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Masters Theses Student Theses and Dissertations

1950

Velocity studies in a vertical pipe flowing full Velocity studies in a vertical pipe flowing full

Robert Franklin Tindall

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Recommended Citation Recommended Citation Tindall, Robert Franklin, "Velocity studies in a vertical pipe flowing full" (1950). Masters Theses. 4881. https://scholarsmine.mst.edu/masters_theses/4881

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VELOCITY S'IUDI~

IN .A

VERTICAL PIPE

FWWING FULL

BY

ROBERT FRANKLIN TINDALL, Jr.

A

THESIS

submitted to the faculty of th

SCHOOL OF MINES AND METALlURGY OF THE UNIVERSITY OF MISSOORI

in partial fulfillment of the work required for th

Degre of

MASTER OF SCIENCE IN CIVIL ENGINEERING

Rolla, Mi sour!

1950

ACKNOWLEDGEMENT

For suggesting this study and offering valuable advice

the 'Writer wishes to express his sincere appreciation to

Professor V. A. C. Gevecker, and Professor E. W. Carlton,

both of whom are Professors of Civil Engineering, Missouri

School of Minea.

r am also grateful to Mr. Orlan King, who, as head of

the departmental shop, offered numerous helpful suggestions

on the construction and fabrication 0 f the equipment used in

these experiments.

11

iii

TABLE OF CONTENTS

Page

Acknowledgment............................................. 11List of Illustrations...................................... iv

List of Tables............................................. vi

Historical Sketch and Background........................... 1

Purpose and Object of Investigations....................... 5

Apparatus.................................................. 6

Testing Procedure.......................................... 15

Results.................................................... 18Conclusions................................................ 34

Nomenclature............................................... 38Bibliography............................................... 39

Vita. . • • •• • • • • • • . . • • • • • • • . . . • • • • • • • • •• • • • •• • •. • • .• • .•• •• ••• 42.

iv

LIST OF ILIlJSTRATIONS

Fig.No.

1

2

Picture of U-Tube Mercury Guagee •••••••••••••••••••••

Picture of Weighing Tank and Scales•••••••••••••••••••

PageNo.

7

3 Picture of U-Tube Mercury Guages, Weighing Tank

and Scales, and By-pass............................... 9

4 Picture of 6 Inch Centrifugal Pump•••••••••••••••••••• 10

5 Picture of 2 Inch Centrifugal Pump•••••••••••••••••••• 11

6 Picture of Stop Watch on Data Board, Micrometer,

Inside Caliphers, and Thermometer••••••••••••••••••••• 12

7 Picture of Intake from 2 Inch Feed Pipe to Test Pipe,

Also Number One Pressure Takeoff•••••••••••••••••••••• 13

8 Picture of Water nowing From Test Pipe to Weighing

Tar1lc. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • l.4.

9 Drawing of Flow of Wi ter for th Exper ent........... 17

10 Temperatu -visco i ty Curve for Some Common

Liqu.1ds••••••••••••••••••••••••••••••••••••.••••..•••• 19

II Temperature-viscosity and Density Cu~ s for ter.... 20

12 Reynold' Number-Friction Factor Chart................ 21

13 Relative Roughness Factors for New Clean Pipe •••••••• 22

14 Friction Factor IIfll and Reynolds' Number•••••••••••••• 23

15 Graph of Vele>city and Reynolds' Number, (Log-Log Plot) 27

16 Or ph of Velocity and Reynolds' Number, (Cooridinate

Graph Plot) ••••••••••••••••••••••••••••••••••••••••••• 28

17 Graph of Pressure Head and Velocity on each

Takeoff, (Log-Log Plot) ••••••••••••••••••••••••••••••• 30

18 Graph of Pressure Head and Reynolds' Number, (Log-Log

Plot)... . . . • .• • • • • • . . • . . . . • • • . . • . . . . . . . . . . . . . .. . . . . . •• 31

19 Graph of Friction Factor "f ll and Reynolds' Number,

(Log-Log Plot) ••••••••••••••••••••.••••••••••••••••••• 32

v

TableNo.

LIST OF TABLES

vi

PageNo.

1 Values of Darcy-Weisbach Friction Factor••••••••.••••• 24

2 Tabulation of Experimental Data••.•••••••••••••••••••• 26

HISTORICAL SKETCH AND BACKGRCUND

Although the origin of the 8 cience of hydraulics is not a

new discovery, the work done in this field was slow in pro­

gress until about the seventeenth century.(l)

(1) Duba, J. G., Formulas for Flow of Fluids, MissouriSchool of Mines Thesis, 8)0, pp. 1-5, May, 1949.

In 1774 a new era in hydraulics was in the making, when

Turin and Bossut established as a fundamental principal that

1

formulae must be deduced from experiment. Bossut' s experimente

were among the first on the flow of water through pipes. Per-

haps the most famous engineer of that day was Antoine de

Che~ who in 1775 developed the basic formula,

v = c -VP'S \ (,1

an ression which carries his name, for the flow in pipe

and open channels.

The development of hydraulics from the seventeenth to

the nineteenth century grew in phenomenal proportions as

countless contributions were made in this field.

In about the middle of the nin teenth century a much

used pipe fomula came into use.

(2.)

Credit for its origin is given to Darcy, Weisbach, Fanning,

or Eytelwein by variQUS authors of the pres nt day. It is

widely known as the Darcy-Weisbach formula and will be so

called in this paper.

At about the same time the law of laminar flow was

first brought to light by Hagen. This work was almost

immediately confirmed by Poiseuille, who expressed his

findings in equation form. In terms of head 10s8, the

equation i ,

2

h - :3~..yL Vf - DJ. g P

(3)

Comparing this equation to the Darcy-Weisbach fonnula, it is

evident that the friction factor is,

(4-)

This relationship has since been Bubstantiated and is in

general use today.

A noticable split in the manner of treatment of hydrau-

lie pipe probl ha tak n pI c sine th 1 tt r part of th

nineteenth century.

JGhn R. Freeman and others were leaders in the detennin-

ation of friction factors and coefficients from experimental

d t. This type of data was widely ccept d and used by

practicing ngineer.

On the other hand, leaders suoh as Bakhm t if, and Rouse

favor a theoretical tr tment of hydraulics.

In the twentieth oentury men like Scobey, d Schoder,

did not continue experiments solely to determine the frieti~n

3

factor or Che~ coefficient. Instead they used their experi-

mental data as a basis for the development of the so called

"exact" or exponential type fonnula.

Since 1883 when Osborne Reynolds performed his cla.ssic

experiments, the parameter which carries hi name,

~ = V D P (5)A(

has proved a boon to the further development of pipe fiow

theory and practice.

Stanton and Pannell of the National Physical Laboratory

in London, ngland, utilized Reynolds number and put it in a

usable form. In 1914 they evolved the much used curve found

by plotting experimental data and corr lating Reynolds number

with the friction factor. other men quickly verified their

It was oon noticed by engineers that pipe roughness

al 0 affect d the friction factor det :nn1nation and new curves

wre plotted from exp rimental data, most of which approximately

par 11el the Stanton and Pann 11 curve in the turbulent flow

region.

Many experiments on th roughnes effect have been mad

since 1930. ikurad s th first to publi h hi finding

in 1933. He noted that th Reyn lds n r-friction f ctor

relation hip in th laminar flow region r main d unchanged,

but that an increase in the relative roughn 8 of pipe cau d

a corresponding increase in the friction factor n the tur-

bulent !.low region. V. L. Streeter published his findings in

1935, on artificially roughened pipe.

Meanwhile engineers interested primarily in the !.low of

water have continued to use long standing formulas such as the

Chezy, Kutter, Darcy-Weisbach, and Hazen-Williams with experi­

mentally determined factors and coefficients.

PURPOSE AND OBJECT OF INVESTIGATIONS

The purpose of this investigation 1s to install a hard

dra'Wll copper pipe approximately i inch in diameter, and

approximately 35 feet long in vertical position.

The copper pipe is to have pressure takeoff points at

various distances along the length of the pipe. The purpose

of thee takeoffs i8 to measure the pressure of the water at

the point of takeoff in the pipe. The water i8 to be forced

into the pipe, and assisted by gravity, thereby causing a

pressur of some measurable quanity greater than absolute

zero pressure.

The discharge was to be by volumetric measurement, as

the pipe was flowing full, through the atmosphere into the

weighing tank.

The object of this invest1gatian is, to study the type

of flow in a v rtical pipe flowing full where gravity a8s1 ts

the lin pressu • The conditions xi ting within a vertical

pipe under free fall are at pre nt unknolm.

The effort of this study is to shed some light on this

unknown subject.

5

6

APPARATUS

The following Figures, 1 through 8 inclusive, show the

apparatus used in making the experimental tests.

Figure 1, page 7 is a picture of the U-Tube Mercury Guages,

numbered 1 to 4 for the 'Way the takeoffs are numbered from top to

bottom on the experimental teat pipe.

Figure 2, page 8 is the picture of the Weighing Tank and

Scales used in the volumetric measurement of water needed to

calculate the rate of discharge for each run.

Figure 3, page 9 is an overall picture of the U-Tube Mer­

cur.y Guages, Weighing Tank and Scales, and By-pass for wat r

wen it ie not needed.

Figure 4 and 5, pages 10 and 11 respectively, show the 6

and 2 inch C ntrifugal Pumps used to furnisl1 'Water for the

experiment.

Figure 6, pag 12, i & pictur of the Stop W. tch on a

Data Board, Micrometer, Inside Caliphers, and Thermometer.

This equipment is used to measure the diameter of the test

pipe, temper ture of the air and water, and th numb r of

seconds needed to run th experiment for a certain number of

pounds of water.

Figure 7, pag 13, shows the entrance of th experimental

test pipe from th 2 inch fe d pipe, d also the numb r one

pressure takeoff.

Figure 8, page 14, shows the water flowing into the

weighing tank during a test run.

Figure 1

U-Tube Mercury Guages

7

Figure 2

Weighing Tank and Scales

8

Figure 3

U-Tube Mercury Guages, Weighing Tank and Scales, and By-pass

9

Figure 4-

6 Inch Centrifugal Pump

10

Figure 5

2 Inch Centrifugal Pump

11

Figure 6

Stop Wtch on D ta Board, Micrometer,

Inside Caliphers, and Thermometer

Figur 7

Intake From 2 Inch Feed Pipe to Test Pipe,

and Number One Pressure Takeoff

1.3

Figure 8

W ter Flowing From Test Pipe Into Weighing Tank

15

TESTING PROCEOORE

The equipment used in making the tests are illustrated

under the heading of apparatus.

The water used in the tests is pumped trom the sump in

the Fluid Mechanics Laboratory, by either the six or tw inch

centrifugal pumps.

There are three valves that can be used in combination

to regulate the flow of water furnished by the pump in use.

In making a test run from beginning to end, first the

diameter of the copper tubing is measured with t he inside

caliphers and micrometer and the measurement recorded. Then

by regulating the flow of the pump in use the reading of the

desired pressure is made wi. thin the range limit of the U-tube

mercury guages. The water furnished by the pumps is allowed

enough ti.me, to stabilize the flow 80 that any disturbance in

the flow will be eliminated. Then readings are recorded of the

differences in the mercury levels of all the pressure takeoffs,

also the height of water to the mercury in each tube connecting

the takeoff of the copper test pipe has to be recorded and sub­

tracted from the pressure head reading, because these tubes are

always filled with water, thereby causing a greater pressure than

is possible at the point of takeoff. The air temperature is

recorded at the beginning of the run and as often as needed

during the experiment. The water temperature 1s recorded at

the end of the te t run.

16

The weighing of water is taken in the following manner.

There should be enough weights placed on the scale to ov rbalance

the weighing tank, the water is then passed from the by-pass into

the weighing tank, and the instant the water flowing in, balances

the scales the stop watch is started, then a known weight is placed

on the scales, when the water balances this known weight the stop

watch is stopped, then by using the by-pass the water is diverted

back to the sump for further use. From this method you have your

known amount of water in the number of seconds indicated by th

stop watch. This last procedure is run two or more times de­

pending on the accuracy needed.

The readings of the U-tubes should be watched during the

run to see that there has been no change of reading duri g the

experiment.

The drawing Figure 9, following this page is a overall

drawing of the flow of water that is used in the experiment.

17

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18

RESULTS

The testing procedure gave the method of taking runs for

this experiment. The following results are a tabulation of 26

runs from the maximum pressure on the number one pressure take­

off, to the minimum pressure of the test pipe, with the test

pipe still flowing full.

The pipe diameter was measured and found to be 0.525 inches,

or 0.04375 feet. The cross-sectional area in square inches is

0.216, or 0.0015 square feet.

The weight of water for all runs was 100 pounds. The weigh­

ing procedure was followed twice for each run. The 100 pounds of

water was a constant figure, but the temperature ranged from 23.5

to 25 degrees Centigrade which gave the weight of water per cubic

foot a varying amount in the second decimal figure.

The distances of the pressure takeoffs 1 to 4, respectively

from the discharge opening are~

32.325 feet or 387.9 inches

24.325 feet or 291.9 inches

16.325 fe t or 195.9 inches

8.325 feet or 99.9 inches

The head of water that is always standing in the takeoff

tubes has to be subtracted from the mercury pressure, and in

the readings for the test runs the mercury heights were taken

from the disch rge opening as the reference datum.

. '.,.(Joo

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Densit.!;1 and Viscosity of Wo.ter- 67478 (,7 45

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. FT .v.>LuES or (VO) t.);1 WATER AT 60·f. (VE OCITY IN SEC x uiAMETEH IN I~ GHES)

20

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YN L S LJM8~R V V,nSCC,DlnFT,V InSEC

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F,!vr" It-FrictIon FCClors fer An) Kind and SIze of Pipe

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43

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PIPE DIAMETER IN FEET, D.1 .2 ~ 4 S 6 .8 I 2 3 4 S6 8 10 2025

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FIe.. 1.3 RELATIVE ROUGHNESS FACTORS FORNEW CLEAN PIPES

,J:'X

ABSCISSA SCALE

~=Kinem~ticViscosity

QG=Discharge:n U.S·9P·mQB =- Di5-charge In b:'1. ::Je r :'r.R -:: Reynold's Ncn:'er

UNITS FOR MAIN

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p :: Viscosity in poises

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Table 1 (2)

L V2.Valu 8 of f in the Darcy-Wei bach Fonnula, h - ft - 0 2.9

For water flowing in straight smooth pipe

Dia.of Pipe Mean Velocity (V) in Feet per SecondIn Inches

0.5 1.0 2.0 3.0 4.0 5.0 10.0 15.0 20.0

1/2 0.042 0.038 0.034 0.032 0.030 0.029 0.025 0.024 0.023

3/4 .041 .037 .033 .031 .029 .028 .025 .024 .023

1 .040 .035 .032 .030 .028 .027 .024 .023 .023

1 1/2 .038 .034 .031 .029 .028 .027 .024 .023 .023

.2 .036 .033 .030 .028 .027 .026 .024 .023 .022

.3 .035 .032 .029 .027 .026 .025 .023 .022 .022

4 .034 .031 .028 .026 .026 .025 .023 .022 .021

5 .033 .030 .027 .026 .025 .024 .022 .022 .021

6

8

.032 .029 .026 .025 .024 .024· .022 .021 .021

.030 .028 .025 .024 .023 .023 .021 .021 .020

10 .028 .026 .024 .023 .022 .022 .021 .020 .020

12 .027 .025 .023 .022 .022 .021 .020 .020 .019

14 .026 .024 .022 .022 .021 .021 .020 .019 .019

16 .024 .02; .022 .021 .020 .020 .019 .019 .018

18 .024 .022 .021 .020 .020 .020 .019 .018 .018

(2) King, H. W., Wisler, c. 0., and Woodburn, J. G. Hydraulic.5th Ed. N. Y., John Wil y and Sons, Inc., 1948, p. 184.

25

The openings in the wall of the test pipe for the pressure

takeoffs was approxiJnately five sixty fourths of an inch.

Figures 10 and 11, pages 19 and 20 respectively were used in

calculating ReYnOlds I number for all t he runs.

Table 1, page 24, and Figures 12, 13, and 14, pages 21, 22,

and 23, respectively, are relationship curves of Reynolds'

number-friction factor, friction factor f, and the relation of

relative roughness.

Tabl 2, page 26 is the tabulation of the experimental

data, a.nd gives the Temperature in degrees Centigrade, Weight

of water per cubic foot for that temperature, Run number, Average

time for each run, the calculated Discbarge, Velocity, Reynolds'

number and pressure for each takeoff. The Reynolds I number was

calculated by using Figures 10 and 11, density and viscosity

charts.

Figures 15 and 16, pages 27 and 28 respectively, are both

graphs of Reynolds' number and Velocity. The plottil18 of the

graphs was done on log-log, and coordinate graph paper. The

dat~ for these graphs was taken from Table 2, page 26.

The explanation and proof is on page 29, and it clearly shows

that the experiment is following the mathematical equation form of

y =mx + b, wh re m is the slope of the line, and b is the intercept.

Assuming the friction factor f to be 0.02. The head loss is

then found by using equatio (2), page 1 in terms of velocity. The

velocity is then foun for the point of takeoff by using Bernou.ll:i'

theorem.

TABLE 2

TABt~TION OF EXPERIME.7AL DATA

Run Temperature Weight e! Water Average Time DiSCharge, Q, in Velocity, V, in Reynolds' Pressure in Feet of Water for each Takeoff

Number Degree Centigrade per Cubic Feot in Seeond8 Cubic Feet per Seeend Feet per Second Number Number 1 Number 2 Number 3 Number 4

1

2

3

4

5

6

7 (Mcu)

8

9

10

11

12

13

15

16

17

18

19

20

21

22

23

2425

26 (Min-)

2J.O

24.0

25.0

24.5

24.5

25.

25.

25.0

25.0

25.

25.0

25.

25.0

25.025.0

25.

62.24

62.24

62.23

62.22

62.21

62.22

62.22

62.22

62.22

62.21

62.21

62.21

62.2162 0 21

62.21

111.4

138.0

85.0

91.8

74.8

64.6

65.5

68.3

70.2

80.3

81.9

85.7

90.5

105.8

115.3136.1

166 0 6

0.014

0.017

Q.012

0.019

0.018

0.021

0.025

0.025

0.024

0.023"

0.023

0.021

0.021

0.020

n.n20

0.020

0.019

0.019

0.018

0.018

0.017

0.016

0.015

O.OIL

0.012

O. 10

9.33

1 .33

8.00

12.67

12.00

14.00

16.67

16.67

16.00

15.33

15.33

14.00

14.00

13.33

13.3'3

13.33

12.67

12.00

12.00

1 .33

10.67

10.00

9.33

8.00

39,810

47,933

33,845

54,f.9f:

52,338

61,665

72,706

72,706

69,784

66,861

65,511

59,827

61,061

58,714­

58,714-

5 ,714

55,807

55,8CY7

52,855

52,855

49,904

46,997

44,0/J:J

41,095

35,237

29,379

- 11.98

- 3.4-1 - 0.91

- 17.96 - 12.10

+ 1.96 + 27.65

- 1.44 ... 0.58

... 11.95 of. 9.86

~ 26.62 + 19.53

• 24.99 + 18.30

+ 21.J1 + 15.71

... 18.03 + 13.40

;- 13. '53 9 .71

+ 12.16 8.90

... 10.65 + 7.81

+ 9.15 + 6.58

+ 7.79 + 5.63

+ 6.43 + 4.53

... 4.66 + 3.30

+ 3.55 + 2.35

+ 1.66 ... 1.26

... 0.56 + 0.17

- 1.35 - 0.93

- 4.49 - 3.51

- 7.48 - 5.29

- , 0.90 - ~.28

- 15.81 - 11.83

- 20.34 - 14.01

- 0.51

+ 1.94

... 4.44­

... 6.72

i- 13.52

t 12.44

+ 10.53

+ 9.04

+ 6.72

... 6.03

... 5.21

l' 4.54

... 3.85

+ 3.17

l' 2.35

T loll?,

l' 0.85

+ 0.1?

- 0.79

- 0.29

- 4.25

+ 0.94

+ 0.12

+ 3.26

to 6.81

+ 5.45

... 4.63

+ 3.26

+ 2.98

i- 2.58

... 1.76

of" 1.61

of' ] .21

t 0.80

t 0.39

- 0.02

- 0.83

- 2.22

- 2.M

- 3.98

- 4.94

100 I .

80

+0

I 0 -I'-~---+-ri-

~"-

~

2

II .IIO~

"I

~

n urn he I" (g)

28

,._-I

-_Q_~Ii) . - ---t::::s

.c

- ---- Q ,-....,....~-crr

""-­~ll)

-Q~

-CJ-~II) ~

- ---.- jI

I

I.- .I

III

I

JII

tI

0- _1..

J'~ft-~~-L~:I~I (I\) 1l-lIJ OI<l/\ I

1 I II I

II

----~-I

~_ . slope:::m

1

lj=mX+b

Velocit~ YS. ReljnoJds ' number

R = Vd (J = V de- l' -r

Coor-dinate Gr-Qph Plot

V= R -'V V- d P

when V= 0 B =0

UJr,e n V::. 3.. R :: Id (0

A(dP= sloF e

o = ,'Yl t e Ii' C e pt 0.tor "9i nof coord'lnQtes,

29

Log- L09 Gro.ph Plot

LogV = L09 R +Logif

s J 0 Fe ~ 1: 1

y = V = cl1' VAn9le tanned:: 45°

11. 0

J} I

~'l I,.-fniH oj;q tt-..,..I~~:-~+H--t4

'" ~O - - SO 4-0 .so ~O·~ 'f0 60 0

Ve' D,C ;t~

f-.

.'fl,

I

f-,j .., •._- ~

--

10

'107 -.-'

,t - -

ir

of

, _. t

I.!

- _I _. _I

r' _. I..

t.,O

~e~ no Ids'

. ..... - ....._~.

- .'

- --_. -- ,--..~--:-

-+-"---~-------

. ~ -'- -I

--_.--J--------

t-'-'~-+-+--+..I' I -E-~-~' -1 ._.

I ' •f-.................· -L-.-+-ro+--- -~----II- f 1 I ~___._-=~f:---.-~~-._-_-.-_--.-_--,,-+---.....-----l-,-.------r--+-..,-JH-........--~::--+.f_--'~-'_,_-_-It-~_'_i.__--:--+-+4__..er..,...a:--,,4

~_._-

.. '-_ ..I

----,r----- - . _.,.-

__ J

.--

,- ---_. -....,.-- ---~.-

--~-' ------"---------f----.'-'L..-...:...--::;...

;r--'--~' -'

~-----,.-- - .

-- ~

10'0

I'- -- t----_.. -_.-,

~--~---- .. ---- -t-.-'I'f""'" -

---'-" ------+----j""f-.,..--:ll,.,..--+~rl_•..11,

~ 4 ..-.------:--....:......----:---J----~-----

tU+­(j

34­o

Q)

~

:)Cf)

<J)

~~r----+------------1~------.......-.-.;~-----+-..--...1-1+--~-~---r----+:.,4-t-4-~~-+-~.;..,j~..,.- .....+-+.....+-...,......;.~1o-'-,....-r--H-O"";-+.-.--i!--.:......+--.+ .........r+--+--~n..

50 .sl-'-------,.~---_+_---::-----:;=--'----__r-t-_+_---:--~>_lr___+__--+__r_+_-.....---+_+_-----J-__,.~_+_~

I~

I .

-.. , '.08

,. ··.. ,07t l'

:-.- .09

. . j0'

C

~I.'. I··..~,

01·~-IVI

i dl'.03

I II

I· I, I '1

I

.- -,.0., I

I ' ' I

, Il' I

. - i·f)5, i

80 90 100.J

80 90

\. III

,_ J

I I

i I

I ,

I ,

I. ,

II

" -

\

70

.1

, ,

-.1 ..III

I'1

. I

I'I,

I:I

: , '1I I ._ . !. I - .. I,

e I'1,

: J. 1'; I

. ~ : - !~-l---.------ - --4--+--r' "I'" ,- .. r

I'... . I : 1

, , ~_ G

: .... _... " ,_ la-'"--•. •:::. tI '

"I'" ..

.: I· . '. 'j , .. L;

I ,.I' .. - ~._---~,.. . .

.. !. I"

-- - ~---~

I'

._. .. :!

, t .. ·..-, ,

. .,.... , •• " P.

, .j •

. ',' .. ..-- ~ .. -.., . : t ' ....

• • • .J

: '1.......

I

..

.. '

- ...- _. -- -~-- ~-

1- . :. ,. I.-: ;- -~'7' - -. ~ .

06 ;- --------+~--'-I-'__'•

.07'

10 20., r

__--:.!._-: _._'_.:-ll.~~~-; ..0'; . I.

.05

~." I0+'-"-------'---+------11--- - - ..~--__T_-~-I~10'I"i--

~03 ~.------'''''''-a-..,..--~.

I ~ .

10'........

I ' . I I

I· ";' ,.. : ..I . I' I. , ... j -, . 'I":"j,'" 1,1

"'!i I • r i . I..

j; . I • i. I,Oll...---'-- -.L_........l.-.:~__......L__ ____i'__L ....L..._ ___!__L___I_ __L_'__J..........__l._~·___ll ~ _

10 20 30 +0 .50 60Re~nolds' number (E)I '/n ,a:s un'lts

33

Figures 17, 18, and 19, pages 30, 31, and 32, respectively

are graphs of Velocity versus Pressure, Pressure versus Reynolds'

number, and Friction f ctor versus Reynolds' number. The data

for all of the listed above graphs are taken from Table 2, page

26, ldth the exception of the Friction factor, which was calculat-

ed by using Bernoulli t s equation and the Darcy-Weisbach equation.

Example:

Bernoulli's equation:

2Pl + V1 Sl- -+2g

=

Pl' P2' W, g, V1 , V2, i!'l' and *2 are all known, from this hL can

be calculated. Th n by using th Darcy-Weisbach quation:

~= f ~ y2D 2g

re ~, L, D, V, and g are known, f can be calculated.

34

CONCIlJSIONS

Reference is made to Figures 15 and 16, pages 27 and 28,

r spectively. These graphs of Velocity versus Reynolds'

number are the result of plotting experimental data, and follow

the analytical proof shown on page 29.

From the conditions of the experiment, the coordinate graph

plots on a slope of ~ , and passes through the origin ofd~

coordina.tes. The log-log plot of the data forms a 45 degree angle

with the horizontal. The intercept is not the origin of the axis

as it is in the preceeding case.

The proof clear~v shows that the data follows the mathe-

matioal equation form. of y = mx+ b. In this case of the coordi-

nate graph plot the intercept b is 0, the slopem of the line is

~. In the case of the log-log graph plot the velocity ha acAPvalue ofd~' when the Reynolds' number has the value ot 1.

Example:

Given: A Velocity

To find: The Pressure

(A)

R ~'-V=X.B =f(V)

35

R

(B)

R= f (P)

This equation will give a series of curves.

f(p) = f(v)

The result of a combination of (A) and (B), which are

empirical and analytical, will produce a graph (C), which will also

be a series of curves.

(e)

v

The result of t he combination of (A) and (B), will produce

a series of curveeon the graph (C). In the range of the experi­

mental data contained herein the Reynolds' number is practically

a straight line. For this reason, in fitting the curves to the

experimental data straight lines were used.

The graphs of Pressure versus Velocity, and Pressure versus

Reynolds' number a1 0 indicated that there is no shock existing

in the reversal of flow from negative to positive pressure.

36

The intersection of the curves on the plots of Pressure

versus Reynolds' number and Pressure versus Velocity indicate

the point at which the transition from negative to positive

pressure takes place. The crossing of all the lines at one point

would suggest that the Reynolds' number for all the takeoffs

would be constant at that particular point.' Therefore, the

Reynolds' number is constant at the point of reversal of flow

from negative to positive pressure. This graph indicates that

there is only one velocity, at which the pressure is t e same for

all the takeoffs on the test pipe. This pressure is zero guage

pressure. Any velocity greater than this critical velocity, a

positive pressure exists within the entire length of the te t

pipe. Any velocity less than the critical velocity a negative

pressur xists within the ntire length of the test pipe.

Figure 19, page 32 is a log-log plot of Friction factor

versus Reynolds' number. The calculated Reynolds' numbers of the

experiment showed that the flow was in the turbulent region.

There has been no opportunity to examine the interior of the

test pipe to determine if pitting has occured. It is believed

that any change of the interior of the pipe is due to corrosion

alone.

Practical application applied to a vertical pipe flowing full

in a f ctory building where on t\'o'O or more floors there are active

takeoffs of a liquid.

The diameter, roughness, and the various other factors in­

volved held to a minimum, the flow of the liquid can be regulated

so that the pressure c an be equalled on every floor, and that a

37

positive pressure maintained at all takeoffs. The elimination of

negative pressures at various points on the line prevent a back­

flow, or siphon action on the operating equipment.

The writer woul.d like to recommend that in future experiments

in this line to vary the diameter of the test pipe, both larger

and smaller diameters used. To use liquids of different viscosi­

ties. Also, to increase the length of the test pipe, within the

limits of the building space used for experimentation.

From a combination of data of the above variations, additional

information could be detennined and used in design problems of

other pipes of different diameters, and different viscosities with

the utmost confidence.

NO NCLA'lURE

---------- e of cross section

D Diameter in feet

38

d

f

g

H

h

Diameter in inches

Darcy-Weisbach friction factor

Acceleration due to gravity

Total head

Head

hf ---------- Head loss due to friction

~ ---------- Pressure head

bv --------- Velocity head

LengthL

P Tot pr ssur

p ------ Unit pressure

Pf ---- Pressure drop in psi

Q ----- Discharge in cfs

Reynolds' numb r

T ---- Temperature in degrees centrigrade

t Time in seconds

v --------- Velocity in teet per second

UT, 2S ----- Specific weight

A( ---- Absolute viscosity

11 ----- Kinematic viscosity

~ ------- Density

39

BIBLIOGRAPHY ON THE FLOW OF

INCOMPRESSIBLE FllJIDS IN PIPES

This bibliography includes only publications in the

English language pertaining directly to the subject for the

period from 1926 to date. For earlier publications the reader

is referred to the fourth listing below.

(1) Bakbmeteff, B. A. Mechanics of Turbul nt Flow.

Princeton University Pr ss, 1936.

(2) Bard 1 1', C. E. Historical ketch of Flow of Fluids

Through Pip • Publication #44, Oklahoma A. & M. Engineering

Experiment tation, tillwater, Oklahoma, April 1940.

(3) Beale, S. L., and Docks y, p. Flow of Fluids in

Pipe. Journal of the In titute of Petroleum. Technologist.

Volume 14, pages 236-262, pril 1928.

(4) Butler, J. B. Descriptive Bibliography on Oil and

Fluid Flow and Heat Transfer in Pipes. Volume 9 Number 4, 1926.

Technical Series Bulletin, Missouri School of Mines and

Metallurgy. 62 pages.

(5) Colebrook, C. G. Turbulent now in Pipes, with

Particular Reference to the Transition Region between Smooth

and Rough Pipe Laws. Journal of the Institute of Civil

Engineers, Volume 12, Number 4, February 1939, pages 133-156.

(6) DaUgherty, R. L. Hydraulics. McGraw-Hill, 1937.

Chapter 8.

(7) Di Tirro, D. A. Fluid Pressure Drop Losses Through

oth Straight Tubing. Product Engineering, Volume 19,

September 1948, pages 117-120.

(8) Dodge, R. A., and Thompson, M. J. Fluid Mechanics.

McGraw-Hill, 1937. Chapter 8, and 9.

(9) Heltzel, W. G. Fluid Flow and Friction in Pipe

Line. Oil and Gas Journal. Vol. 29, No.3, June 5, 1930,

page 203.

(10) Kemler, E. Study of Data. on Flow of Fluids in Pipes.

Transa.ctions of A.S.M.E., Vol. 55, Hydraulics, 1933, pp 7-32.

(11) King, H. W., Wisler, C. 0., and Woodburn, J. G.

Hydraulics, 5th ed., 1948. John Wiley & Sons. Chapter 7.

(12) Lea, F. C. Hydraulics. dward Arnold & Co.,

London, 1938. Chapter 5.

(13) Lee, C. H. The Flow of Vi cous Liquids Th ough

Pipe. ngineeri • Volume 125, No. 25, pp 498-499, pril 27,

1928.

(14) MOody, L. F., Friction Factor for Pipe Flow. A. S. M. E.

Transactions, 1944, Vol. 66, pp 671-684.

(15) Moody, L. F. Approximate Formula for Pipe Friction

Factors. Mechanical Engineering, Vol. 69, December 1947, pp 1005­

1006.

(16) Nikuradse, J. Laws of Fluid Flow in Rough Pipes.

(A translation from an article published in German in 1933)

Petroleum ngineer, Vol. 11, March pp 164-166; &3", PP 75,78,80,

82; June, pp 124, 127-128, 130; July, PP 38, 40, 42; August

1940, PP 83-84, 87.

(17) Nissan, A. H. Flow of Liquids under Critical Condi 10ns.

Journal of the Institute of Petroleum, Vol. 28, PP 257-273, November

1942.

(18) Pigott, R. J. •

41

Flow of Fluids in Closed Conduiis•

Mechanical Engineering, Vol. 55, August 1933, pp 497-501.

(19) Towl, F. M. f. The Pipe Line Flow Factor in the

Hydraulic Flow Formula (Darcy-Weisbach) and Its Relation to

Density and Viscosity. 26 Broadway, N. Y.

(20) Vennard, J. K. Elementary Fluid Mecha.nics. John

Wiley & Sons, 2nd ed., 1947. Chapter 8.

(21) Pipe Friction-Tentative Standards of Hydraulic

Institute. Hydraulic Institute, N. Y., 1948, 82 pages.

VITA

Robert Franklin Tindall, Jr. was born on September 4,

1925 at Sa! t Joseph, Missouri, the son of Robert and

Virginia Tindall.

He received his grade school education in the public school

at DeKalb, Missouri. Further education was received in the

pUblic school at Saint Joseph, Missouri. In June 1943 he

graduated from Benton High School, then w:>rked for the summer

until September, 1943.

t that time he enlisted in the Un1ted States Marine Corps

Reserve and served as a Field Artillery Fire Control Operator

lxnti1 his honorable discharge in December, 1945.

In January, 1946 he enrolled at aint Joseph Junior College

and gr du ted from there with a Sixty Hour (60) Certificate in

Science in June, 1947.

In June, 1947 he enrolled at Missouri School of Mines and

Metallurgy and graduated from there with the degree of Bachelor

of Science in Civil Engineering in Yi&Y, 1949.

He was married to Lorene Kathryn Beger, daughter of Mr. and

Mrs. H. E. Beger of Saint Joseph, Missouri, in August, 1948.

Upon graduation he accepted a tour of ctive Duty with the

United States ~.

In September, 1949 he enrolled in the Graduate School of

the Missouri School of Mines and Metallurgy and has been in that

capacity to date.