optimal dimensions of pennsylvania highway drainage inlet
TRANSCRIPT
Lehigh UniversityLehigh Preserve
Fritz Laboratory Reports Civil and Environmental Engineering
1978
Optimal dimensions of pennsylvania highwaydrainage inlet gratings, April 1978A. W. Brune
A. W. Spear
K. C. Loush
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Recommended CitationBrune, A. W.; Spear, A. W.; and Loush, K. C., "Optimal dimensions of pennsylvania highway drainage inlet gratings, April 1978"(1978). Fritz Laboratory Reports. Paper 486.http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/486
COMMONWEALTH OF PENNSYLVANIA
Department of Transportation
Bureau .of Materials, Testing and Research
Leo D. Sandvig - DirectorWade L. Gramling - Research Engineer
Charles J. Churilla - Research Coordinator
PennDOT Research Project 74-2Optimal Dimensions of Inlet Gratings
OPTIMAL DIMENSIONS OF PENNSYLVANIA HIGHWAYDRAINAGE INLET GRATINGS
byArthur W. BruneAndrew D. SpearKenneth C. Loush
This report was prepared in cooperation with the PennsylvaniaDepartment of Transportation and the Federal Highway Administration
The contents of this report reflect the views of the authors whoare responsible for the facts and the accuracy ,of the data presentedherein. The contents do not necessarily reflect the official viewso.r policies of the Pennsylvania Department of Transportation or ofthe Federal Highway Administration. This report does not constitutea·standard, specification, or regulation.
Lehigh University
Office of Research
Bethlehem, Pennsylvania
April 1978
Fritz Engineering Laboratory Report No. 401.2
6
Technical ~eport Documentation Page
1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.
FWHA-PA-RP-74-24. Ti tie and Subti tl e 5. Report Date
OPTJMAL DJMENS IONS OF PENNSYLVANIA HIGHWAYDRAINAGE INLET GRATINGS
April 19786. Performing Organization Code
FEL 401.2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~8.Pe~ormin9 Organi%~ion Report No.7. Author' $)
Arthur W Brune, Andrew D Spear, Kenneth C Loush9. Performing OrganizQtion'Name and Address 10. Work Unit No. (TRAIS)
Final Report
11. Contract or Grant No.
. PA-RP-74-2
14. Sponsoring Agency Code
Fritz Engineering Laboratory 13Lehigh UniversityBethlehem, FA 18015
Pennsylvania Department of Tr'ansportationHarrisburg, PA 17120
12. Spons'oring Agency Nom. and' Address
13. Type of Report and Period CoveredI----~-~----------------------_........---...
15. S4Pplemen-tary Notes
Prepared in cooperation with the U S Department of Transportation,Federal Highway Administration
16. Abstract
The results of testing an experimental model are presented about the optimaldimensions of gratings on drainage. inlets that are installed in triangular channels, both grassed and paved, along highways. Each channel was on a grade ofeither 0.5%, 2%, or 4%.
Each grating was a half-scale model of the prototype. The capacity of eachgrating was obtained by actual m~asurement. The width of each grating, 36 in. forthe' prototype in a paved channel and. 48 in. in a grassed channel, was held constant throughout the tests whereas the length of grating 'ranged from 18 in. to48 in.
The tests showed that, with an increase in length of the inlet, the capacityincreased; the increase depends also upon the grade of the channel, the swaleslope, and the back slope. In a grassed channel equal side slopes carry morewater than unequal side slopes; both at slopes of 6:1 are superior to both at 12:1;and a flat grade enables more water to enter a grating than a steep grade. A goodmodulus of th~ capacity of an inlet is that flow rate of which 98% enters into theinlet and 2% bypasses the inlet.
17. Key Words
Capacity of inlets, ,channels, drainage,design capacity, efficiency, grat~ngs,
. highway drainage, inlets, model tests,models, runoff, water
18. Oi stri bution Statement
No restrictions. This document isavailable to the public through the
.National Technical Information Service,Springfield, VA 22161.
19. 'Securi ty Clossif. (or thi s repart)
Unclassified
20. Security Classif. (of this page)
Unclassified
21- No. of Pages 22. Price
102
Form DOT F 1700.7 (8-72) Reproducti on of comp Ieted page authori zed
ABSTRACT
The results of an investigation on an experimental model are presented
about the optimal dimensions of gratings on highway drainage inlets that are
installed in channels along highways in Pennsylvania.
The channel considered was triangular in shape with swale slopes rang
ing from 48:1 to 12:1 for the paved channel and from 12:1 to 6:1 for the
grassed channel and with back slopes ranging from 3:~ to 1/8:1 for the paved
channel and from 6:1 to 1/2:1 for the grassed channel. The grade of the
channel was either 0.5%, 2%, or 4%.
Each model grating was built to half of the scale of the prototype.
Through model laws other prototype-model relationships were established.
The capacity of each grating was obtained by actual measurement. The width
of each grating, 36 -in. for the prototype in a paved channel and 48 in. in
a grassed channel, was held constant throughout the tests whereas the length
of grating ranged from 18 in to 48 in.
The tests showed that, with an increase in -length of the inlet, the
capacity of the-inlet increased; the increase depends also upon the grade
of the channel, the swale slope, and the back slope. Additionally, in a
grassed channel equal side slopes carry more water than unequal side slopes,
that both at slopes of 6~1 are superior to both at 12:1, and that a flat
grade enables mor~ water to enter a grating than a steep grade. A good
modulus of the capacity of an inlet is that flow rate of which 98% enters
into the inlet and 2% bypasses the inlet.
ii
TABLE OF CONTENTS
ABSTRACT
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
1. INTRODlJCTION
1.1 PROBI..ID-f STATEMENT1.2 BACKGROtJ~m
1.3 OBJECTIVES
2. MODEL LAWS
2.1 GE1-lERAL REMARKS2.2 HYDRAULIC SIMILIT1JDE
2.2.1 Geometric Aimilitude2.2.2 Kinematic Similitude2.2.3 Dynamic Similitude
2,3 DIMENSIONLESS ~rrmrnERS
2.4 FROUDE MODEL LAW2.5 MANNING MODEL T..AW2.h CONCLUDING REMARKS
3. MODEL ROlTGHNESS
3• 1 GENERAL REMARKS3.2 FINDING AN APPROPRIArE ARTIFICIAL SURFA~E
3.2.1 "Astroturf"3.2.2 Test Procedure3.2.3 Results and Conclusions
4 • EXPEF..I'MENTAL INVESTIGATION
4.1 LABORATORY EQUIPMENT
4.1.1 General Requirements of the Model4.1.2 Apparatus4.1.3 Model Construction
4 •2 THE DRAINAGE INLET
4.2.1 The Drainage, Inlet in Grassed Channels4.2.2 The Drainage Inlet in Paved Channels
iii
ii
iii
v
vi
1
123
5
56
677
89
1014
15
1515
161617
18
18
181923
26
2631
4.3 PROCEDURE
4.3.1 Flow Measurements4.3.2 Depth and Width Measurements4.3.3 Technique
5. RESULTS
5.1 INTRODUCTION5.2 INLt;T TIl GRASSED CHANNEL WITH MILD SLOPES5.3 INLET IN GRASSED CHANNEL WITH STEEP SLOPES5 .4 NOMINAL CAPACI'I"f OF GRATINGS IN GRASSED CHANNELS5.5 rnLET m PAVED CHANNEL '
6. DISCUSSION
6.1 REMARKS6.2 rnLET IN GRASSED CHANNEL WITH MILD SLOPES6.3 INLET:rn GRASSED CHANNEL WITH STEEP SLOPES6 .4 NOMINAL CAPACITY OF INLET IN GRASSED CHANNEL6.5 INLET IN PAVED CHANNEL6.6 PHOTOGRAPHS OF FLOW TO AN INLET
7 • CONCLUSION
7 • 1 mLET m GRASSED CHANNEL WITH MILD SLOPES7 .2 TIlLET IN GRASSED CHANNEL WITH STEEP SLOPES7 .3 NOMINAL CAPACITY OF INLET IN GRASSED CHANNEL7.4 INLET m PAVED CHANNEL7.5 ARRANGEMENT OF GRATING BARS
8. RECOMMENDAT'IONS
9 • ACKNOWLEDG'El1ENTS
10. NOMENCLATURE
11. BIBLIOGRAPHY
12 • APPENDIX
iv
34
343638
40
4041426064
69
696971727274
79
7979808181
82
83
84
85
86
Table
2.1
3.1
5.1
5.2
5.3
5.4
5.5
5.6
5.7
6.1
A.2
A.3
A.4
A.5
A.6
A., 7
LIST OF TABLES
Mddel Scales for Froude and Manning Similitudes
Experimental Results for tlAstroturf" Manning Roughness
Capacity of Prototype Gratings in Grassed Channels, MildBack Slopes (English Units)
Specific Capacity of Prototype Gratings in Grassed Channels,Mi.ld Back Slopes (English Units)
Capacity of Prototype Gratings in Grassed Channels, SteepBack Slopes (~nglish Units)
Specific Capacity of Prototype Gratings in Grassed Channels,Steep Back Slopes (English Units)
Nominal Capacity, Q~8' of Gratings in Grassed Channels, DressedSlopes (English. Units)
Capacity of Prototype Gratings in Paved Channels (English Units)
Specific Capacity of Prototype Gratings in Paved Channels(English Units)
Flow in a Paved Channel; Prototype Flow Rate
Capacity of Prototype Gratings in Grassed Channels, MildBack Slopes (S1 Units)
Specific Capacity of Prototype Gratings in Grassed Channels,Mild Back Slopes (SI Units)
Capacity of Prototype Gratings in Grassed Channels, SteepBack Slopes (8I Units)
Specific Capacity of Prototype Gratings in Grassed Channels,Steep Back Slopes (5I 'Units)
Nominal Capacity, Q98' of Gratings in Grassed Channels, DressedSlopes (8I Units)
Capacity of Prototype Gratings in Paved Channels CSI Units)
Specific Capacity of Prototype Gratings in Paved Channels(SI Units)
v
11
17
44
48
52
56
64
65
66
74
88
89
90
91
92
93
94
LIST OF FIGURES
Figure
2.1
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
5.1a5.1b5.2
5.3
5.4
5.5
5.6
5.7
Similitude of Highway Inlet Gratings
Schematic Diagram of Model
Cutaway View of Testing Apparatus
Testing Apparatus
Upstream View of Testing Apparatus
Upstream End of Model Apparatus
Inlet Grating for Grassed Channel with PrototypeDirnens ions
Installation of Model Grating in Grassed Channel
Inlet Grating for Paved Channel with Prototype Dimensions
Installation of Model Grating in Paved Channel
Sample Data Sheet-for Flow at Inlet with Dressed Slopes
Device for Measuring Depth and Width of Water
Dr~ssed Slopes Adjacent to InletInlet with Nondressed SlopesCapacity vs. Length of Grating, Grassed Channels with MildBack Slopes; Prototype; 0.5% Grade
Capacity VB. Length of Grating, Grassed Channels with MildBack Slopes; Prototype; 2% Grade
Capacity vs. Length of Grating, Grassed Channels with MildBack Slopes; Prototype; 4% Grade
Specific Capacity vs. Length of Grating, Grassed Channelswith Mild Back Slopes; Prototype; 0.5% Grade
Specific Capacity vs. Length of Grating, Grassed Channelswith Mild Back Slopes; Prototype; 2% Grade
Specific Capacity vs. Length of Grating, Grassed Channels withMild Back Slopes; Prototype;· 4% Grade
6
20
22
24
27
27
29
30
32
35
37
4343
45
46
47
49
50
51
5.8 Capacity vs. Length of Grating, Grassed Channels with Steep Back 531Slopes; Prototype; 0.5% Grade
vi
Figure
5.9 Capacity VB. Length of Grating, Grassed Channels with Steep 54Back Slopes; Prototype; 2% Grade
5.10 Capacity VB. Length of Grating, Grassed Channels with Steep 55Back Slopes; Prototype; 4% Grade
5.11 Specific Capacity VB. Length of Grating, Grassed Channels with 57Steep Back Slopes; Prototype; 0.5% Grade
5.12 Specific Capa-city vs. Length of Grating, Grassed Channels with 58Steep Back Slopes; Prototype; 2% Grade
5.13 Specific Capacity vs. Length of Grating, Grassed Channels 59with Steep Back Slopes; Prototype; 4% Grade
5.14 Efficiency of Inlet Gratings VB. Flow Rate in Grassed Channels 61with Dressed Slopes; Prototype; 0.5% Grade
5.15 Efficiency of Inlet Gratings VB Flow Rate in Grassed Channels, 62with Dressed Slopes; Prototype; 2% Grade
5.16 Efficiency of Inlet Gratings vs Flow Rate in Grassed Channels 63with Dressed Slopes; Prototype; 4% Grade
5.17 Capacity vs. L~ngth of Grating, Fave.d' Ch_a.nnels~ Prototype; 67Grades of O~5%, 2%, 4%
5.18 Specific Capacity VS~ Length bf Grating, Paved Charinels; 68Prototype; Grades of O~5%, 2%, 4%
6.1
6.2
6.3
6.4
6.5
Flow in a Paved Channel;
Flow in a Paved Channel;
Flow in a Paved Channel;
Flow in a Paved Channel;
Flow in a Paved Channel;
0.5·Q( )max
Q(max)
2 Q(max)
2.5 Q(max)
3 Q("max)
vii
76
76
77
77
78
1. INTRODUCTION
1.1 Problem Statement
Runoff along highways from precipitation must be removed
from the paved surfaces and adjacent areas. The surface runoff is
channeled into drainage inlets and is removed by way of a subsurface
system of conduits.' The drainage inlets are spaced along the road
way at intervals which are determined by the design engineer.
Two difficulties exist with inlets currently being installed
in drainage channels by the Pennsylvania Department of Transportation:
{l) water bypasses the inlet owing to the fact either that the inlet
is too narrow or that the inlet spacin~ allows too large of a flow to
accumulate in the channel; and (2) part of the inlet grating is not
covered entirely with water at times of high flow.
In consideration of these problems, a program of research was
undertaken using a channel, that was either paved or grassed, to deter
mine the optimal ratio of length:~idth of grating based upon the effi
ciency of the inlet in catching the water flowing in the channel. The
,back slopes of a channel ranged from 1/2:1 to 12:1 and ,the swale slopes
ranged from 6:1 to 48:1; the side slopes were not necessarily the same
for both grassed and paved channels. The lengths of the prototype inlet
ranged from 18 to 48 inches. The widths of the inlet were 48 inches in
the grassed channel, and 36 inches in the paved channel.
1
1.2 Background
The problem of draining ,highway areas has been solved
commonly by employing empirical or intuitional approaches, notwith
standing that drainage systems are of paramount importance in high
way design. Drainage channels and inlets are placed along the road
ways to catch surface runoff and to guide 'it into a subsurface
drainage system. Withqut such d~ainage, flooding would occur
causing damage to the pavement and base materials, deposition of
sediment in low-lying areas, and hinderances to traffic safety.
Until recently, estimation of the capacity of inlet grat
ings had been based on past experience; furthermore, little consi
deration was given 'to different channel configurations or irregular
ities in the channel s~rface. Obviously, the hydraulic performance
of any inlet grating must be known before it can properly be uti
lized along the highway.
PennDOT Research Project 68-31 at Lehigh University en
titled "Development of Improved Drainage Inlets", which also used
a model study, was completed in January, 1973 in accordance with
PennDOT Agreement Numbers 42237 through 42237-H between Lehigh
University and the Commonwealth of Pennsylvania. As a result of
this project, reports were presented to PennDO~ summarizing and
evaluating (1) the results of past papers and studies pertaining
to highway drainage inlets (Yucel, 1969); (2) new capacities for
2
inlets installed in paved channels cYee, 1972), and (3) new capaci
ties for inlets installed in grassed channels (Appel, 19,73).
The investigators noted throughout the investigation that, for
almost all flow rates, some water in the channel bypassed the drainage
inlet because the width of the inlet, perpendicular to the direction
of flow, was too narrow. This bypassing of water could probably .
be prevented by increasing the width of the grating.
Another observation of some importance was that the entire,
grating surface was not utilized in catching water f~owing toward
-it during high flow si,tuations. Part of some bars on
the grating and all of other bars were exposed to the atmosphere in
-many instances. Specifically, those in the downstream portion of
the grating near the channel invert were not covered by water.
Based upon these observations, an investigation was war
ranted to determine the optimal arrangement of the length:width
ratio for an inlet grating which most efficiently utilized the sur
ficial area of the grating and intercepted the maximal amount of
inflow.
1.3 Objectives,
The objectives of this research program are:
1. To develop a single grating for installation in grassed
and paved highway drainage channels based upon maximal
3
surficial efficiency and inflow interception
rates, and
2. To document, by means of photographs, those conditions
which determine the optimal length of each respective
inlet grating for every ·channel configuration.
4
2 • MODEL LAWS
2.1 General Remarks'
Two common procedures used in solving hydraulic problems
are analytical methods and model studies. An analytical method
might be more rapid and perhaps more economically feasible at times;
however, certain situations do not lend themselves to analytical so
lutions owing to their complexity. Model studies, on the other
hand, ca~ simulate the prototype situation while providing visual as
well as statistical' means of evaluation. A model is usually smaller
than the prototype; thus it is cheaper to fabricate. Working with
a smaller apparatus in a controlled environment provides greater
ease in handling, preparation, and repair. For these reasons, a
model study was chosen to' study the highway drainage inlets.
Prior to testing, the similitude between relevant proper
ties of the model and the prototype must be computed, so that events
'which are noted in the model can be properly related to the proto
type. This similitude is determined through model laws. Once the
basic prototype:model scale rat~o is known, data from the model
study can be changed into the associated physical quantities, such
as velocity, discharge, or depth, in the corresponding prototype.
The length ratio of 2:1 was determined for the prototype:
model after considering (a) the space available in the laboratory,
(b) the available pumping facilities, (c) the cost of fabricating
5
and operating a model of that size, (d) the effect of surface
tension, and (e) the facilities were already installed.
It should be noted that the literature available on
model laws is extensive and complete, notably, Stevens et al.
(1942), Graf (1971), Morris (1963), and Hansen (1967), to name a
few.
2.2 Hydraulic Similitude
The correlation between physical quantities in the model
and the prototype is called the similitude. For complete similar~
ity between model and prototype, three similitudes must be satis-
fied:
Om
they are geometric, kinematic, and dynamic similitudes.
Lp
Inlet
MODEL PROTOTYPE
Fig. 2.1 Similitude of ~ighway Inlet Gratings
2.2.1 Geometric Similitude
Two obj ects' are said to be geometrically similar provided
the ratios of corresponding dimensions are equal. For the model
6
and prototype iliustrated in Figure 1, geometric similitude will
exist providedD L
L = --E. = -E.H. D L
m m(1)
where L denotes the length of the inlet, D the depth of flow, and
~ the scale ratio. The subscripts, p and m, indicate prototype
and model, respectively. The similarity between areas and volumes
can be easily obtained as well from the scale ratio:
L 2A
=--E. andR A
m
L 3V
=--E.R V
m
(2a)
(2b)
where A and V are representative area and volume, respectively.
2.2.2 Kinematic Similitude
Two flow regimes are said to be kinematically similar
provided (1) the flow fields have the same shape, and (2) the pro-
totype:model ratios of velocities and accelerations are the same.
2.2.3 Dynamic Similitude
Dynamic similarity exists between prototype and model
provided corresponding forces are parallel and have the same proto-
type:model ratio of forces for all related points in the flow
fields. From Fig. 1 the force ratios can be expressed as:
F' F"F - -E...- - -E...
R - F ' - F 11m m
7
(3)
where FR is the force ratio; F ' and F " are forces in the proto-p p
type, and F ' and F " are the corresponding forces in the model.m m
The forces which can affect a flow field are those due to inertia
F1 , gravity F , pressure F , viscosity F , elasticity FE' and Bur-g p v
face tension FT- Because water is nearly incompressible and because
the model used is fairly large, elasticity and surface tension are
negligible and can be ignored in this study. Thus, ,for complete
dynamic similitude" the following equation must be satisfied:
(Fr ) (F ) (F ) (F )gp P.p v
FR
= P = == =p
(L~ )(FI
) (F ) (F ) (F )g m P m vm m
2.3 Dimensionless Numbers ~
In a hydraulic model study, certain combinations of
variables forming dimensionless numbers are more valuable than in-
dividual variables. In this case, the Euler number of Eu, the
Froude number or Fr, and the Reynolds number or Re are important
dimensionless numbers. These numbers are expressed in the fol1ow-
ing manner:F !J.p L2
!1PEu = --E. = =--FI 2L
2 2pv pv
F 1/2 ~ 2 2)1/2
Fr (-.1.) = pv L v= =(gL)1/2F 3
a pL g
ReFr pV2L2
pvL= -= = --
F lJv L 11v
(5 )
(6)
(7)
8
where p is density, v is a characteristic velocity, 6P is a pres-
sure difference, g is the gravitational acceleration, and 11 is the
dynamic viscosity. Only two of these three dimensionless numbers
are independent, which means that the third number can be obtained
provided the other two are known; thus dynamic similitude is pos-
sible provided two of these numbers are simultaneously satisfied.
Unfortunately, acquiring complete similarity using only two of
these dimensionless numbers is usually impossible owing the limita-
tions, such as certain characteristics of water and the limited
space and facilities available. In most hydraulic engineering
problems, however, some forces are orders of magnitude greater
than others, which allows some relationships to be ignored. In
this way, dynamic similitude can be obtained using but one dimen-
sionles~ number. For this study, the force 'of gravity is considered
greater than the force of friction, which indicates that Froude
similarity alone is sufficient to ensure dynamic similarity between
the model and the prototype.
2•4 Froude: Model ,: Law
The Froude number for both the model and prototype can be
expressed as follows:
vFr = --~~
(gL) 2
P
=v~
(gL) 2m
9
(8)
For equal accelerations of gravity, the resulting velocity ratio
(9a)
is :
~{~)For a scale ratio of 2.0, as used in the present study, the velocity
ratio becomes:
v ~
-E = (2.0) 2 = 1.41v
m(9b)
From Eq. (2) and (9a) the flow-rate ratio can be computed as:
(lOa)
Therefore, with L = 2.0 in this study:
(lOb)
Using this equation with the model flow rate, the corresponding
prototype flow rate can be calculated. A complete list of Fronde
model similaritie's is presented in Table 2.1.
2.5 ,Manning-Model Law
The effect of frictional forces on the flow regime has -
been ignored thus far, yet the frictional effect of the channel
roughness (grass) on the flow pattern must influence the type of
channel flow as well as the efficiency of the drainage inlet.
Hence it would be favorable to consider both the frictional and
the gravity forces simultaneously. As was mentioned in Section
2.3, it is impossible to satisfy the Froude and Reynolds model
10
I-'\--l
_.-- ~l·____-_~-.~
Froude Lehigll t'lap.ning Lehigh Scale Lel1igh ScaleS il!!il ~ t tIde Scale Simi.litude Paved ChClnnel Grassed- Cllannel
-> ~~~~""~"""'--;__T
Len.gell, L L 2.0 1 2.0 2.0.LJr r rI
v'J,.-, CJqj ·rii:J 4J 2 r')
.r-t H Area, A 11 4 .. 0 L "M 4.0 4.0to Q) r r· r:>"\ ,~ ,- --~ 0r---i H~
Volume, V L 3 8.0 L 3 8.0 8.0r r r
Ti.me, T L 1/2 1 .. 41 TJ 1/ 3In 1.47 1.38(,') r r r r
u CJ.- !·,...i ·rl
L 1/2 L 2/3/n.w oW
VelocitJ', v 1.41 1.36 1.27cr1 ~a Q.) r r r rGJ Po.c:: a
·11 H~A-.
or 5/2 L 8/3/nI
Discharge, Q 5.66 5.44 5.10L .r r r r
-
nr
0.0140.012 n
r0.0350.028
Table 2.1 Model Scales for Froude and Manning Similitudes
laws simultaneously provided the same fluid is used in both the
model and the prototype. Another means of correlating friction
and gravity must be adopted.
In open-channel flow, the Manning anal~gy is commonly
introduced, which is derived from the Manning. equation:
1. 49 ~2/3 Sl/2v =
n(11a)
The Manning analogy can be. given for model and prototype as:
(~2~3:l/2)p = (~2~3:l/2)m (lIb)where ~'is the hydraulic radius for the channel, S is the slope of
the energy line, V is the mean velocity, and n is the Manning rough-
ness coefficient. Because geometric and kinematic similitudes ate
present between the model and the prototype, then S = S , and Rm p -11
can be reduced to a suitable dimension L. Therefore Eq. (lIb)
becomes:
(12)
Using Eq. (9a), Eq. (12) can be expressed as
(13)
12
Rearranging Eq. (12) enables the flow-rate ratio to be shown as:
Q (L )8/3 n~ = --E. --E. (14)Q L n
m m m
Pertinent flow characteristics are indicated in Table 2.1.
To solve Eq. (14), the roughness coefficient for the
model and prototype', must be known. The prototyp~ roughness, that of
natural grass in this case, is 0.035 according to Chow (1959). ~
artificial grass known as "Astroturf" was used on the model to
simulate grass and was found to have a roughness coefficient of
0.028, as determined by tes'ts' performed at Lehigh University. The
actual roughness ratio (n In = 1.125) is in close agreement withpm'
the ratio (n In = 1.122) as obtained from Eq. (13). Using thep m
actual roughness ratio and the scale ratio, Eq. (14) becomes for
a grassed channel:
Qn~ = 5.10 (lSa)~
Introducing the n:n ratio and the length ratio, LR
= 2.0,p m
Eq. 14 then becomes for a paved ch~nnel:
~= 5.45Q;n
Turbulent flow is necessary in both the prototype and
the model for the l1anning 'analogy to be applicable _ Nearly all
open-channel flow in nature is turbulent, whereas flow occurring
in a simulating model,might very well be laminar. To ensure
turbulence-, the model should operate in such a way as to yield
a high Reynolds Number, Re.
13
(ISb)
The Reynolds Number ratio is
(Re) (vL)p =
(VL/ = 2.72 (16)(Re)
m m
A preliminary test was performed on the model, from which it was
determined that turbulent flow did exist (Re > 7000).
2. 6 Conclud~ng .~Rem.arJts
Table 2.1 shows that the Froude similitude, involving
gravitational effects, a~d the Manning analogy, involving friction-
al effects, give similar results. Either set of numbers could be
used in this study. Because the gravitational· forces are of ob-
vious importance in this case, Froude similitude has been selected
to transform model results into prototype data.
14
3. MODEL ROUGHNESS
3.1 Grassed Channel
The prototype surface, the highway embankment, is cover~d
with natural grass. Inasmuch as natural grass would be difficult
to install and maintain in a laboratory model, an artificial replace
ment had to be found with roughness characteristics such that its effect
upon the flow regime would be comparable to that of the natural
grass. Fulfilling both the Froude and Manning similitudes, Eq. (13)
can be used to establish the ratio of prototype roughness to model
roughness. Wieh a prototype'Manning coefficient of 0.035 and a
scale ra,tio of 2.0, the model Manning coefficient becomes 0.031,
which is the Manning roughness coefficient that the ar~ificial
surface must have~
3.2 Appropriate Artificial., Surface: "Astroturf"
An artificial surface with a satisfactory Manning roughness
coefficient was readily obtainable; this was "Astrot,urf". "Astroturfll,
a landscape surface produced by the Monsanto Chemical Company, is an
imitation grass measuring 15/16 inch (2.38 em) in height, made of green
pliable plastic strips attached in groups of eight, spaced equidistantly
at 2/5 inch (1.02 em) from each other, and attached "checkerb9ard style"
to a 1/16 inch (O~16 em) thick mat. The strips in each clust~r, collec
tively resembling a small bush. are well tangled and present an overall
appearance similar to that of natural grass having equal height. The
roughness of the "Astroturfll was investigated in a glass-walled rectan
gular channel, 24 feet (7.31 m) long, 18 inches (0.46 m) wide, having a
15
two percent longitudinal slope. A point gage mounted on a carriage which
ran the length of the flume was used to take base level and depth measure-
ments for different discharges. Manometers attached to a Venturi meter
in the supply line indicated the discharge that was flowing for a given
situation. Depth readings, which were found to be constant, were taken
for a series of distances, the measurements indicating uniform flow over
the channel surface.
A description of the artificial turf used and how it was te·sted
follow herewith.
Table 3.1 gives the range of discharges, the correspon~ing
depths, and the calculated Manning roughness coefficients for the
tests here mentioned.
Discharge Depth }fanning
3Roughness
cfs (m /sec) ft (m) Coefficient
0.35 (0. 010) 0.13 (0.040) 0.0310.52 (0.015) 0.17 (0.052) 0.0310.74 (0.021) 0.20 (0.061) 0.0290.98 (0.027) 0.25 (0.076) 0.0301.21 (0.034) 0.27 (0.082) 0.0280.45 (0.013) 0.30 (0.092) 0.0280.69 (0.019) 0.33 (0.101) 0.0281 •.87 (0.052) 0.35 (0.107). 0.028 .,
TABLE 3. 1: EXPERIMENTAL RESULTS FOR "ASTROTURF" MANNING ROUGHNESS
The average roughness coefficient was determined to be
0.028. Apparently, the Manning roughness coefficient of "Astroturf"
had not been previously determined; therefore, a ~omparison with
16
results of other 'investigators was not possible. However, according
to Chow (1959), the roughness coefficient for natural grass ranges
from 0.010 to 0.050; PennDOT, at this time, assumes a coefficient
of 0.035 for calculations involving natural grass. The roughness
coefficient obtained in this study, 0.028, was thus found to be
within this range, and therefore, "Astroturf" was suitable for
use in simulating n~tural grass in the model study.
The Manning coefficient for pavement as used by the Pennsyl
vania Department of Tran~portation is n = 0.014, which is in good
agreement with the .. literature (Chow, 1959). Plywood, 3/4 in. (1.91 em)
in thickness was used in the model to simulate the paved surface of the
prototype. The Manning coefficient of plywood, as determined from flwne
tests performed at Lehigh University to be n := 0.• 012, again is in
accordance with the literature (Chow, 1959). This roughness coeffi-
c,ient was used throughout the study where a paved surface was used.
17
4. EXPERI}mNTAL INVESTIGATION
4.1 Laboratory Equipment
4.1.1 General Requirements of the Model
A full-sized model is ideal in performance tests of dif
ferent inlet openings; however, as mentioned in Section 2.1, owing
to the limitation of the space a~ailable, the cost involved, and the
maximal discharge available in the laboratory, a prototype: model
length ratio of 2:1 was chosen.
Uniform flow was required in the channel upstream from the
inlet; consequently the channel had to be long enough with little
distortion to insure this. Baffles or vanes could be installed at
the headwater of the channel to aid in forming uniform flow •.
The frame supporting the model had to be rigid yet versa
tile. Uncontrolled fluctuations in slopes during testing would lead
to faulty data, whereas controlled slope adjustments were required
to enable a full testing program of the inlet grating. Simple and
rugged mechanisms for changing slopes and inlet grating lengths were
required in order to reduce the time interval between tests.
The surface roughness of the channel must be designed to
resemble closely the surface of the prototype. Tests must be run to
find model surface materials which are easy to handle and which
exhibit Manning roughness c~~fficients that closely resemble those of
natural grass and concrete pavements.
18
For accurate results, care must be taken that no leakage
occurs in the entire system and that flow rates be measured as accu
rately as possible.
4.1. 2 Appa,ratus
A schematic diagram of the testing arrangement is shown
in Fig. 41. Either or both of two pumps (B) raise water from the
main sump (A) into the pressure tank (D). The two pumps can be
operated, separately, in parallel, or in series by adjusting the
three valves (C).
Each pump is driven by a Westinghouse 9B Type HF, 220
volt AC, induction motor equipped with a rheostatic control. One
motor is rated at 40 hp, and the other at 35 hp. During a test,
the pumps were adjusted to a rate of discharge that was constant
over a period of time.
Each pump is a DeLaval single-stage, double-suction, cen
trifugal pump, Type I. One pump had a 10~inch (25.4 em) suction line
and an 8-inch (20.3 cm) discharge line, whereas the other pump had
an 8-inch (20.3 cm) suction line and a 6-inch (15.2 em) discharge line.
The cylindrical pressure tank (D) was 5~ feet (1.54 m) in
diameter, and 34 feet (18.7 m) high. The rate of discharge delivered
19
No
o
F G A -Sump
B "PumpC -Valveo - Pressure TankE - Supply ValveF - Hg- Water ManometerG ~ Liquid-Wate·r Manometer
H - OrificeI - Inlet GateJ - Channel
K - SplitterL - Volumetric TankM- M·onifold Dischar.ge .PipeN- Head Tonk
Fig.4.1 SCHEMATIC DIAGRAM OF li0DEL
Q = 0.428 HO•SOO
(17)
where H is the pressure drop across the orifice in feet of water and
Q is the discharge in cubic feet per second.
From the head tank (N), the water flowed through the
channel (J) toward the inlet (I). The water intercepted by the in
let was directed by a manual splitter (K) into a 420-cubic foot
(11.9 m3) volumetric tank (L). Any flow that bypassed the inlet was
channeled into the main sump (A).
The testing tank which held the model was rectangular in
shape (see Fig. 4-2): 33 feet long (10.1 m), 16 feet wide (4.9 m),
and 3 feet deep (0.9 m). The tank was constructed on ~-inch (0.64 m)
steel plate framed by 3-inch (7.6 em) by 3-inch (7.6 em) angle iron,·
and it rested on 2-inch (5.1 em) by 7-inch (17.8 em) channel beams
21:·
22 '
IIIV
(I)::.J
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I
II
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II
II
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I
I
II
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I
II
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I
I
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which were placed transversely on 4-foot (1.2 m) centers along the
entire length of the testing tank.
The head tank containing the manifold discharge pipe was
2~ feet (0.76 m) long, 16 feet (4.9 m) wide, and 4 feet (1.2 m) deep.
Fig. 42 is a cutaway view of the testing tank, and Fig. 4.3
shows the model placed in the testing tank. A conveyance channel
(R) carried the water intercepted by the drainage inlet to' an open-
ing (T) which was connected to the splitter and thence either to the
volumetric tank or to the main sump. Another opening (D) nearer
the downstream end of the testing tank was connected directly to
the main sump. During the actual testing period, gates 1 and 4 were
closed so that all intercep,ted flow went to the spli tter for measur,e-
ment if desired and all bypassing flow went directly to the main
sump via opening (U).
4.1.3 Model Construction
Two steel frames were constructed to support the swale, .
slope (0) and back slope (P) which formed a triangular channel, as
shown in Fig. 4. Th'e swale and back slopes, which were 28 feet
(8.5 m) long, 12 feet (3.66 rn) and 3~ teet (1.1 m) wide,respectively,
were representations of a similar situation in the prototype, i .'e. ,
the roadside area. Both frames were made of 84 x 9.5 I-beams welded
together. The welded joints were reinforced by clip angles to pre-
vent failure and to minimize deflection. The outer edges of the
23
H
M
H Orifice
(0) Plan View
Q
M Manifold DischargePipe
N Head Tank
o Swole Slope
P Bock Slope
Q Side -Slope AdjustmentRods
R Conveyance Channel
S Main SupportingI-Beam
I Inlet Grates
T· Opening to VolumetricTank
U Opening to Sum'p
tT
·tu
(b) Elevation View
Not to Scale
Figure 4.3 Testing Apparatus
24
frames were made'of 87 x 15.3 I-beams.
Both frames were covered with 3/4-inch (1.9 em) outdoor
plywood.; each piece, measuring 4 feet (1.2 m) by 8 feet (2.4 m),
was treated with preservative and with enamel paint. The joints of
the plywood were covered with 2-inch (5.1 em) self-adhesive tape
which was then also painted'. "Astroturf" was then stapled in long
3-foot (0.92 m) wide sheets to the plywood slopes leaving the drain
age inlet open. Hinges were welded to the invert of the channel to
prevent lateral separation of the swale slope from the back slope,
and also to allow rotation of the frames about the invert whenever
changes in the side slopes were desired.
The invert rested on a W8 x 40 I-beam (8), which is 29
feet (8.8 m) in length and is hinged at its downstream end. The
proper longitudinal slope was obtained by providing the proper
height of support; this was performed by manually placing blocks
under the upstream end of the I-beam with the downstream end being
fixed. A survey using a rod and engineers' level was made to verify
the channel slopes. Support at midspan was added also using blocks
to reduce any midpqint deflection. An overhead crane in the lab
oratory was used to raise the upstream end into position.
The main supporting beam was cut just upstream and down
stream from the inlet (see Fig. 4-3) and a box section, made of the
same type of I-beam was installed to replace the piece that was cut
25
from the main beam. This modification was made to enable the water
intercepted by the inlet to fall directly into the conveyance
channel without splashing over any obstacle and to facilitate e~
placement of the grating itself.
The outer edge of each frame was supported by tw'o 3/4-inch
(1.9 em) threaded tension rods (Q), enabling the changing of each
side slope independently of the other. Layers of ~-inch (1.3 em)
hardware cloth were soldered together to form a I-foot (0.31 m) thick
mat which was placed at the upstream end near the head tank. the cloth
acted as a baffle to aid in developing uniform flow in the channel
upstream from the inlet.
4.2 The':n-tainage IIile-t
4.2.1 The Drainage Inlet in Grassed Channels
The drainage inlet grating for grassed channels and as used
in this study was made of wood with ~iagonal bars (see Fig. 4.6). The
overall drainage inlet size of the model was 36 inches (0.92 m) in
length and 24 inches (0.61 m) in width, corresponding to 72 inches
(1.8 m) by 48 inches (1.2 m) in the prototype. For median slopes the
grating was placed symmetrically with the invert, whereas forswale (cut)
slopes one edge coincided with the invert. The width was held constant;
however, the length of the drain was altered by covering downstream
portions of it with metal plates mounted on triangular wedges which
coincided with the slope of the sides. ~'Astroturf" was attached to
the metal plates to give continuity of surface roughness. A rubber
skirt was installed around the inlet and under the wedges to prevent
leakage. Figure 4.7 shows the installation of a model grating in a
grassed channel.26
Figure 4.4 is a picture of the apparatus looking upstream. The
position of the inlet grating is shown as it was installed in the grassed
median, which in the model is covered with "Astroturf". Dressing of the
slopes adjacent to the inlet is not shown. On the right side is the dis
charge end of the model. The slope near the observer was termed the swale,
and the far one, the back slope.
Figure 4,.5 is a view of the head tank, showing the hardware cloth
that was placed downstream from the tank in order to aid in developing
uniform flow in the channel.
27
Figure 4.4 Upstream View of Tes,ting Apparatus
Figure 4.5 Upstream End of Model Apparatus
28
Fig. 4.6 Inlet Grating for Grassed Channelwith Prototype Dimensions
29
_._-_..._-_.._-...,~ - r. Direction of
SVioie Slope
Flc)\\.f
Back Siope
Rubber Skirt
(b) Elevcltion View
, Figu~e 4.7 Installation of Model Grating in Grassed Channel
~o
4.2.2 The Drainage Inlet in Paved Channels
The drainage inlet grating for paved channels and as used
in this study was made of wood with diagonal bars (see Fig. 4.8).
The overall grating size of the model was 36 in. (0.92 m) in length
and 18 in. (0.46 m) in width, corresponding to 72 in. (1.84 m) by
36 in. (0.92 m) in the prototype. The grating was installed with one
side directly along the invert of the swale slope. The width was held
constant at 18 in. (0.46 m) for the model, while the length of the grating
was altered by covering downstream portions of it with thin metal plates.
A rubber skirt was' installed around the inlet and under the plates to
prevent leakage. The plates were covered with enamel paint to give
continuity to surface roughness. Figure 4.9 shows the installation of
a model grating in a paved channel.
31
I" X 5 11 Strip
I" Woodel1 Rod
-----...--------
iigure 4.8 Inlet Grating for Paved Channelwith Prototype Dimensions
32
1·.
1811
21 11
~t1uG.
2711
30"36
B
42 11
4.8 11
Direction of Flow +-- Curb
Inlet Grating
Swale
Swale
3 "1'4 Plywood
( a) Plan View
(b) Elevation View
Curb
Curb
Figure 4.9 Installation of Model Grating in Paved Channel
33
4 •3 Procedure
4.3.1 Flow Measurements
As mentioned in Section 4.1.2, the flow rate into the head
tank and subsequently into the channel was determdned by reading
manometers attached to a 4-inch (10.2 em) orifice installed in the
supply line. The liquid manometer, which had a specific gravity' of
2.95, was used at low discharges yielding accurate readi~gs, whereas
the mercury manometer, which had a specific gravity of 13.6 was used
. at higher discharges because it fluctuated far less than the liquid
manometer at high flow rates. No particular flow rate was chosen as
a transition point for switching from one manometer to the other.
The switch "was. made during testing for convenience, as the precision
of both manometers was within the accuracy of the other measurements
taken. Figure 4.10 is a sample data sheet used during the study.
Water flowed down the channel and was totally or partly
intercepted by the inlet depending upon the flow rate. The inter
cepted water was then channeled to the split.ter which directed it
to a volumetric tank for measurement or to the main sump for re
circulation. That flow which bypassed the inlet was directed into
the main sump. The total flow, Ql' was calculated either from the mano
meter readings and Eq. 16 or, ~for very low·rates of flow~ as the sum
of Q2 and Q3' The intercepted flow, Q2' determined by measuring water
levels in the volumetric tank over a suitable time interval.. 11le by-
passing flow, Q3' was obtained by taking the difference between Q1 and ~
Q2. Very low flow rates were' determined by noting the time required
to obtain a known volume of water.
34
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I i
37
35
'//(?i "5
4.3.2 Depth and Width Measurements
Depth measurements were taken in the invert at stations
1 ft. (0.31 m), 2 ft. (0.61 m), and 3 ft~ (0.92 m) upstream from the
inlet during each test. A point gage graduated to 0.001 ft.
(0.03 em) was used for all depth measurements. The depth was deter
mined by subtracting the gage reading for the channel bottom at the
invert from the gage reading at the water surface. The point gage
was mounted on an aluminum beam 3~inch (7.6 em) by 5-inch (12.7 em),
which spanned the model perpendicular to the channel invert, and
was supported by a monorail system at each end that enabled it to
travel freely above the channel. This facilitated depth measurements
at any point in the channel.
For this experiment, steady uniform flow was required -up
stream from the inlet for accurate measurements. Near the grating,
reduction in the vertical and lateral dimensions of flow existed ow-
ing to the convergence of the water into the 'grating, thus disturbing the
uniform flow. In this situation, it was desirable to maintain a
cross-sectional area of constant shape. Consequently, width of flow
measurements were taken at the same stations as menti~ned above to
serve as a check. A tape measure mounted on the aluminum beam was
us~d as a range finder together with a plumb bob that was lowered to
the" edge of the wat.er. This is shown in Fig. 4.11.
36
Fig. 4.11 Device for Measuring Depth and Width of Water
37
4•3 •3 TechTlJ.a ue--Before each test, the appropriate longitudinal slope was
set using a surveyor's level as a guide. Next the side slopes were
adjusted as required using a triangular template and a level, and
then the length of the open grating was set. Inasmuch as setting
the longitudinal slope was the most time consuming and difficult
of the adjustments, all tests with the same longitudinal slope were
performed in succession, thus reducing the number of these more
difficult changes to a minimum.
Subsequently, the pumps were started, and the supply valve
was opened to provide a flow rate which was visually determined to
be the maximum flow rate possible without allowing any water to by-
pass the drainage inlet.
After a period 0'£ several minutes had elapsed to allow
steady flow to develop, the splitter was set to direct the inter-
cepted flow into the volumetric tank for 60 seconds. The increase
in volume divided by time gave Q2. Next the reading of the mano
meters at the orifice in the supply line enabled Q1
to be calculated,
and consequently Q3
was determined, which was zero for no bypassing
flow. Finally, the different depth and width measurements were
made and recorded, and photographs were taken.
38
The run was completed by following the_ same procedure for
flow rates of 175%, 150%, 125%, and 50% of the maximal flow rate as
determined in the first step. Occasionally the flow rate of 200% was
used. The experimental data are summarized in part in Section 5.
The equation for the 4-inch orifice, Eq. 17, was examined at
low rates of flow which produced readings on a leg of the manometer,
using a liquid with a specific gravity of 2.95, that ranged from 0.05
inch to 0.3 inch. Each flow rate was compared with that obtained
volumetrically. The error within that range lay between +25% and
-6%. For flow rates above those mentioned, that is, from a prototype
flow of' 0.8 cfs and higher, the discrepancy was a maximum of 6%.
39
5. RESULTS
5.1 Introduction
The results of the tests that were performed on the models are
shown in tabular and graphical forms. The tables are given for the
prototype units; the same is true of the graphs. The results of tests
made on gratings, installed in grassed channels are shown, followed by
the results for paved channels.
The tables and graphs are presented in conventional or English
units, that is, feet and seconds, and in System Internationale or SI
units, that is, meters and seconds. The SI tables are given in the
Appendix.
In order to make comparisons between gratings of different
lengths, an attempt was made to establish a common base. The Q100
flow.
is the maximum that is intercepted by an inlet with zero bypass, or Q3
= O.
However, owing to the accuracy of the equipment and to different personnel
making the tests, the Q100 flow was somewhat subjective. The units
associated therewith are cubic foot per second (cfs) and cubic meter per
second (m3 / s) .
The next step was to ,divide that flow rate, QI00' by the length of
the grating. The resulting quantity is called Specific Capacity; this
is the capacity per unit length of grating. The concomitant units are
either cubic foot per second per foot (cfs/ft) or cubic meter per se-
3cond per meter (m / s/m) •
Previously tests had been made by Lehigh University personnel on
standard gratings used by PennDOT; those tests were accomplished in
PennDOT Research Project 68-31. The results of some of those tests are
included in this report.40
5.2 Inlet in Grassed Channel with Mild Slopes
The capacities of gratings installed in grassed channels having mild
slopes, such as medians, are listed in Table 5.1 for grades of 0.5%, 2%,
and 4%, and they are plotted in Figures 5.2, 5.3, and 5.4 as well. Addi
tionally in the tables are shown the results of slopes that were dressed
at 2:1 adjacent to the inlet, Fig. 5.1a. The purpose of a dressed inlet is
to aid in directing the flow of water into an inlet. On those plots a
solid line designates the results for a back slope of 6:1, and a dashed ~
line designates the results for a back slope of 12:1. The data for those
con~itions but nondressed, Fig. 5.lb, are shown in the diagrams as a dotted
line.
The specific capacity of each grating is listed in Table 5.2 and is
plotted in Figures 5.5, 5.6, and 5.7, for grades of 0.5%, 2%, and 4%,
respectively; the swale an~back'slopes are indicated also. The result
of each test having a back slope of 6:1 is shown as a solid line, whereas
the result for a back slope of 12:1 is shown as a dashed line.
The specific capacity is the least for a grating on a 4% grade, and
the other grades are equal in specific capacity. The graphs show that any
of the three grades having equal slopes, swale and back, has a higher
capacity than a grade with unequal side slopes. The plots reflect the
advantage of having equal side slopes, especially at 6:1; on grades of 0.5%
and 2% this feature is particularly outstanding. This point was not as
noticeable in the results of tests on the Type 4-ft Special and the Type
6-ft Special which had been previously investigated.
Throughout most of the investigatiDn of inlets installed in grassed
channels, the side edges of the top of the grating were below the lower
41
edge of each side slope. However, for some of the last tests~ inserts
were made to be placed adjacent to the grating. The inserts had a slope
of 2:1 and dressed the slopes adjacent to the inlet so as to direct flow
from the slopes into the grating. Figure 5.~shows the slopes as they were
dressed at 2:1, the upstream dressing being shown in white and the side
slopes as gray.
5.3 Inlet in Grassed Channel with Steep Slopes
Table 5.3, Capacity of Prototype Gratings in Grassed Channels, Steep
Back Slopes (English Units), shows .the Q100 rate of flow in cfs that each
grating captured without any water bypassing the inlet. The grades used
were 0.5%, 2%, and 4%. The swale slope was either 6:1 or 12:1, and the
back slope was either 1/2:1 or 2:1. The data are plotted in Fig. 5.8 for
a grade of 0.5%; in Fig. 5.9 for a 2% grade; and in Fig. 5.10 for a 4% grade.
In order to compare the results, each capacity in the two foregoing
tables was divided by its pertinent length of grating to give its specific
capacity in cubic foot per second per foot of length of grating; this
information appears in Table 5.4. The specific capacities are shown in
graphical form in Fig. 5.11 for a grade of 0.5%; in Fig. 5.12 for a 2%
grade, and in Fig. 5.13 for a 4% grade.
42
, I
l· . ~ ~, \
Fig. 5.1a Dressed Slopes Adjacent to Inlet
Fig. 5.1b Inlet with Nondressed Slopes
43
TABLE 5.1 CAPACITY OF PROTOTYPE GR1\TlliGS IN GR1\SSED
CHANNELS, MILD BACK SLOPES (English Units)
Capacity (cfs) Q1 ()()
Grade Slope Length of Grating (in.Y
(%) Swale Back 18 24 30 36 42 48 48 72
(1) Table 5. 7, Report 364.4, column he~ding "TYPE 4-FT': C"t\.PACITY(cfs) WITHOUT DIKE"
(2) Table 5.7, Report 364.4, column heading "TYPE 6-FT: CAPACITY(cfs) WITHDUT DIKE"
*Slopes dressed at 2:1
44
0.3 ...--.en·.~
E
0.1
72
• >-t--u~«u0.2
•
24 36 48 60
LENGTH OF GRATING (in)0.5 % GRADE
,.12: I ,,;
.',,*',.' 6~ I ",..'
'. .",.-------."".,~
::::;::.--. I2: I
•••.••Nondressed ••••• "
. .•••••••••.y'
•
8
2 .........--...........&--------........---...--'----.------~--- ....12
4
6
L·ENGTH OF GRATING (m)
0.5 1.0 1.5
Swale Slope Back Slope
/.0.414 •
1.2
Figure 5.2 Capacity VS. Length of Grating" Grassed Channels
with Mild Slope; Prototype; 0.5% Grade."
45
LENGTH OF GRATING (m)
0.5 1.0 1.5
Swale Slope Back Slop.e
•
12
•
• 0.3•••10 ••
,....... Nondre·ssed .- .....-.-en • (IJ•..... • ~(.) • •......... • E•-• ~
:>- • ••l- S • >-•- • l-t) •• -~
•0.2 c..>••
~•« . •- <tU •• (.)6 •.
••12: 1
• .... -~. "
.--..... --- " . ......~ ~", 12:1 __ ~
4 • ,.-"...-.--' 12: I .".'"---.fIII' -,. ...-_ 6'1.,
·~·~12: I 0.1• •
7224 36, 48 60LENGTH OF GRATING (in)
2 % GRADE
2 ...... ......-------------.l.--- ..-..---...-.-........~------12
Figure 5~3' Capacity vs. Length of Grating, Grassed Channels
with Mild Slopes; Prototype; 2% Grade.
46
LENGTH OF GRATING (m)
0.5 1.0 1.5
Swale Slope Back Slope
12
........U)
to'E
...........
>-I--
0.2 u~a.«u
0.1
0.3
•
•
12: I --- .. -·---......-.. -.. .. .. --- .-·-----'-27 i·----_................-_-.6= I
24 36 48 60 72LENGTH OF GRATING, (in)
4% GRADE
Nondressed .... ", 6: I . •
.........: /.~ressed. ",-
'2: I .... "";,•..,.' "--."y. 6:'
.~-_.... -- .......
.~.~.2 "........-----_.-.-.........---------~--- ...........--_........_......-......-.--
12
4 '
10""'"'"en....0
'-'"
>-I- a-u~«u
6
Figure 5.4 Capacity vs. Length of Grating, Grassed Channels
with Mild Slopes; Prototype; 4% Grade.
47
TABLE 5.2 SPECIFIC CAPACITY OF PROTOTYPE GRATINGS IN GRASSED
CHANNELS, MILD BACK SLOPES (English Units)
Specific Capacity (cfs/ft length)
Grade Slope Length of Grating (in.)
(%) Swale Back 18 24 30 36 42 48 48 72
k 12:1 6:1 1.96 1.59 1.40 1.01 0.812
12:1 2.57 2.18 1.97 1.16 1.05
* 6:1 6:1 4.39 3.96 3.82 3.77 4.04 3.71 2.24 2.156:1 4.72 4.50 4.14
12:1 2.07 1.70 1.50 1.08 1.01
2 12: 1 6:1 2.23 1.81 1.52 0.85 0.74
12:1 2.49 2.21 2.10 0.94 0.75
* 6:1 6:1 2.72 2.46 2.70 2.77 3.23 3.19 2.25 1.836:1 3.93 4.30 4.23
12: 1 2.41 2.01 1.88 1.18 0.91
4 12: 1 6:1 1.47 1.36 1.24 0.77 0.52
12:1 2.45 2.01 1.79 0.81 O.§4
* 6:1 6:1 2.08 1.84 1.68 1.79 1.66 1.98 2.18 1.826:1 1.28 2.24 2.47
12: 1 2.19 1.59 1.36 0.92 0.66
(1) (1)
Source: Table 5.1, CAPACITY OF PROTOTYPE GRATINGS IN GRASSED CHANNELS(English Units)Each capacity in Table 5.1 is divided by ,:the pertinentlength of grating.
Note: "(1) See notes 4 and 5, Table 5.1*Slopes dressed at 2:1
48
LENGTH ,OF GRATING (m)
0.5 I.0 1.56
Swale Slope Back Slope
0.5
5 .........c............... -. C'.&:, ••••••• Nondressed c....Q)C' ••••s:::
.~.~:~./'"0.4Q) l+-
0,.... 4 E....."- "-(I) Dressed • U).... ~(.)
E.........0.3 ............
>- 3 >-J-- f--u -<t Ua. ., «« " 12: I 6: I a-u ...,
0.2<t., u
2........
u . " '. u- ~6:1lL. -.,.12: I I.L..- , .... -u .~: u
lJ.J wa. 12: I 12:1 ] a..en e ___ ...........- ... __
0.1 en'._--------, -.-. ' ,- --6= I =-
24 36 46 60LENGTH OF GRATING (in)
0.5 % GRADE
72
Figure 5.5 Specific Capacity VB. Length of Grating, Grassed Channels
with Mild Back Slopes; Prototype; 0.5% Grade.
49
LENGTH OF GRATJNG (m)0.5 ).0 1.5
0.5.............c:....OlCQ)
0.4 '4-·0
E"(J)
~
0.3E........,
>t--U<:ta.<C0.2 uulI-
UWa.a. J (/)
Back Slope
•
e.. 12: J...-12: I ... ----...... _.-"_~-.. --. ... , ----..-
6:1
5
Swale Slope
........
.c....~ Nondressed.Q) .,••••••••••.-•.... 4 .'..... I'
""en.....(J
.........
>- .~.----..
t: 3" ./
~ :~.~./Dressed
5 ·,~,,12: I.",,----.o 2 · "'-_§ -~(1JJ 12: I •a.CI)
OL..... ...L.... ~.............L..__---........-------'----.......
24 36 48 60 72>,LENGTH OF GRATING (in)
2 % GRADE
Figure 5.6 Specific Capacity vs. Length of Grating, Grassed Channels
with Mild Back Slopes; Prototype; 2% Grade.
50
LENGTH OF GRATING (m)0.5 1.0 1.5
5....-...c..0's::CD
.... 4'4--
"'-Vi'+-0
-..."
>f--3-()~<tU
~ 2lJ..-UL1Ja..en
Swale Slope
Nondressed
12: I
Back Slope
__ . 12: I-......::.- .. - =::.-:.6: I ....
0.5
E'-~fC')
0.3 .§>I--U~
0.2 ~
u-LL~
ULLJ.0-
0.1 en
O ......_-..a.....- -....- ....... ---...-.--.......-~
24 36 48 60
LENGTH OF GRATING (i'n)4 % GRADE
72
Figure 5.7 Specific Capacity VB. Length of Grating, Grassed Channels
with Mild Back Slopes; Prototype; 4% Grade.
51
TABLE 5 _,3 CAPACITY OF PROTOTYPE GRATINGS IN GRASSED
CHANNELS, STEEP BACK SLOPES (English Units)
Grade Slope Capacitv ,(efs) \.(100Len£th of GratinQ (in.)
(%) Swale Back 18 24 30 HDiaQ
~ 6:1 ~:l 5.43 8.04 9.91 13.58
2:1 4.13 4.98 5.66 16.41
12:1 ~:1 2.77 4.30 5,04 8,09
2:1 4.53 5.66 6.40 7,30
2 6:1 ~:l 4.41' 5.55 7,24 9.34
2:1 4.64 4.98 5.49 10.19
12: 1 ~:l 2.43 3.57 4.02 8.09
2:1 4.13 4.70 5.43 7.41
4 6:1 ~:l 3.17 4.30 5.60 9,11
2:1 4.02 5,09 5.·94 9,00
12:1 ~:l 1,81 2.77 3.68 6.40'
2:1 3.00 3.62 5,15 5.94
(1)
•
(1) Tabl-e--.5:i, Report 364_4-,'ryp-eH inlet 'grating--with-diag~~ai--
bars.
52
16
14
12
0.5LENGTH OF GRATING (m)
1.0 1.5
.6: I,2: I
0.4
.. .,.........~ 0.3 enen ".....
10rt)
u • E......................
>- 6: I ,>-r- 1/2: I }--U -u«
-12:I,Y2:1 cd:0- 8 •« a.<:tu
·12:1,2:1 u0.2
12: I ,." 6: I, Type H6 2: I ;'"t'" • 2: I/ ,,"
~ "~ ./.~ "/ ~. '"" .
4 ·AI I, '/2: 1 O. II
2
24 36 48 60 72LENGTH OF GRATING· (in)
0.5 % GRADEFigure 5.8 Capacity vs. Length of Grating, Grassed Channels
with Steep Back Slopes; Prototype; 005% Grade
53
'LENGTH OF GRATING (m)0.5 t.O r.5
0.3
10'6:1,2:1
.. 6:1,1/2 :1
8 - 12:1, V2:1"........,..
......--.• 2:1, 2:1 CJ)
cri • "-'+- 0.2 roE(.)~
'-'"
>- 6: I, Ty·pe H>-I- 6 2:1 r--u /. . -
<t """,~ UC. .' ,'" <:(
<:(' .,,"'- II' a.. ",. <tu • ,(/11 12: I u4
." ,2:1/-
• 0.1~2: I) 1/2: I
•
2
24 36 48 60 72LENGTH OF GRATING (in)
2 % GRADE
Figure 5.9 Capacity vs. Length of Grating, Grassed Channels
with Steep Back Slopes; Prototypes; ·2% Grade.
54
LENGTH OF GRATING (m)0.5 1.0 r.5
0.310
•6: I, 1/2 :16:1,2:1
8
>-I-- 6-u~<X:U
2 .
•12: I, 1t2 :1
-12:1,2: I
Type H
~0.2 tOE
>f---U
~«u
0.1
24 36 48 60 72LENGTH OF GRATING (in)
4 % GRADE
Figure 5.10 Capacity vs. Length of Grating, Grassed Channels
with Steep Back Slopes; Prototype; 4% Grade.
55
TABLE 5.4 SPECIFIC CAPACITY OF PROTOTYPE GRATINGS IN GRASSED
CHANNELS, STEEP BACK SLOPES (English Units)
Grade(%)
SlopeSwale Back 18
Specific Capacity (~fs/ft2
Length of Grating (in..,)H Dlag
k2
2
4
6:1
12:1
6:1
12:1
6:1
~:1
2:1
~:1
2:1
~:l
2:1
~:1
2:1
3.62
2.75
1.85
3.02
2.94
3.09
1.62
2.75
2.11
4.02 3.96
2.49 2.26
2.15 2.02
2.83 2.56
2.78 2.90
2.49 2.20
1'.79 1.61
2.35 2.17
2.15 2.24
2.72
3.28
1.62
1.46
1.87
2.04
1.62
1.48
1.82
12:1
2:1
~:1
2.68
1.21
2.55
1.39
2.38
1.47
1.80
1.28
. 2:.1 2.00 1.81 2.06 1.19
Source: Table 5.3 CAPACITY OF PROTO~YPE GRATINGS IN GRASSED CHANNELS,STEEP BACK SLOPES (English Units)Each capacity in Table 5.3'i8 divided by the pertinentlength of grating.
Length of Type H grating is 60 in or 5 ft; FennDOT StandardDrawing "Miscellaneous Inl ets - Supplemental Sheet~t, Revised July 20, 1955.
56
LENGTH OF GRAT ING (m)O.E) 1.0 I.e>
6p--.-----.......-.......------------..-----......
0.5
5 ,................... ..c.s:::. +-..... 0)0'1 Cs:: 0.4 Q.)Q) 6: 1,1/2: I
E.... 4 /0 • "-.... en" "-en ro"l- • Eu......... ..........
-6:1,2:1 0.3 >-~I- :3 12: 12: I I-- ......,. ' -u .... ·6:1, 1f2q u'-<x: " " " <t0- 6: I '., · a..<to 1 '" <X:u 2: I '.
0.2 uu 2 ~.~ u- · 12:1,1/2:1 -lJ.. .12:1., V2:1 l.L..- -u (.)
1.LJ -12:1,2:1 UJa.. a.en C/)
Type H 0,(
24 36. 48 60 72LENGTH OF GRATING (in)
0.5 % GRADE
Figure 5.11 Specific Capacity VB. Length of Grating, Grassed Channels
with Steep Back Slopes; Prototype; 0.5% Grade.
57
6 0.5LENGTH OF GRATI NG (m)
1.0 1.5
0.5
5~
....-.-. .c
.c: .....+- en0» c:c: 0.4 Q)eLl
+- 4 E'+- """- (J)
(f) ~.....(..) E........., ...........
>- :3 · 6: I 1/2: I >-I- .. , I-- .~.-----. -U U~ " ,6: I 2: I <J:0- '- ',., 0-<:( , " <!u 12: I, " .... ::.:: 6:1,2=1 uu 2 2: I •- •6:1, V2:I uI.L. ~.~
l.L- •12: I, 1;2: I -u . . UW 12: 1,1/2: I -12:1,2:1 wa. a..CJ)
O. fen
Type H
24 36 48 60 72LENGTH OF GRATING (in)
2 % GRADE
F~gure 5.12 Specific Capacity VB. Length of Grating, Grassed Channels
with Steep Back Slopes; Prototype; 2% Grade.
58
LENGTH OF GRATING (m)0.5 1.0 1.5
6-----------.--.---..----~....---------.
0.5
5 .........~ ..c.J: ~...- enen c:c: 0.4 (1)QJ
4 E....".....U)
" ~(/)
'+- Eu......., ...........
0.3 >->-t- 3 I-- -u .6:1~2·1 u<t .......... . <ta.. ...... a...........« 6: I ~ J/~: <tu 0.2 u....-.
2 • • u Q
U fill'"
.6: I, V2: I.... ',....- " -IJ.. lJ...12: 1,2: I 6:1,.2:1 -- uU
lJJ .,.,.....,...-.• 12:I , V2 :I .
wa. ~. 0-en · I2: I, I/2: I ·'2:1 ,2: I en
0.1
Type H
24 36 48 60 72LENGTH OF GRATING (in)
4 % GRADE
.Figure 5.13 Specific Capacity vs. Length of Grating, Grassed Channels
with Steep Back Slopes; Prototype; 4% Grade.
59
5.4 Nominal Capacity of Inlet in Grassed Channel
The capacity of a grating that has been termed Q100
is the
highest flow rate that enters the grating with none bypassing. However,
it is not a good mudulus of the "reasonable capacity of a grating. A
better measure of capacity is one wherein some water is permitted to bypass
or overflow the grating, although the percent~ge that is bypassing at a
so-called nominal capacity is a subjective matter.
Nevertheless a series of tests were made on the gratings installed in
grassed channels with dressed slopes and side slopes of 6:1. In each test
the rate.o£ flow wa.s carefully increased until approximately 10% of the flow
was bypassing the inlet. The relative capacities, as efficiency, are
plotted on Figures 5.14, 5.15, and 5.16, for grades of 0.5%, 2%, and 4%,
respectively, ustng prototype grating lengths that ranges from 18 in. to
48 in. in increments of 6 in. Efficiency in percent is plotted on the y
axis, efficiency being defined as the ratio of the rate of water flowing
into the grating to the rate of water approaching the grating; the approach
flow rate of the prototype is plotted on the x axis.
By agreement with personnel from PennDOT an efficiency of 98% was
selected as the nom~nal capacity of the gratings; at that percentage, as
marked on the plots, the slope of each curve no longer is changing markedly
as it does in going from an efficiency of 100% to 98%.
The Nominal Capacity, Q98' of Gratings Installed in Grassed Channels,
Dressed Slopes (English Units) is shown in Table 5.5.
60
100
98
.........~o....., 96,-o"C\J(3
.,..
G94z'w-u-lL.
IJ.. 92.W
90
FLOW RATE IN PROTOTYPE (m3/~)0.1 0.2 0.3 0.4 0.5 1 0.6I I I I II
Grade0.50/0
Length of Gratingo ISII
C 24 11
At 30 11
• 36 11
II 42".it 48 11
Length ofGrating (in.)
0.7r
5 10 15 20 25FLOW RATE IN PR'OTOTYPE (cfs)
Figure 5.14 Efficiency of Inlet Gratings VB. Flow Rate in Grassed
Channels with Dressed Slopes; Prototype; 0.5% Grade.
61
48\ . \
\42 \
36, ,,. ,30 \,Length of
Grating (in.)
Length of Gratingo ISuC '24 11
A 3011
• 36"II 42 11
6. 48"
FLOW RATE IN PROTOTYPE (m3/s)O. I 0.2 0.3 0.4 0.5 0.6 0.7
----I I I I I' r--rGrade2 %
98
1.00
90
.........t!-'-' 96-o
"-(\J
o
~ 94zLJ.J-U-u..tb 92
5 10 15 20 25FLOW RATE IN PROTOTYPE (cfs)
Figure 5.15 Efficiency of Inlet Gratings vs. Flow Rate in Grassed
Channels with Dressed Slopes; Prototype; 2% Grade.
62
Figure 5.16 Ef~iciency of Inlet Gratings vs. Flow Rate in Grassed
FLOW RATE IN PROTOTYPE (rn3/s)O. I 0.2 0.3 0.4 0.5 0.6 0.7
---------..-r---....,..-1-"""-1"-"-"---'-1---rr---'I--l-Grade4%
98
100
....-.-~0~96
-0
"N0 0..
Length of&94z GratinglJJ 0 1811
-U [J 24 11
- 3011LL.. A
~ 92 • 36 11
42 11 ,II ,• 48 11
I,90
Length of,Grating (in.)
18
885 10 15 20 25
FLOW RATE IN PROTOTYPE (cf.;) )
Channels with Dressed Slopes; Prototype; 4% Grade.
63
TABLE 5. 5 NOMINAL CAPACITY ~ Q98" OF GRATrNGS~
IN GRASSED CHANNELS, DRESSED SLOPES (English Units)
1 Capacity (cfs)II Prototype Length of Grating (in)
..... .........-__ "".-..."""'"..,._.,....Ir,o..........-.._._
I
Grade118(%) 24 30 36 42 48I
0.5 9.18 ,11.88 14.62 16.54 19.25 21.12
2.0 7.90 10.60 13~55 15.40 17.48 19.76
4.0 5.78 8.92 10.52 13.26 15.72 18.18
. Side slopes are 6:1.
5.5 Inlet in Paved Channel
Table 5.6, Capacity of Prototype Gratings in Paved Channels (Engl'ish
Units)~ lists the Q100
rate of flow to each inlet without any water by
pass.ing the ope.ning; the units of measure .being cubic foot per second.
These data have been plotted in Fig. 5.18 ,for grades of 0.5%, 2%, and 4%.
The specific capacity·, cubic feet per second per foot of length is
listed in Table 5.7, and the data are plotted in Fig. 5.19.
64
TABLE 5.6 CAPACITY OF PROTOTYPE GRATINGS IN PAVED CHANNELS (English Units)
Capacity (cts) -tl1OO
SlopeLength of Grating (in,,)
Grade 4-ft 6-ft- (%) Swale Back 18 21 24 27 30 33 36 42 48 Special1 Specia12
0\lJ1
1:2
2
4
12:1 1/8:1 1.47 1.74 1.77 1.83 2.09 2.11 2.22 2.46 2.66
12: 1 1/8: 1 0.91 1.25 1.42 1.75 1.98 2.66 .2.87 3.25 3.83
12:1 1/8:1 0.40 0.54 0.70 0.85 1~22 1.43 1.57 2.04 2.30
1.47
2.77
3.40
2.66
4.02
4.08
1 Tab l e 4.2, Report 354.3, p 42arable 4.3, Report 364.3, p 43
TABLE 5. 7 SPECIFIC CAPACITY, OF PROTOTYPE GRATINGS ·IN PAVED CHANNELS (English Units)
_____ ._ ... . .~~ ... _.~ .__~Eecific C~paci~y (cis/it) I
Length of Grating (in.)SlopeGrade
(%) Swale Back 118 21 24 27 30 33 36 . 42 484-ft
Special6-ft
Special
Q\(j'\
±2
2
4
12:1 1/8:1 0.981 0.995 0.885 0.813 0.836 0.767 0.740 0.703 0.665 0.368
12:1 1/8:1 0.607 0.714 0.710 0.778 0.792 0.967 0.957 0.929 0.958 0.693
12:1 1/8:1 0.267 0.309 0.350 0.378 0.488 0.520 0.523 0.583 0.575 0.850
0.443
0.670
0.680
Source: TABLE 5.6 CAPACITY OF PROTOTYPE GRATlNG IN PAVED CHANNELS (English Units)Each capacity in Table 5.6 is divided by the pertinent length of grating.
LENGTH OF GRATING (m)0'.5 1.0 1.5
Swale Slope 12: 'I
5
0.154
,................ enen
Back Slope I/a: I ~'t-
Eu.........,'-'
>- 30.10 ~t-- -u u
~ «c.m'<2:
2 <:((.) u
0.05
. I
24 36 48 60 72LENGTH OF GRATJ NG (in). .
Figure 5.17 Capacity vs. Length of Grating, Paved Channels;
Prototype; Grades of 0.5%, 2%, 4%.
67
LENGTH OF GRATING (m)
1.0 1.5 .......-..,......... 0.5 E...."-,enen
Swale Slope 12:1 O.2~......0 E........,
2 .......>- >-l-
I--- -UO. I
u~ Back Slope l/e: I Grade <t
a.«2 0/0 <tu
U4U
U4 °/0 2...-l.L.l.L.,- 0.5 -UUW wa..
48 60 72 0..en 24 36 (J)
LENGTH OF GRATING (in)
Figure 5.18 Specific Capacity vs. Length of Grating, Paved Channels;
Prototype; Grades of 0.5%, 2%, 4%.
68
6. DISCUSSION
6.1 Remarks
Each plot of,capacity against length of grating for anyone inlet
shows that the capacity increases as the length of grating is incr~ased;
or the longer the inlet, the more water it can take. This was an expected
result.
In considering th'e relation of specific capacity to length, a similar
condition does not occur. Rather for some gratings the relation is almost
constant, whereas for others a decrease, although slight, is noticed with
an increase in length.
6.2 Inlet in Grassed Channel with Mild Slopes
The plots of capacity 'VB length for an inlet in a grassed channel
that has mild side slopes, Figures 5.2, 5.3, and 5.4, show an increase in
capacity as the length of the inlet is increased. The capacity is highest
£or a grade of 0.5% and 16west for a grade. of 4%; this point is very
noticeable for eq,ual side slopes of 6~ 1. For side slopes with the other
ratios used, that difference is not marked. Side slopes that are equal
lead to higher capacity of an inlet than an installation with unequal side
slopes, probably owing to the fact that the center of gravity is toward ,the
flatter slope and not in coincidence with the invert as is true of an inlet
installed on a grade having equal side slopes.
On each of the plots, Figures 5.2 to 5.7, two sets of lines are
shown for the condition wherein both side slopes were equal at 6:1. The
solid line refers to the data obtained for the condition where the slopes
adjacent to the inlet were dressed at 2:1; the dotted line refers to the
69
condition in which the slopes were not dressed~ The lines for the dressed
slopes show an increase in capacity with an increase in length, as do the
other lines. The Specific Capacity plots, Figures 5.5 to 5.7, generally
show a decrease of specific capacity with an increase in length, except for
equal side slopes of 6:1 on a 2% grade.
The data seem to indicate that an inlet with dressed slopes has a
lower capacity than one with no dressing. Howev~r several points must be
borne in mind in considering the results as shown in Table 5.~. Each flow
rate was that which. was designated as QIOO' meaning the maximal amount of
water that could enter the inlet with none either overflowing or bypassing
the inlet. In comparing the raw-data sheets for the different test con
figurations, there was an obvious difference in the Q100 as recorded. The
difference, as seen in Table 5.1, appears to be due to a change in observ
ers, and, consequently, each Q100 is subjective. The difficulty in
selecting Q100 can be noted in Table 6.1. Depending on the observer, Q100
could have been selected from the range between 0.555 cfs and 1.09 or 2.18
efs. A second factor ca~sing the difference in rat~s of flow in the model,
the two conditions at the inlet were determined 'to be on one leg of the
manometer as low as 0.02 inch and as high as 7.7 inches, the latter being
in the data for the 2% grade.
A superior .measure of the capacity of an inlet is that flow bf which
a small amount over,flows or bypasses the inlet. This was done in the deter.
mination, of the nominal capacity of the inlets on the dressed slopes during
which tests as much as' 10% was permitted to bypass th-e inlet. The nominal
capacity is that where 2% of the approaching water overflowed or bypassed
the inlet, and the overflow as well as the water falling into the inlet were
70
both measured volumetrically, not depending on the manometer and orifice.
Consequently, the Q98 is a better estimate of the inflow. The results for
the Q98
of the dressed inlet were greater than the flow for an inlet with
slopes that were not, dressed.
6.3 Inlet in Grassed Channel with Steep Slopes
Figures 5.8, 5.9, and 5.10 are capacity plots for prototype gratings
installed in a grassed channel with steep side slopes, showing the relation
between capacity and length of grating exposed to the approaching flow of
water for grades of 0.5%, 2%, and 4%, respectively. The results from pre
vious tests of the Type H inlet grating were also plotted, and those results,
in spite of the different width of grates (31 in.,), tend to fall along the
paths of the concomitant gratings used in the current study. Each line has,
of course, the general shape that occurs as the length of any inlet becomes
greater. The capacity of the inlet increases with an increase in length 'of
the inlet. Particularly noticeable is the higher capacity in a channel that
has a swale slope of 6:1 for almost'each condition tested, that channel
having both a hig~er capacity and a steeper slope than the channel with a ·
swale slope of 12:1. For comparative purposes such a plot must be modified
by dividing each capacity by the length of the particular grating involved,
resulting ih the specific capacity of each grating in units of cfs/ft of
length. These data were plotted in Figures 5.11, 5.12, and 5.13 for the
same grades as mentioned previously. The plot for almost every grating
sloped downward with increasing length. No particular geometric combina
tion of grade and side slopes was outstanding. The back slope of ~:1 was
unusual in that, with swale slopes of 6:1 and 12:1, it showed the highest and
lowest specific capacity for grades of 0.5% and 2%, respectively.
71
6.4 No~irtal Capacity of Inlet in Grassed Channel
Table 5.5 lists the capacity of each grating in a grassed channel
having slopes d.ressed at 2: 1 adjacent to the inlet; the data are taken from
Figures 5.14, 5.15, and 5.16 at a condition where 2% of the water approach-
ing the inlet bypasses .the grating, which is another way of stating that
98% of the approaching water enters into the inlet.
The tabulation shows a great increase in capacity as the grating
is lengthened, but a decrease in capacity as ·the grade is increased from
O~5% to 4%. However the increase in length has a greater effect on capa-
city than the increase in grade.
Specifically, for each 6-in. increase in length the capacity~
increased an average of 2.4 cf's, ranging. from a low of 1.60 cfs to a high
of 3.14 c£s.; both of these· occurred, on the 4% grade. In ·cons idering the
change in, capacity for an inle~ of anyone length on different grades,
the data show an average de'crease in' ,capacity of 1. 7 c~s, the lowest such
change being 0.71 cfs and ~he highest change as 3.03 cfs.
6.5 Inlet in Paved Channel
Figure 5.17 is a plot, for a prototype inlet installed in a paved
channel, showing the relation between capaci~ and length of grating
exposed to the approaching flow of water. As is to be expected, the
72
capacity increases with. length of grating; this is also shown by the points
pertaining to the Type 4-ft Special (26~ in. wide) and the Type 6-ft Special
(26~ in. wide) which points were determined in a previous study.
The trends of the 2% and 4% lines are approximately the same, whereas
the 0.5% line is somewhat flatter, crossing the 2% line near the center of
the range of tests. The capacity of inlets installed on a ,2% grade ranges
from ~ cfs to 1 cfs greater than that of inlets on a 4% grade. D
Figure 5.18, which shows the specific capacity of ~hose gratings,
obviates or nullifies the effect of the length of inlet with the result
that the lines are approximately horizontal-. Inlets installed on a 4%
grade have less specific capacity that those on flatter grades.
Both Figure 5.17 and 5.18 show that the grade~of a channel is a very
significant feature about the rate at ~hich water can enter an inlet.
On the graphs are plotted the results of tests previously conducted
on the Type 4-ft Special and the Type 6-ftSpecial inlet gratings. The
graphs show that the capacities of those in~ts, in spite of the different
'width of grates (26~ in.» fall in the same range as ~hose that were
observed in this study.
73
6.6 Photographs of Flow to an Inlet
Figures 6.1 to'6.5 are photographs which show the area of an inlet
grating that is covered for different rates of flow. The geometry of the
situation consisted of a grade of 0.5%, a "swale" slope of 12:1, a back
slope of 3:1, and a model length of 9 inches or a prototype length of 18
inches. A pictorial series of flows to an inlet in a paved channel was
chosen to be shown because flow in a paved channel can be seen in a photo-
graph far better than flow in a channel covered with an artificial turf.
Table 6.1 lists the pertinent- data about the flow.
Table 6.1 Flow in a Paved Channel; Prototype Flow Rate (cfs)
Q Q1 QZ- Q
3Efficiency Figure
-~- -- --!.ll. '0.5 .555 .555 6.1
1.0 1.09 1.09 100 6.2
2.0 2.18 2.15 .03 98.6 6.3
2.5 2.77 2.54 .'23 91.5 6.4
3.0 3.28 2.95 .33 90.1 6.5
Prototype length: 18 in.; width: 36 in.Grade: .0.5%Swale Slope: 12:1Back Slope: 3:1
In Figure 6.1 the water extends to three-fourths of the width of the
inlet; a very· small- length of the inlet has water on it. Figure 6.2 shows
the wate'r extending to the full width of the inlet; no flow is bypassing the
inlet. Figure 6.3 has twice the flow rate of Figure 6.2 with a decrease of
efficiency of 1.4%. Much of the grating is not covered with water. The
74
wooden bar marked in l/2-foot intervals was placed so as to show clearly
the extent of the water up the swale slope. Figure 6.4 has a flow of 2.5
Q, and Figure 6.5, a flow of 3Q. Notwithstanding the "large increase
of approach flow, Figure 6.5 shows that almost one half of the grating has
no water on it, although the inlet is capturing nine tenths of the water
coming to it.
75
Figure 6.1 Flow in a Paved Channel; 0.555 cfs
Figure 6.2 Flow in a Paved Channel; 1.09 cfs
76
Figure 6.3 Flow in a Paved Channel; 2.18 cfs
Figure 6.4 Flow in a Paved Channel; 2.77 cfs
77
Figure 6.5 Flow in a Paved Channel; 3.28 cfs
7Q
7. CONCLUSION
The investigators have drawn the following conclusions from the
study:
7.1 Inlet in Grassed Channel with Mild Slopes
Figures 5.2, 5.3, and 5.4, Capacity VB Length of Grating for three
different grades, show that the capacity of a grating increases with an
incr~ase in length. Furthermore, the capacity for anyone length decreases
as the grade of the channel becomes steeper.
Additionally, a channel which has equal side slopes has a greater
capacity than one with unequal side slopes, and, provided a channel has
equal side slopes of 6:1, it will have a capaci-ty that is greater than one
with 12:1 slopes; for the flatter grades this difference is outstanding.
Figures 5.5, 5.6, and 5.7, Specific Capacity VB Length for three
different grades, generally indicate that a decrease in specific- capacity
occurs as the grati~g is made longer.
7.2 Inlet in Grassed Channel with Steep Slopes
In referring ·to Figures 5.8, 5.9, and 5.10, Capacity VB Length for
the three grades, the higher capacity of a grassed channel, having a swale
slope of 6:1 and a back slope of either 2:1 or ~:1, is immediately evident,
whereas a swale slope of 12:1 and a back slope of ~:1 always shows as
having the least capacity. The plots again show that an inlet is able to
capture more water as its length is increased.
79
Additionally, ~he plots point out that, as tests went from a grade
of 0.5% to a grade of 4%, the capacity of the particular combinations of
side slopes decreased, indicating that flatter slopes have a greater capa-
city than steep slopes.
The figures ·further show that in 5 of 6 instances a swale slope of
6:1 has a higher capacity tha~ a swale slope of 12:1, and that a back slope
of ~:1 usually has a higher capacity than a back slope of 2:1 for the 6:1
swale slope, whereas,for the 12:1 swale slope, the 2:1 back slope has the
higher capacity.
Generally, the plots of Specific Capacity vs Length, Figures 5.11,
5.12, and 5.13, show a decrease in specific capacity as an inlet is
lengthened.
d
7.3 Nominal Capacity of Inlet in Grassed Channel
The nominal capacity of a inlet should be based on the grating
catching 98% of the approaching flow and letting 2% of that flow pass by
the grating because a capacity based on all of the approaching flow being
caught by the grating· leads to only a small difference in capacity for
different lengths of grating. With some water bypassing or overflowing the
'inlet, more of the grating will be used to capture the approaching water
with the result that the nominal or Q98 capacity is larger than the Q100
capacity where no water bypasses the inlet. This point is clearly seen by
observing the efficiencies of 100% and 98% in Figures 5.14, 5.15, and 5.16,
Efficiency VB Flow Rate for the three grades considered.
80
7.4 Inlet in Paved Channel
The capacity of an inlet installed in a paved channel increases with
an increase in length of the inlet, the rate of increase being almost con
stant for anyone grade. The flatter grades had higher capacities than the
4% grade, and thus are preferable to the steeper grade. The spread in
capacity between the 4% line and the highest line is almost constant over
the lengths of inlets tested.
7.5 Arrangement of Grating Bars
That no one configura~ion of grating bars at the surface of an
in~t is able to capture more of the approach flow than any other configura
tion, for an inlet that is installed in a conventional channel, triangular
in shape, along a highway, whether the channel be grassed or paved.
81
8. RECO~ENDATIQNS
As a result of the study, the following points are recommended
about inlets being installed by PennDOT along highways:
8.1 That grassed channels be designed to have equal side slopes.
8.2 That grassed channels have equal side slopes of 6:1 in preference to
equal side slopes of 12:1.
8.3 That highways be designed so that flow channels have flat grades in
preference to steep grades.
8.4 That' the nominal capacity here. shown be used for an inlet with a
width of 48 in., a lengthof 27 in., having diagonal bars, and installed
in a grassed channel:
Grade Slope Capacity(%) Swale Back (cfs)
0.5 6:1 6:1 13.3
2 6:1 6:1 12e1
4 6:1 6:1 ge7
The capacities were obtained by interpolation from data in both
Table 5.5 and Figures 5.14, 5.15, and 5.16.
8.5 That the practice be continued of dressing slopes immedia tely
adjacent to an inlet which is installed in a grassed channel.
82
9. ACKNOWLEDGEMENTS
This research was sponsored by the Pennsylvania Department of
Transportation in conjunction with the United States Federal Highway
Administration. It was conducted in Fritz Engineering Laboratory
(Department of Civil Engineering) of Lehigh University in Bethlehem,
Pennsylvania, by the following personnel of the Hydraulics Depart
ment: Dr. Arthur W. Brune, Project Director, and Mr. Andrew D. Spear,
Research Assistant, and Mr. Kenneth C. Loush, Research Assistant.
The Director of Fritz Engineering Laboratory is Dr. Lynn S.
Beedle; the Chairman of the Department of Civil Engineering is
Dr. Da~d A. VanHorn; the Director of the Office of Research is
Professor George R. Jenkins.
The authors are indebted to MI. Elias Dittbrenner who assisted
in the work, to the secretaries of Fritz Laboratory who typed the
manuscript~, and to,Mr. Jahn M. Gera who prepared the drawings.
Recognition is here given to personnel of PennDOT who aided
materially in the study; s'pecifically, Mr. Charles J. Churilla, FE,
Research Coordinator, whose guidance was very helpful. Additionally,
the authors offer their thanks to Mr. David Fetterman, PE, Bureau of
Design, and, from District 8-0, Mr. William J. Green, FE, and Mr.
Marshall M. Sellers, PEe Appreciation is also extended to the follow-
ing personnel of FHWA: Mr. Kenneth Foster and Dr. D. C. Woo.
83
A
D
Eu
Fr
g
L\H
L
L , LRrn
I1P
Q
Q1Q2Q3Re
~S
v
vP
1.1
cfs
ems
FHWA
PennDOT
p subscripted
m subscr.ipted
10. NOMENCLATURE
2area of flow, ft
depth of flow, ft
Euler number
Froude number
2gravitational acceleration, ft/sec
change in head, in.
length of inlet, in.
scale ratio
Manning roughness coefficient
difference in pressure, psi
flow rate, cfs
total flow rate, cfs
intercepted flow rate, cfs
bypassing flow rate, cfs
Reynolds number
hydraulic radius, ft
slope of energy line
velocity, fps
volume of flow, ft 3
density, Ib-sec2/ft4
dynamic viscosity, (lb-sec/ft2 )
cubic feet per second
cubic meters per second
Federal Highway Administration
Pennsylvania Department ofTransportation
prototype
model
84
11. BIBLIOGRAPHY
1. Appel, E., A.W. Brune, and W.H. GrafHYDRA.lTLIC PERFORMANCE OF PENNSYLVANIA HIGHWAY DRAINAGEINLETS INSTALLED IN GRASSED CHANNELS; Lehigh University,Fritz Engineering Laboratory Report No. 364.4,Bethlehem, Pa. (Jan. 1973)
2 • Chow, V. T.OPEN-CHANNEL HYDR.A.ULICS; McGraw-Hill Book Company, NewYork, New York (1959)
3. Einstein, H. A. and E. S. El-SamniHYDRODYNAMIC FORCES ON A ROUGH WALL; p. 521, Review ofModern Physics, Vol. 21 (1949)
4. Graf, W. H.HYDR.A.ULICS OF SEDIMENT TRANSPORT; pp. 385-398, McGraw-HillBook Company ~ New Yor.k, New York (1971)
5. Hansen, A. G.FLUID MECHANICS; pp. 395-413, John Wiley, New Y.ork, NewYork (1967)
6. Johns Hopkins UniversityTHE DESIGN OF STORM-WATER INLETS; Department of SanitaryEngineering and Water Resources, Report of the StormDrainage Research Committee, Baltimore, Maryland (June1956)
7. Larson, C. L. and L. G. StraubGRATE INLETS FOR SURFACE DRA.INAGE OF STREETS AND HIGHWAYS;University of Minnesota, St. Anthony Falls Hydraulic Laboratory, Bulletin 2 (June 1949)
8. Morris, H. M.APPLIED HYDRAULICS IN ENGINEERING; The Ronald PressCo~any, New, York, New York (1963)
9. Stevens, J. C. et al.HYDRAULIC MODELS; The Committee of the Hydraulic Divisionon Hydraulic Research, ASeE, Manual of Engineering Practice25 (1942)
10. u. S. Army Corps of EngineersSURFACE DRAINAGE FACILITIES FOR AIRFIELDS; EM 1110-345-281(1964)
85
11. Yee, P. P.HYDRAULIC PERFORMANCE OF HIGHWAY DRAINAGE INLETS USED INPENNSYLVANIA; Master's Thesis, Lehigh University,Bethlehem, Pennsylvania (1972)
12. Yee, P.P., W.R. Graf, and A.W.BruneHYDRAULIC PERFORMANCE OF PENNSYLVANIA HIGHWAY DRAINAGEINLETS INSTALLED IN PAVED CHANNELS; Lehigh University,Fritz Engineering Lab., Report No. 364.• 3, Bethlehem, Pa.(Nov. 1972)
13. Yucel, 0., G.M. Lee, A.W. Brune, and W.R. GrafDEVELOPMENT OF IMPROVED DRAINAGE I~TS, P1!A:SE 1: LITERA-TURE SURVEY, Lehigh University, Fritz Engineering Laboratory Report No. 364.2 (1969)
86
12. APPENDIX
The Appendix contains the identical tables of capacity that are in
Section 5, Results, of this report except th~t the data in each table are
given in units of the International System or SI units. The conversion
from English units to SI units was based on 1 foot for 0.3048 meter and
1 cubic foot per second for 0.02832 cubic ~eter per second.
87
TABLE A.l CAPACITY OF PROTOTYPE GRATINGS IN GRASSED
CHANNELS ,. MILD BACK SLOPES (SI Units)
Capacity (m3/s)
Grade Slope Length of Grating (til) I
(%) Swale Back 0.46 0.61 0.76 0.91 1.07 1.22 1.22 1.83
~ 12: 1 6:1 0.083 0.090 0.099 0.114 0.138
12:1 0.109 0.123 0.139 0.131 0.178
* 6:1 6:1 0.186 0.224 0.270 0.321 0.401 0.420 0.253 0.3656:1 0.201 0.255 0.293
12:1 0.088 0.096 0.106 0.122 0.172
2 12:1 6:1 0 •.095 0.103 0.107 . 0.096 0.125
12:1 0.106 0.125 0.149 0.106 0.127
* 6:,1 6:1 0.116 0.139 0.191 0.236 0.321 0.361 0 ..255 0.3126:.1 0.167 0.244 0.300
12:1 0.103 0.114 0.133 0.133 0.154
4 12:1 6:1 0.063 0.077 0.088 0.087 0.088
12:1 0.104 0.114 0.127 0.091 0.109
* 6:1 6:1 0.088 0.104 0.119 0.152 0.164 0.224 0.247 0.3096:1 0.054 0.127 0.175
12: 1 0.093 0.090 0.096 0.104 0.112
(1) (2)
(1) Table 5.7, Report 364.4, column heading "Type 4-Ft: Capacity(cfs) without DikeI'; converted using 0.02832 m3 /s
(2) Table 5.7, Report 364.4, column heading "Type 6-Ft: Capacity(cfs) without Dike"; converted using 0.02832 m3 /s
*Slopes dressed at 2:1·
88
TABLE A •.2 SPECIFIC CAPACITY OF PROTOTYPE GRATINGS IN GRASSED
CHANNELS, MILD BACK SLOPES (8I Units)
Specific Capacity (m3/sjrn length)
Grade SlopeLength of Grating (m)
(%) Swale Back 0.46 0.61 0.76 0.91 1.07 1.22 1.22 1.83
k 12:1 6:1 0.180 0.148 0.130 0.093 0.0752
12:1 0.237 0.202 0.183 0.107 0.097
* 6:1 6:1 0.408 0.368 0.355 0.350 0.375 0.345 0.207 0.1996:1 0.437 0.418 0.386
12: 1 0.191 0.157 0.139 0.100 0.094
2 12:1 6:1 0.207 0.169 0.141 0.079 0.068
12:1 0.230 0.205 0.196 0.087 0.069
* 6:1 6:1 0.253 0.229 0.251 0.289 0.300 0.296 0.209 0.1706:1 0.363 0.400 0.395
12:1 0.224 0.187 0.175 0.109 0.084
4 12: 1 6:1 0.137 0.126 0.116 0.071 0,048
12:1 0.226 0.187 '0.167 0.075 0.060
* 6:1 6:1 0.193 0.171 0.156 0.166 0.154 0.185 0.202 0.169.- 6:1 0.119 0.208 0.230
12: 1 0.202 0.148 0.126 0.085 0.061
(1) (1)
Source: TableA.l ,CAPACITY OF PROTOTYPE. GRATINGS IN GRASSED CHANNELS(SI Units)Each capacity in Table A.I is divided by the pertinent )ength ofgrating.
Note: (1) See notes 4 and 5, Table A.. l*Slopes dressed at 2:1
89
TABLE A·. 3 CAPACITY OF PROTOT'Y'PE GRATINGS IN GRASSED
CHANNELS, STEEP BACK SLOPES (Sr Units)
Grade SlopeCapacity (m3/s)
(%) Swale BackLength of Grating (m)
0.46 0.71 0 .. 76 H Diag (1)
~ 6:1 ~:l 0.154 0.228 0.281 0.385
2:1 0.117 0.141 0.160 0.465
12:1 ~:1 0.078 0.122 0.143 0.229
2:1 0.128 O~160 0.181 0,207
2 6:1 ~:1 0.125 0.157 0.205 0.265
2:1 0.131 0.141 0.155 0.289
12:1 ~:l 0.069 0.101 0.114 0.229
2:1 0.117 0.133 0.154 0.210
4 6:1 ~:1 0.090 0.122 0.159 0.258
2:1 0.114 0.144 0.168 0.255
12: 1 ~:1 0.051 0.078 0.104 0,181
2:1 0.085 0.103 0.146 0,168
(1)
(1) Table 5.1, Report 364.4, Type H inlet grating with diagonalbars. Length of grating is 60 in or 1.52 m
90
Grade(%)
Slope Length of Grating (m)Swale Back b.46 0.61 0.76 H Diag
k2
2
4
6:1
12:1
6:1
6:1
12:1
~:1
2:1
~:1
2:1
~:1
2:1
~:1
2:1
1z:1
2:1
~:1
2:1
0.335 0.374 0.370
0.254 0.231 0.211
0.170 0.200 0.188
0.278 0.262 0.238
0.272 0.257 0.270
0.285 0.231 0.204
0.150 0.166 0.150
0.254 0.218 0.203
0.196 0.200 0.209
0.248 0.236 0.221
0.111 0.128 0.137
0.185 0.169 0.192
0.253
0.306
0.151
0.136
0.174
0.151
0.138
0.170
0.168
0.119
0.111
Source: Table A.3 CAPACITY OF PROTOTYPE GRATINGS IN GRASSED CHANNELS,STEEP BACK SLOPES (SI Units)Each capacity in Table Ae3is divided by the pertinentlength of grating
Length of Type H grating is 60 in or 1.52 m; PennDOT StandardDrawing "Miscellaneous Inlets - Supplemental SheetA", Revised July 20, 1955
91
TABLE A.5 NOMINAL CAPACITY, Q98' OF GRATINGS IN GRASSED
CHANNELS, DRESSED SLOPES (S1 Units)
Capacity (m3/s)
GradeLength of Grating (m)
,(%) 0.46 0.61 0.76 0.91 1.07 1.22
0.5 0.260 0.336 0.423 0.468 0.545 0.598
2.0 0.224 0.300 0.384 0.436 0.495 . 0.560
4.0 0.164 0.253 0.298 0.376 0.445 0.515
Side slopes are 6:1
92
TABLE A.6 CAPACITY OF PROTOTYPE GRATlNG8 IN PAVED CHANNELS (81 Units)
Capacity (m3/s)
Length of Grating (m)Slope ·
Grade(%) Swale Back 0.46 0.,53 0.61 0.69 0.76 0.84 0.91 1.07 1.22
4-ftSpecia11
6-ftSpecia12
\.0LV
~
2
4
12:1 1/8:1 0.042 0.049 0.050 0.052 0.059 0.060 0.063 0.070 0.075 0.042
12:1 1/8:1 0.026 0.035 0.040 0.050 0.056 0.075 0.081 0.092 0.109 0.078
12:1 1/8:1 0.011 0.015 0.020 0.024 0.035 0.041 0.045 0.058 0.065 0.096
0.075
0.114
0.116
1 Table 4.2, Report 364.3, p 42; units converted.2 Table 4.3, Report 364.3, p 43; units converted.
TABLE A.7 SPECIFIC CAPACITY OF PROTOTYPE GRATINGS IN PAVED CHANNELS (S1 Units)
Specific Capacity (m3/s/m length)
Length of Grating (m)
Grade Slope(%) Swa1e Back 10.46 0.53 0.61 0.69 0.76 0.84 0.91 1.07
4-ft1.22. Special
6-ftSpecial
\.0.p.
~
2
4
12:1 1/8:1 0.091 0.093 0.082 0.075 0.078 0.071 0.069 0.065 0.062 0.034
12:1 1/8:1 0.057 0.066 0.066. 0.073 0.074 0.089 0.089 0.086 0.089 0.064
12:1 1/8:1 0.024 0.028 0.033 0.035 0.046 0.049 0.050 0.054 0.053 0.079
0.041
0.062
0.063
Source: TABLE A.6 CAPACITY OF PROTOTYPE GRATINGS IN PAVED CHANNELS (81 Units)Each capacity in Table A~6is divided by the pertinent length of grating.