,453

42,295

54,637

63,636

32204

91,366

112.051

120.432

0.000

10.957

19.445

32567

46,359

67,572

80.541

94.055

104.635

113.737

138.240

edicted Ra

b

-0,11 1 -228

-4,45 !

-6,62 i

,J.79 [

-13,13 \

-15.30

-17,46

•19,63 , -21311 1

-

Data With Cotiec Unit Con'jei

qO=dPc

iPa^

117 23

117.60

117.36

117.03 11S.09

117.43

117 41

117.03

117.02

116,80

116,34

233 30

232.36

232.63

232 93

231.7S

233 10

232.14

232 26

231.69

230.56

231.94

Ti Coefficíe

Pi.g

IPa)

117 35

110.33

37.32

8041 60.38

22.92

-31.39

•84.12

•137.60

-265.50

-325.13

230.70

221.57

21147

188 31

152.85

77 56

27.23 -44.12

-110.64 •172 62

-355,95

ít

: c alpha

0.16 1000 1,24

2,33

0456

0440

3,41 ! 0,435

4,50 0,432

5J3 ['""o^^s 6,67 : 0429 775

.3

0 42'"

0 4..6 9 92 1 0 4w7

11 "0 n427

edqOand rionî

M íkg.'Jl

0 OOOE. O

2.373E-n4

4563E- 4 6 626E-04

S.e36E-04

1117E-03

t.402E- 3

1.678E-03

1.376E-03

2.2SSE-03

2.463E-03

O.OOOE. O

2.237E-04

3.970E-04

e.643E-04

9.465E- 4

1330E-03

1 644E-03

1320E- 3

2J3eE-03 2.322E- 3

2322E-03

J

Cp.i

0.313 0582

0.222

-0.138

-0,498

-1219 -1573

-1340

-2 300

-2.660

- • - - - —

Data

iPi] 0 000

2 346

8 653

13.205

30.321

51.636

31.549

116306

145.378

217.026

250 7ri6 O.

2076

6.536

13.333

37 149

78 925

112.128

152 913 189.249

223.606

330 330

í E f

l

1

t

1

• - . • . - •

,,

--"— -"""-

Reducticn Result

qi|iqO__

0 0000

0,0139

01556

0,2619

0,4402

6946

0 3377

12466

1 S5S2

21457

0 0000

0,0033

0.0281

0.0737

01603

0 3336

0 4330

0 6584

0.8163

0 9633

14242 1

i

JiP'i

10

0.9

07 " 05

0.2 -0 3

•0.7

•12

•2.3

-2 8

10

10

03

.S 0.7 0 3

0,1

•0.2 " -0.5

-0.7

-1.6

93

Table C.12: Tabular Data - Multiple Openings - 7.14 (Cp= 1.0) and 8.73 (20 deg. Offset)

Tamb » Pamb =

tho amb =

iooireot lon =

73 23.9 1192

1,053

F 285,3 InHci kgím'3

Openinq 1

d1 =

A1 =

kA1 =

Cpl =

kAi;íAríAr!;2_=j

0,281lin 00071374 m

4 001E-Û5

1,5339

10186

a.88

m"2

i

; (20 deg sep)

Openln'5 2

d2 =

A2 =

kA2 =

Cp2 =

kfi2^Mfi.2]-2 =

0,3433

000373252

5,989E-05

2.5542

0,7396

7.11

in . m

m-2

- •

_ - . -

!

101252,8

K

Pa

Raw Data

dPc

(in H201

0.4383

0.4391

0.4386

0.4337

0.4393

0.4360

0.4360

0.4372

0.4372

0.4400

0.4364

0.8649

0.8653

0.8532

0.8632

0.8645

08613

0.8645

0.8638

0.8617

0.8632

0.8674

0.4367

0.4374

0,4334

0,4370

0,4373

0,4360

0,4367

0,4397

0,4372

0,4380

0,4381

0,3631

0,3692

0,8664

0,3706

0,8733

Pi.a tin H2Û1

0.4721

0.4544

0,3762

0,1104

- .1S36

-0.6754

-1.0026

•0.4023

-0.0663

0.3800

0.1863

0.3043

0,3333

0,8227

0.7305

0.6135

0.4837

-0.0055

-Û.515

-11114

•1.3312

-1.9298

0.3719

0.3210

0.2100

0,0752

-0,0959

-0.2665

-0,5217

-0,6346

-0,3403

-13714

-1,5723

0.7374

0.6653

0.5121

0,2336

-0,0303

Q tSCFM)

0.000

5.057

12.034

22.914

30,781

40.325

44.383

36.336

27.337

11.888

20.536

0.011

4.368

11.440

16.650

21.020

25.032

36.511

44.327

52356

66.385

61.366

0,000

6,645

15.348

22.046

29.379

35,654

44,033

48,729

56011

64,670

69.309

0.000

6.941

16,621

25,309

33.110

Data With Coiiected q and IJnit Con'.'ei ionî

qO=dPc

(Paj

114.63

114.83

114.70

114.71

114.87

114.01

114 03

114 3 3

114.33

115.07

114.13

226.17

226.28

224.63

225.73

226 06

225 33

226.03

225 90

225 33

225.74

226.34

114,20

114,33

114 31

114,27

114.35

114,02 114,20

11493

114 32

114.55

114.56

227.01

227.30

22657

227.66

223.54

Pi.g

tPa)

117.25

112.84

33 43

27,43

-46,60

-167,73

-243,98

-99,91

-16,53

94,37

46 26

224,72

22197

204.31

13141

153.S5 12012

-136

-127.83

-276,01

-345,43

-479.26

92.36

79.73 6214

18,63

-23,81

-66,17 •123,65

-170.02

-233.52

-340.57

-330.61 133,12

165.36

127.13

7167

•22,55

u

tl<3's| 0 O OE.OO

1, 32E-04 2.467E-04

4.e7SE- 4

e.234E-04

8.233E-04

9.164E-04

7 225E-04

5.716E-04

2 427E-04

4.193E-04

2.24eE- 7

3.339E-06

2.33eE-04

3 339E-04

4.292E-04

5 121E-04

7.454E-04

9.152E-04

l. 8tE- 3

1.151E-03

1.253E-03

O.OO E-

1.357E-04

3.134E-04

4.501E-04

5.998E-04 7.279E-04

a930E-04

9.949E-04

t.t44E-03

1.320E-03 t.415E-03 aO OE- O

1417E-04

3.393E-04

5.ie7E-04

7.781E-04 •3 fl i F . n i

Data Reduction Result

^i (Pa)

0 000

2733

15.815

57.341

103.473

177,587

220,002

136.749

85 602

15 434

46.052

0.000

2.5SS

14.293

30 275

48.253

63.705

145.580 219.453

306.261 347.207

411.261

0.000

2.162 11.481

23.683

42 066

61956

94.497 115.728 152.902 203.331 234.122

0.000

2.343

13.464

31.213 70,785 11'iS<!R

...sêM...

0 0000

0.0243

01379

0,4999

0.9003

15676

13234

11361

0 74S3

01341

0.4035

0.0000

0.0114

0.0636

01341

0.2135

0 3048

0.6433

0 9715

1.3532

1.5381

1.3130

0.0000

0.0138

0.0393

0.2073

0.3673

0 5434

0.S274

10064

13375

17734

2.0436

O. O

O0103

0.0534

0,1371

0,3097

n R n m

Cp.i

10

10

0,8

0,2

• ' ' • *

•0,9

•0.1

o"8

0,4

1.0

'" "1.0 0,9

0,8

07

0,6 0,0 •0.6

0,8

"Ã 05 0,2 -0,2

-_o._e

0,8

0,7

0-6

0,3

-0.1

-n5

94

Table C.12: Tabular Data - Multiple Openings -7.14 iCp= 1.0) and 8.73 (20 deg. Offset) continued

T a m b »

P â m b =

iho amb =

qoottection =

Comb Ai =

JgtígOJmln =

dla. [m) dla. (in)

73 29.3 i,'Í32 1,053

F InHg

kg ím~3

n e d Open ings

3.990E-05 m*2

0.02825313

1,128E-02

0 .444026336

296.9

101252,8

K

Pa

! : Raw Data

dPc

(in H2Û)

0.4360

0.4363

0.4364

0.4367

0.4337

0.4372

0.4357

04410

0.4370

0.4382

0.4382

0.S679

0.3726

0,3703

0.3723

0.8700

0.8721

0.8674

0.3676

0.8733

0.8662

0.8707

qiíqO

0.023

0,225

0,423

0,620

0.817

1,014

1211

1408

1,606

1.803

2000

Pi.q (in H2 )

0.4200

0.3331

0.3124

0.2310

0.1544

0.0423

-0.1428

-0.2969

-0.5322

-0.9166

-1,2242

0.8257

0.7795

07093

0.5755

0.4529

0.2361

0.0538

-0.1409

-0.5208

-0.3023

-1.7301

F

Q (SCFM)

. 1

9.786

22.143

32.387

40.541

43,238

61,120

71,840

83,319

39,219

110,380

0,000

3.871

21017

35,501

45,411

56,661

63,816

80,177

35,646

105,872

137,453

ledlcted R i

Data Vith Coiiect IJnit C nvet

qO=dPc

(Pa)

114.01

114.26

114.12

114.19

114.38

114.32

113.34

11532

114 23

114.53 114.60

226 37

228.19

227 53

225 24

227.52

223.07 _

226 8 2 "

226 88 223.54

226.62

227.63

Pr.g

tPa)

104.29

95.14

77.59

57.36

33 33

10.60

-35.47

-73,73

-132,16

-227,37

-304,03

205.06 133.69 176.14

142.92

11247

73.53

13.35

-35,00 -129 33

•133.33

-444.55

mCoefliclent

* Y —|— • T a

-0.08

-0,62

-117

-1,72

-2,26

-2,31

-3,35

-3.90

-4,44

-4,99

-5,54

b c alpha

-0 40 0 48 1000

-3,20

1 -6,01

-8.81

-11.61

-14,41

-17,22

-20.02

133

: 3.28

4,63

6,03

, 7,49

1 3,33

0.532

0.498

0,486 0,479

0,475

0,473

10 29 0471

-22.82 , 11.69

-25.62

-23.43

1 13,03

t 1443

0,463

1 0,468

1 o^'^ê?

fd qO and ons

Q (kq^;!

2,042E-0S

1998E-04

4.622E-04

6.612E-04 8.277E-04

1.006E-03

1.24SE-03

14e7E-03

1713E-03

2 026E- 3

2.2e4E- 3

0 OOE.OO

2 15E-04 4231E- 4 7.24SE- 4

9.27tE-04

lt57E- 3

1 405E-03

1.637E-03

1.953E- 3

2.162E-03

2.S0eE-03

Cp.i

0.740

0,389

-0,017

-0,425

-0.835

-1,244

-1654

-2,064

-2,474

-2,384

-3,234

Data Redijcnoi

qi (Pa)

0,000

1,677

3.593

18.374 28,790

42,553

65,436

30,403

123.360

172441

215.357

0 000

1.707

7.737

22,077

36.122

56.237

82 953

112.603 160.245

196.342

330.977

qiíq

0.0000

0.0147

0.0753

0 1603

0.2504 0 3722

0 5743

0.7340

1.0735

15043

1.3732

0 0000

0.0075

0 0340 0.0367

01533

0.2466

0^657

0.4363

0.7012

0.8668 1.4536

Result

Cp.i

0.9

O.S

07

0.5 0.3

0.1

-0.3

•0.6

-1.2

-2.0 -27 0.9

O.S

0,8

06 0.5

0.3

0.1

-0.2 -0,6

•O-S -2.0

r— i

95

Table C, 13; Tabular Data - Multiple Openings - 8,73 iCp= 1.0) and 8.73 (10 deg. Offset)

Tamb = Pamb =

rho amb =

q correction =

73 30.3

1.208 1 1053

F

BHJ,. kgím"3

,- - „

L„„ í Openlnq 1

d1 =

A1 =

kA1 =

Cp1 =

líArtAri A1V2 =

c d2 =

A2 =

kA2 =

Cp2 =

kA2'(AiíA2)"2 =

0,3438 |in

1 0,00373262

5,3S9E-05

1,6369

1 0102

6,55

(10 deg sep)

Jpenin'j 2

0,3438

0 00373252

5 939E-06

1,9591

0,919

7.84

m

m*2

in

m

m"2

i

i

295.9

102607,3

dPc

(inH2 )

04741

0,4726

0 4727

0,4753

0.4713

0,4722

O4701

0,4635

0,4722

0,4746

0,4735

0,9189

09157

0,9171

09161

0,9079

0,9116

0,9121

09140

0.9093

0,9173

0,9112

04601

0.4607

0.4603

0.4575

0.4552

0.4533

0.4569

0.4534

0.4536

0.4600

0.4544

0.8994

0.9031

0.3002

0.8331

0,8933

0.8932

K

Pa 1

1 '

Raw Data

Pi.a (m H2 )

0.4995

0.4861

0.4200

0.2211

0.0250

-0.3330

-0.6695

-10680

-1.3229

•0.8451

0.4506

0.9655

0.9294

08331

0.6600

0.3258

0.1195

-0.2291

•1.0431

-15441

•2.2003

-2,2350

0,4675

0.4439

0,3732

0,2927

0,1576

-0,0563

-0,2942

-0.6822

-0.9662

-1.2216

-1,3933

0,3040

0,3632

0.7778

05637

0.3132

0.0497

Q (SCFM)

.o

5.334

16.262

30.634

33.410

52.566

53.432

67.273

71.747

63.034

13.070

0.002

10.142

21137

31.346

45.377

52.054

60.833

78.767

36.336

94.853

36.179

0.000

5,022

12,801

13,387

26.764

36.470

44.530

55.635

61.736

67.000

72.284

0.001

6.356

14.634

26.571

37.225

45.506

•ata Vith Coriected qO and Ijnit Con'jersions

qO='JPc

(Pa)

123 38

123.53

123,62

124,46

123.26

123.47

122.94 122 77

12347

124 03

123.81

240.31

239.47

233.34 "

239 30"

237.42

233 33

238 52

233 01

237.78

240.04

233.23

120.32 12 .4S 120.37 113.63 11305 113.84 119.43

120.13

119.31

120.29

113.83 ' 235 20

236.13

235.42

236.12

J33.60 233 57

Pr.g

(Pa|

124 04

12071

104.31

54,91 6.22

-3510 -166 27

-265.24 -328 53

-203 88

111.90

233.78

230.31

206.39 _

' íe'ís ' 80.92

29 67

-66 89

•259.04

-363.47

-646.57

-563.34

116.11

110.24 34.16

72.69 33.11

-13.33

-7307 -169.41

-233.35

-303.34

-347.41

224.50

214.37

193.16

141.24

77.73 Î233

Q IMís l

OOOOEí O

1212E-04

3.32 E-04

6,244E-04

8, 4eE-04

1. 73E- 3 1.213E- 3

1.374E-03

14e5E-03

1 237E-03

2.e6SE-04

4 083E-0S

2,071E-04 4.32:6Í-04 6'522E-04

9.2e4E-04

1.063E-03

1.242E- 3

1603E- 3

17e3E-03

1.937E-03

1.964E-03

O.O E.OO

1.025E-04

2.614E-04

3.95SE-04

5 462E-04 7.44eE-04

3.1 2E-n4

1.136E-03

1,262E-03

1,368E-03 1476E-03

2042E-03

1,400E-04

2,993E-04

6.425E-04

7^600E-04 3,291E- 4

Data Reduction Results

qi IPa)

0 000

1.634 12.713

44.386

74,637

132 331

169.376

217.690 247.571

191092

3.216

0.000

4.947

21.533

43.032

33.029 130.317

178.009

233.338

353.481 432 753

444.890

0.000

1.213

7.SS1

18.076 34 425

63.363

95.531

148.864

133.659

215,335 261 231 0 000

2,261

10.370

33.955

66.644 99 593

qi/qO

0 0000

0.0137 0.1029

0.3616

.eoeo 1 0763

1.3313

17732

2.0050 1.5400"

0.0664

0 0000

0.0207

0.0300

0.2051

0.4171 0 6467

0.7463 1.2434 1.5076'

1.8028

18670

0.0000

aot t

0.0655

0.1511

0.2892 0 5338

O.S OO

12332

1,5316"

1,7343 2,1143

0,0000

0.0036

0.0440

0.1444

0.2353 0 4264

Cp,i

10

10

0.4

0 9

10

09 0 7

0.3 0.1

-0 2

~

1.0

0.9

0 6

0.6

0.3 -0.1

-06

10

0.9

0.3

0,6

0,3 01

96

TableC,13: Tabular Data - Multiple Openings -8.73 (C„= 1.0) antd 8.73 (10 deg. Offset) continued

Tamb » Pamb =

tho amb =

q correction =

73 30.3 1.208

1053

F inHq kgím"3

295.9 K 102607.3 iPa

Comblned Openlnjjs

Ã't = (atígO]mln =

dia, (mj

dia. (in)

1.198E-04 0.013923768

1235E-02 6.486206623

m*2

dPc

(in H2 )

04501

0.4432

0.4480

0,4461

0,4476

0.4434

0.4430

0.4451

0.4449

0.4470

0.4473

0.8861

0.3340

0.8802

0.8330

0.8780

0.8808

0.3S16

0.8739

0.S7S3

0.8842

0.8767

qiíqO

0.014

0.213

0,411

0,610

0,808

1.007

1,206

1.404

1603

1301

2000

Raw Dála

Pr,q |inH2 )

04817

0,4541

0,4033

0,2868

0.1413

-0,0363

•0,1363

•0,3603

-0,5391

-0,8446

-1,2634

0,3303

0,3776

0,8215

0,6567

0,4033

0,3050

0.0812

-0.1308

-0.3043

•0.5007

•o.seoi

F

Q (SCFM)

0,000

12.373

26.240

45.265

60.329

77,254

83,402

97,216

110,281

123,009

139,183

0,002

13.203

29.378

52.886

76,039

33,461

96,353

103.707

117,593

126.313

141,629

Unit C:on',/eision£

q =dPc

(Pa)

117.63

117.20

117.15

116.66

117.11

116.36

117.43

116,40

116,34

116.33 116.93

231.71

231.13 230.13

230.90

229,61

230,33

230,54

223,84 229,69

23121

229,00

Pr.g

tPa|

113.62

112,77 100 16

70,97 35,24

-9.13

-48,76

-86,98

-146,23

-203 76

•312 76

23103 217,34

204 00

163,08

100,31

75,73

20,16

-32,47

-75,71

•124,34 •213,53

ledicted Ram Coefficlent i

a

0.02

0.27

0,53

Ô,73 1,04

1,30

1,55

1.81 2.07

2,32

' ' 2,58

b

-0,22

-3,33

-6,44

-9,56

-12.67

-15.78

-18.83

-22,01

-25,12

-28,23

c , alplia

0,20 1000

176

3,31

4.87

6,43

7,98

0,552 0,538

0,533

r 0,530

0,529

3.54 ! 0.628

11.03

12.65

0527

0.526

14.21 0 526

15.76 0.526

0

(kgi's)

O.OOOE.O

2e29E-04

5.357E-04 9.240E-04

1 242E-03

1577E-03

1805E-03

1.985E-03

2.252E-03

2.611E-03

2S42E- 3

4. S,3E- S 3.717E-04

e.lOOE-04

1. S0E-03

1.653E-03

1.704E-03

1.973E- 3

2.213E-03

2,401E- 3

2573E-03 2332E-03

Data Reduction Results

IPa)

0.000

1.334

8.279 24625

44.433

71.759 33 363

113.634

146.229

131.331 232,335

.OO

3.336

10.733 33 629

69.611

33.733

113.020

142.035 166.263

131.335

241177

qi/qO

00 00

0.0170 0 0707

0.2111

0 3799

06188 .3002

0.3762

12563

16565

19912

0 0000 172

0.0466

0.1466

0 3032

0.3635

0.4902

0.6132

0.7239 0 3237

10532

, Cp.i

1.0

1.0 0.9

0.6

0 3 -01

-0 4

-0.7 -13

•18

•2.7

1.0 0.3

0.9 0.7

0.4

0.3

0.1

-0.1 -0.3

-0.5 •0.3

- r~~"" Cp.i

0,913

0.685

0.231

-0.124

-0.478

; .333

-1.188

-1543

-1.893

-2253

-2608

1

--

\ i \ .

1

97

Table C.14: Tabular Data-Multiple Openings-7.14 (Cp= 1.0) and 7.14 (10 deg. Offset)

T .

Pamhs fho amb =

q oorrection =

30,3

1208

1 0 5 3

'

0

dl=

A1 =

kA1 =

C.pl =

kAr(AríAir2 =

OF d2=..

ÍnHS 1 Kgím"3

l e n l n q l

0.281

0.0071374

4.001E-05

1.6193

1.0213

,_ 6.48

in

m

m'2

j

- i i 1

(lOdegsep)i

enlng2

0.28l|in

0 0071374 m

A2 =

kA2 =

Cp2 =

k.A2'(AríA2)~2 =

4. i:i1E- 5

1.8821

0.9163

7.53

m ' ^

i

Si'eôí.s

dPc

(in H201

0.4613

0.4610

0.4632

0.4541

0.4535

0.4526

0.4437

0.4532

0.4523

0.4494

0.4523

0.8335

0.S357

0.8322

0.8345

0.8340

0.8968

0.9005

0.3323

0.8863

0.8873

0.8339

0.4610

0.4614

0.4640

0.4647

0,4670

0,4613

0.4634

0.4611

0.4613

0.4669

0.4614

0.9106

0.9138

0,9083

0.9183

0.9152

K

LP«

Raw Data

Pi.3 (in H201

0.4843

0.4626

0.3631

0.2765

0.1616

-0.0172

-04166

•0.7424

-1.0911

-0.7296

-0.4767

0.9361

0.9177

0.7975

0.4970

0.1169

•0.6002

-1.5439

-2.4415

-2 252?

•1,7114

-0,7018

0,4682

0.4023

02131

•0.0370

-0 6223

-1.4622

-1.0463

•0.6235

-0.3174

0.0452

0,2455

0.9170

0.8666

0,6322

0,2377

-0,2762

Q (SCFM)

0.000

5.656

13.756

17.941

22.279

27.195

35.846

41.777

46.452

41.491

37.161

0.000

6.664

14.774

25.671

34.819

46.691

58.120

65.884

64.512

53.363

48,084

0,000

7.033

16.607

25.722

37.024

49.306

43.660

36,925

30,834

21,884

15.262

0.000

5.288

16338

25.332

37.658

Data With Coirect Unit Con'jers

'qO=dPc

(Pa)

113.01

117.93

118.61

118.75

11853

11334

117.33

113.50

113.28

117.63

118.43

233.66

234.24

233.32

233.31 2.33.78 234.52 23549 233.48 23178

2J2 3

2^2 75

120 56

123 65

1J..6

12151

1221'

12iit4

1J17

120.57

120.63

122.08

120.65

23311

233.95

237.52

240.15

239.34

Pr.g

(Pal

120.40

114,86

90.16

63.42

37 64

-4 26

-103.44

-134.37

-270.37

-131.13

-118.13

232.43

227.31

138.06

123.43

23.03

-143.06

-384.65

-606,32

-553,43

-426,01

-174.28

11623

100.03

""~'6"2'3l" ""

•24.03

-154^66

-3S3 13

-253.83

•154A5

-73.82

1123

60.96

227.72

216 22

157 00

73.94

-68.59

"d qO and ons

Q

(tgísl

O.OOOE.OO

lt55E-rj4

2.303E-04

3.ee3E^04

4 549E-04

5 552E04

7.313E-04

3.529E-04

9.434E-04

3 471E-04

7.5S7E-04

0 OOOE.O

1.156E-i:i4

3. 16E-04

5241E-04

7.t03E-04 9 533E- 4

t.l87E-03

1.345E-03

1.317E-03

t.212E-03

9.317E-04

O.OOOE-00

1.437E-04

3.391E-04

6.252E-04

7 653E-04

1.007E-03

3.314E-04

7.539E-04

6.295E-04

4.463E-04

3.tieE-04

0 000E«00

1 080E-04 _

3.348E-04

5 234E-04

7.6S3E-04

Data Reduction

V (Pa)

0.000

3.448

20.333

34.633

53 491

73702

138.475

138.090

232.539

185.523

143.321

0.000

3.457

23.623

71.020

130 654

234.940 364.034

467.789

44S.512

379.643

249.163

0.000

5.340

23722

71.302

147.726

261.393

205.427

146.337

102.461

51611

25.102

0.000

3.014

23.377

72471

152,823

qiíqO

0,0000

0.0232

0,1721

0.2921

0.4510

0 6736

1.1802

1.6872

1,3653

1,5736

12566

OOOOO

0,0143

0,1008

0,3036

0.55S3

1.0018

15458

2;:i036

1 9351

1.6362

1.0653

0.0000

0.0443

0,2449

0,5367

1,2095

2,1717

16953

1.2187

0.3494

0.4223

0.2031

0.0000

0,0126

0,1220

0,3018

0,6385

C p,l

1,0 i n

n 0

3

f;

0.3

0 0

-0.3

-1

1

1

n 0

0

0.8

0.5

0

-0 .1

,6

-0.7

10

0.8

0.4

-C 2

-r c 0

,7

1

,5

10

c c c -

.3

.7

.3

).3

98

Table C. 14: Tabular Data - Multiple Openings -7.14 (Cp= 1.0) and 7.14 (10 deg. Offset) continued

Tamb = Pâmb =

73 [P 1 235.9

30 3 inHq 102607.3

iho amb = 1208 q coiiection = 1.063

k,giim*3

_ _ . Combined pening>

Ar = S.002E-n5

[qiíqOjmin = 0 0162107

- - • -

m~2

"î

'.

dPc

(in H20)

0.4467

0.4432

0.4477

0.4448

0.4502

0.4436

0.4435

0.4468

0.4483

0.4483

0.4495

0.8901

0.8311

0.8854

0.3336

0.3834

0.3824

0.8833

0,8833

0.8829

0,8869

0,8864

\

' "

\ i

qiriqO

0,016

0,215

0,413

0,611

0,810

1,003

1206

1,405 "

1603

1802

2000

K

Ph ^

1

Ra',',' Data

Pr.g

(in H201

0.4790

0.4410

0,3706

0,2792

0,1298

-0.0673

-O3005

-0.5132

-0.8346

-1.0535

-1.2785

0.9354

0.3678

0,7156

0,4605

0,1747

-0,2339

-07346

-12553

-13123

-2.0464

-23214

Q

ÍSCFMj

0.000

11.508

21728

30,809

42.177

53.041

62.367

70.590

83.309

89.322

35,313

0,011

14.967

30.675

47.915

60,843

77,718

33,863

104.374

117.714

121.809

127.595

Predicted R;

f

1 '' ': \

Data Vitt-i Coriected q and Unif Con'.'eisions

qO=dPc

(Pal 116 Sl

117.20

117.06

116.32

117.74

117 30

117.54

116.33

117.36

117 40

117.54

232.76

233.03

23165

232.37

231.00

230.74

231.14

230.98

230.89

23192

23130

Pi,g

IPa)

118,36

103.51

92.03

63.34

32.25

-16.33

-74.62

-127.46

•207.27

•263.11

-317.52

232.31

215.50

177.72

114.36

43,33

-59.33

-197.34

•311.75

-450.21

-508.22

-576.50

m Coefficient

a b ; 0 : âlpha

0.02

0.23

•0.24 0.23

- 1 2 3 _ j 1.72

0,43 i -6.22 0.64

0 85

-3.20

-12.13

1,06 -16,13

1.000

i 0,554

__ 3.21 1 0.537

4.71 ' 0.531

6.20 0.52S

7.63 0.526

1,27 -13,17 • 9.19 0.525

1.48 -21,15 j 10,63

Te'g i ' -24,14 1 12,Í7 1,89 i -27,13

210 ; •30.11

í 0.524

1 0.523

13.67 1 0,523

15.16 í 0,523

0

(Iqísl

0 O OE. O

2 35 E-04

4 43eE-04

e.2S0E-04

3.eilE- 4

1. 83E- 3

1.284E-03

1.441E- 3

1.701E-03

1.824E- 3

1.94eE-03

2193E-07

3. 56E- 4

e.2e3E-04

3,7S3E- 4

1.242E-03

1537E-03

13teE- 3

2.143E-03

2.403E-03

2.4S7E-03

2.605E^03

Cp.i

0.316

0.596

0.250

-0.096

-0.441

-0.737

-1133

-1.473

-1,824

-2,170

-2.516

Data Reductior

qi

(Pa)

0,000

3 563

12 720

25.573

47.927

75.737

106.482 '

134.251

186 933

214.956

244.757

0.000

6.036

25.351

61354

33.755

162.731

237.316

296 .'339"

373.325

333.751

438.629

qi(qO

0.0000

0.0304

0.10S7

0.2199

0.4071

0.6462

0,9059

1.1431

1.5933

1.3310

2.0323

0.0000

0.0253

0.1036

0.2662

04313

0.7053

10267

12354

1.6169

17237

18923

1

Re ult

10

0,9

0,8

06 0,3 -0,1

-o.e -1.1

-1.3

•2.2

-27

10

0,9

0,8

0.6

0.2

-0.3

-0.9

-1.3

-1.3

-2.2

-2,5

i

1

í

i

!

99

PERMISSION TO COPY

In presenting this thesis in partial fiilfillment of the requirements for a

master's degree at Texas Tech University or Texas Tech University Health Sciences

Center, I agree that the Library and my major department shall make it freely

available for research purposes. Permission to copy this thesis for scholarly purposes

may be granted by the Director of the Library or my major professor. It is

understood that any copying or pubHcation of this thesis for fmancial gain shall not

be allowed without my further written permission and that any user may be Hable for

copyright infringement.

Agree (Permission is granted.)

" ^ Date

Disagree (Permission is not granted.)

Student Signature Date