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sT.g}$VERSITY OT MINNESOTA

ANTHONY FALTS HYDRAUTICTORENZ G. STRAUB, Director

Technical Pcper No. 3, Series B

;i:, :; :::i r; .".r n;,;

LABORATORY

Hydraulic Data Comparisonof Concrete and Corrugated Metal

Culvert Pipes

byTONENZ G. STRAUB

cmdHENRY M. MOBNIS

IulY, 1950Minnecpolis, Minnesotq

I'NIVERSITY OF MINNESOTA CENTENNIAI . I95Il85l .

RESERVE coPy

UNIVERSITY OF MINNESOTA \\ii)i~~;~U~L COpy ST. ANTHONY FALLS HYDRAULIC LABORATORY

LORENZ G. STRAUB, Director /'

Technical Paper No.3, Series B

Hydraulic Data Comparison of Concrete and Corrugated Metal

Culvert Pipes

by

LORENZ G. STRAUB

and HENRY M. MORRIS

July, 1950 Minneapolis, Minnesota

1851 • UNIVERSITY OF MINNESOTA CENTENNIAL • 1951

I'!{TVEBSITY OT MINNESOTA

ST. ANTHONY TAttS HYDRAI'LIC LABORATORYtOnENZ G. STRAUB, Director

Technicql Poper No. 3, Series B

Hydraulic Data Comparisonof Concrete and Corrugated Metal

Culvert Pipes

byTORENZ G. STRAUB

cmd

HENRY M. MONRIS

IulY, 1950Minnecpolis, Minnesotq

I'NIVEBSITY OF MINNESOTA CENTENNIATl85l . . l95l

UNIVERSITY OF MINNESOTA

ST. ANTHONY FALLS HYDRAULIC LABORATORY LORENZ G. STRAUB, Director

Technical Paper No.3, Series B

Hydraulic Data Comparison of Concrete and Corrugated Metal

Culvert Pipes

by

LORENZ G. STRAUB

and

HENRY M. MORRIS

July, 1950 Minneapolis, Minnesota

1851 • UNIVEFI.SITY OF MINNESOTA CENTENNIAL • 1951

C O N T E N T S

L i s t o f f l l u s t r a t i o n s . o c . c r c c . . . . . . . c o .

r . r N m o D u c l T o N . o . .

Page

iii

I

IrI. RESUIIE OF EXFER,IUts,ITAI. PROGRAIIA . S c o p e o f T e s t s . c . . c . . o . . . c . . . cB . S u r u n a r y o f R e s u l t s " . c c . . . . , . . . . o . o

N T . M E T T O D S O F T E S T I N G A N D A N A L Y S I S . . . . . O " . ' C ' O

rV. ANALYSIS AND DISCUSSION OF 8E.SUtlE . . O ' O 'A . G e n e r a l A n a l y t i c R e l a t i - o n s . . . . o . . . . . . o c oB. Friction Losses for Full Flow o .C. Friction Losses for Part-Full FIow . .D" Entranee Losses cE. Outlet LossesF. Comparison of St" Anthony Falls Iaboratory Results

w i t h O t h e r D a t a . o o . o o 2 L

Aeknowledgnent c o o o o . . . . c c . . c . . c c . o . o c . " zLI

G 1 o s s a r y c o o o c . o o . o . . c o . . , o . . . c r 2 5

12

599

1318L92L

It

CONTENTS

List of Illustrations • • 0 • •

I. INTRODUCTION . . . . . . . . . . . . II. RESUME OF EXPERIMENTAL PROGRAM

A. Scope of Tests • • • . • o • • • • • •

B. Summary of Results ••••

III. ME'rnODS OF TESTING AND ANALYSIS • • • 0 0 • • •

IV. ANALYSIS AND DISCUSSION OF RESULTS • • • 0 • 0

A. General Analytic Relations • • B. Friction Losses for Full Flow C. Friction Losses for Part-Full Flow • • • • D. Entrance Losses • • • • • • • • • o •

E. Outlet Losses ••• 0 • • 0 • • • • • • • • • • • •

F. Comparison of St. Anthony Falls Laboratory Results with Other Data • • • • • • • •• 0 •

Acknowledgment

Glossary o 0 • • • • 0 0 0 0 0 • • • 0 0 • 0

ii

Page

iii

1

1 1 2

S 9 9

13 18 19 21

21

24 2S

Figure

I

2

3

b

6

7

B

9

! r 9 r 9 I t ! ! ! q r S a r r 9 g g

35-in. Concrete Culvert Test Installation . o . . c

Flush Headnall at fnlet to 36-in.. Concrete Culvert . .

Outlet of 3Gin. Diam Corrugated Culvert (FlowingP a r t l y F u l l ) . o , . . . c

Experinental Rating Curves (Concrete CulvertsF l o w i n g P u l l ) . . c c . ! . . , c

Experimental Rating Curves (Comugated MetalC u l v e r t s F l o w i n g F u l l ) . . . . o o

Experirnental Rating Curves (Concrete CulvertsF l o r i n g P a r t l y F u l l ) . . . . . .

Experinental Rating Curves (Corrugated Meta1 CulvertsF l o w i n g P a r t l y F u l l ) . c o o . . r

Conparison of Friction Factors (Concrete and CorrugatedM e t a l C u l v e r t s ) , . . . . a . o o . o . o

Corryarison of Roughness Coefficients (Concrete andC o m u g a t e d M e t a l C u l v e r t s ) . . . o . c . c . o

Page

6

7

t0

11

l-]-I

Figure

1

2

3

5

6

7

8

9

LIST OF ILLUSTRATIONS

36-in. Concrete Culvert Test Installation

Flush Headwall at Inlet to 36-in. Concrete Culvert • · Outlet of 36-in. Diam Corrugated Culvert (Flowing

Partly Full) . . . . · · · · · · · · · Experimental Rating Curves (Concrete Culverts

Flowing Full) . . . · · · · 0 · · · · · · · · · · · Experimental Rating Curves (Corrugated Metal

Culverts Flowing Full) · · · · · · · · · · · · · · · Experimental Rating Curves (Concrete Culverts

Flowing Partly Full) · · · · · · · · · · · · · · · · Experimental Rating Curves (Corrugated Metal Culverts

Flowing Partly Full) · · · · · · · · · · Comparison of Friction Factors (Concrete and Corrugated

Metal Culverts) · · · · Comparison of Roughness Coefficients (Concrete and

Corrugated Metal Culverts) · · · · · · · · ·

iii

· · · ·

· · · · · · · · · · · ·

· · · ·

· · ·

· · · ·

· 0

·

·

· 0

·

Page

6

1

8

10

11

12

12

15

16

g I ! E 4 q ! I g ! A T A g 9 g I A E I g 9 { 9 Eg . 9 r g . & q r s a r q g . q B & g q . { r s 9 g E L ! !

s g ! r r E r . I I l s !

I. INTRODUCTION

F\r11-scale tests were eonducted at the St" Anthony Fa1ls lfydraulic

Iaboratory of the University of Minnesota primarlly for the purpose of obtain-

ing pipe friction and entranee loss coefflci-ents for concrete and corrugated

netal culvert pipes, i*rich would be mor e aecurate and dependable than those

eurrently recommend.ed in culvert design literature. Compariion of these test

data is presented in this paper and reconmendations are given for design values

of the coeffieients under various flow conditi-ons"

The e><perinental studies were made'were installed and maintained with excellent

accuracy was possible in these tests for all

3 ft in diameter were investigated"

on new culverts, all of which

aligrunent. A high degree of

of the eulverts. Sizes up to

Analytical studies were made of ttre data obtained fron the experi-

mental obsenrations whi-ch are significant to basic pipe flow theory where

systenatie forrn roughness and large dianeters "orn" i.rto*consideration.

II. RESU}E OF EXPffiIMENTA1 PROCfi.AM

A. Scope of T.ests

A total of nine culverts were tested, ranging in size from 18 inches

in dianeter to 36 inches in diameter, each with an overall length of approxi-

nately 193 ft. The culverts fal1 into three groups as followsl

(a) Circular eoncrete pipes

(U) Cireular eorrugated netal pipes

(") Corrugated metal pipe arches

fn each group, tests were rnade with pipe diameters of 18 inches, 2! lnehesl

and 36 inches. In the case of the pipe arch sections, the identifying di-mension

refers to a circular section of equal periphery.

Each pipe was tested when flowing fu11 and also rhen flowing partly

ftlll, and a wide range of diseharges nas used for each of these two nain flor

HYDRAULIC DATA COMPARISON OF CONCRETE AND CORRUGATED METAL

C U L V E R T PIP E S

I. INTRODUCTION

Full-scale tests were conducted at the st. Anthony Falls Hydraulic

Laboratory of the University of Minnesota primarily for the purpose of obtain

ing pipe friction and entrance loss coefficients for concrete and corrugated

metal culvert pipes, which would be more accurate and dependable than those

currently recommended in culvert design literature. Comparison of these test

data is presented in this paper and recommendations are given for design values

of the coefficients under various flow conditions.

The experimental studies were made on new culverts, all of which

were installed and maintained with excellent alignment. A high degree of

accuracy was possible in these tests for all of the culverts. Sizes up to

3 ft in diameter were investigated.

Analytical studies were made of the data obtained from the experi

mental observations which are significant to basic pipe flow theory where

systematic form roughness and large diameters come into consideration.

II. RESUME OF EXPERIMENTAL PROGRAM

A. Scope of ~ests

A total of nine culverts were tested, ranging in size from 18 inches

in diameter to 36 inches in diameter, each with an overall length of approxi

mately 193 ft. The culverts fall into three groups as follows:

(a) Circular concrete pipes

(b) Circular corrugated metal pipes

(c) Corrugated metal pipe arches

In each group, tests were made with pipe diameters of 18 inches, 24 inches,

and 36 inches. In the case of the pipe arch sections, the identifying dimension

refers to a circular section of equal periphery.

Each pipe was tested when flowing full and also when flowing partly

full, and a wide range of discharges was used for each of these two main flow

2

eonditions. Friction and entrance loss deterninations rere made for all runs.For the partly full flow condition, uniform subcritical flow was established

as the basis for measurements"

Technical Papers No. lr and No. 5r Series B, respectively, describein detail the irydrauU-e tests on the concrete culvert pipes and the corrugatednetal eulvert pi-pes separately. Horuever, the salient test results for bothtlpes of culuerts are presented in this paper (Technical Paper No. 3) "

Each pipe, with the exception of the 2,h-in. eoncrete pipe and the2l+-in. corrugated pipe arch, vras tested under. two types of entrsrce condi-

tionsl nanely, (f) int-et projecting 2 fI into the headwater pool, ana (2) inlet

flush with the headnrall-" The two pipes mentioned as exeeptions were testedonly with projecting inlets"

B. Sr:unary of Results

The main quantities determlned for use in culvert design were theManning roughness coefficiett ro and the entranee loss coeffici-ent, K"r whichare defined in terms of Eqs. (1) and (2) respectivelyl

a = + $ * z / t , t / z, )

r t -v

= K

e e z g

( r )

( 2 )

For the pipe flowing ful1n the test results are sumlarized j-n TableI. This tabulati-on shows maxirnum, mlnimum, and average values of n and K" for

each pipe. The unnner in rvhich the coefficj-ents varied is also indicated"

A sinilar sunmary tabulation for the partly full flow conditionappears in Table If.

the significance to be attached to the indicated variations in thecoufficients is discussed later in this report" For aceurate analysis ordesign, these variations must be properly considered" However, for the usual-eulvert design this degree of accuracy would not be warranted. Reeonrnendeddesign values, assuming new, straight pipe., are given in Table rlr, based onthe results of the studies deseribed in this report.

*A11 synbols are defined in the Glossary on page Zl.

2

condi tions. Friction and entrance loss determinations were made for all runs.

For the partly full flow condition, uniform subcritical flow was established

as the basis for measurements.

Technical Papers No. 4 and No.5, Series B, respectively, describe

in detail the hydraulic tests on the concrete culvert pipes and the corrugated

metal culvert pipes separately. However, the salient test results for both

types of cul¥erts are presented in this paper (Technical Paper No.3).

Each pipe, with the exception of the 24-in. concrete pipe and the

24-in. corrugated pipe arch, was tested under ' two types of entI"'al'lCe condi

tions; namely, (1) inlet projecting 2 ft into the headwater pool, and (2) inlet

flush with the headwall. The two pipes menti oned as exceptions were tested

only with projecting inlets.

B. Summar~y of Results

The main quantities determined for use in culvert design were the

Manning roughness coefficient n* and the entrance loss coefficient, K , which - e are defined in terms of Eqs. (1) and (2) respectively:

v2 H = K -e e 2g

(1)

(2)

For the pipe flowing full , the test results are summarized in Table

I. This tabulation shows maximum, minimum, and average values of n and K for - e

each pipe. The manner in which the coefficients varied is also indicated.

A similar summary tabulation for the partly full flow condition

appears in Table II.

The significance to be attached to the indicated variations in the

cOl.-fficients is discussed later in this report. For accurate analysis or

design, these variations must be properly considered. However, for the usual

culvert design this degree of accuracy would not be warranted. Recommended

design values, assuming new, straight pipe, are given in Table III, based on

the results of the studies described in this report.

*All symbols are defined in the Glossary on page 23.

3

TABI.E I

SUUIIART OF TEST NESUL1S . PIPES FIXtrIilG FI,jI,L

Pipe No. of?estc Uaxinu! lIinimlD Average Tlpe of Veliatlon

UANilI}.IG ROUGHNESS COEFflICTENT

18i dian corrugated

ZLn dian corrugeted

36tr dian corrugated

t l

LtL '

0.0251o.o25?o.o2b7

o.0222

0.02280.0216

o.o2\20.o2tQo.o2J2

Increaees as Reynolds No. increaseo

Decreages as dianeter lncreeses

Group 36 o.0252 0.@16 o.o2t9

18tt corrugated plpe arch

2!n corrugated plpe erch

J6n corrugated pipe arch

237t

o.02550.0215O.g2.h0

0.0210

0.0217

0.0215

o.0239

o.0?]6

o.0232

Increases as lteynolds t'lo. Lncreaaeg

Decreasee as dleneter lncroaaes

Group i9 0.0255 0.0zlo 0.0237

I8n dlan concret€

2lrtr dlen concrete

36n dlan concret€

L2

9u

0.ot080.0rol0.0108

0.0091o.oorJ0.0103

0.009?

0.0100

0.0106

Decreaees as tbynotde }{o. lncr€sgea

Increeseg as dianeter lncreaaea

Group t2 0.0t08 0.0091 o.0ro1

EN]RANCE IOSS COEFFICIENT, 'ROJECIINO I}ILET

I8r dj,an corrugated

2lrrl diarn conugated

36n dlan corrugated

Il

6

6

0. 89

0.88

0.85

0.63

0.78

o.62

o.79n A r

0.75

Randon

Group I6 0 .89 o.62 0. ?8

XBr corrugated pipe arch

ZLn corrugated plpe arch

J6r corrugated pipe alch

L2

6

7

r .08o.96r .03

o.720.66o.76

0.90

0.89 Randou

0.88

Group 25 r.08 o.6( 0. 89

18tr dlan concrete

2Li diam concrete

35n dian concrete

b8A

0. 12

o.19

0 . 2 r

0.09

0.0?

o. 12o. rlo.16

Increases as diact€r ii.lcreases

Oroup I6 0 .21 0 .07 0. 12

ENIIIANCE IOSS CoEFFICIEXT, FLUSI{ INLET

18n dian corrugated

2lrr dlan corrugat€d

J6r dian corrugat€d

I

76

0.60

0.56

0.68

o.250.50o. L3

v. ua

o.53n < a

Ibndorn

0roup 20 0.68 o,25 O.lr9

18r eorrugated plpe erch

2Ln corrugated plp€ arch

35tr corrugated pipe arch

9

2

0.59

u.4)

o.tp

o.33

o.5r

o.39Randon

Group I I o,59 0.t3 o.t9

l,8n dian concrete

ZLn dlan concrete

16r dtan concr€te

0.13

0.12

0.05

0.05

0.08

Grop L2 0.]3 0.05 0.09

Increaaes aB dlaDoter increasea

3

TABLE r

SUlO4ARY OF nsT RESULTS - PIPES FWIUNG FULL

Pipe No. of l!aximum llinimum Average Type of Variation Tests

MANNING ROUGHNESS COEFFICIENT

18" diam corrugated 11 0.0251 0.0222 0.0242

24" diam corrugated 13 0.0252 0.0228 0.0242 Increases as Reynolds No. increases

36" diam corrugated 12 0.0247 0.0216 0.0232 Decreases as diameter increases

Group 36 0.0252 0.0216 0.0239

18" corrugated pipe arch 23 0.0255 0.0210 0.0239

24" corrugated pipe arch 7 0.0245 0.0217 0.02)6 Increases as Reynolds No. increases

36- corrugated pipe arch 9 0.021i0 0.0216 0.0232 Decreases as diameter increases

Group 39 0.0255 0.02)'0 0.J237

18" diam concrete 12 0.0108 0.0091 0.0097

24" diam concrete 9 0.0104 0.0093 0.0100 Decreases as rteynolds No. increases

36" diam concrete 11 0.0108 0.0103 0.0106 Increases as diameter increases

Group 32 0.0108 0.0091 0.0101

ENTRANCE LOSS COEFFICIENT, PROJECTING INLET

18" diam corrugated 4 0.89 0.63 0.79

24" diam corrugated 6 0.88 0.78 0.81 Random

36" diam corrugated 6 0.8£- 0.62 0.75

Group 16 0.89 0.62 0.78


24" corrugated pipe arch 6 0.96 0.66 0.89 Random


Group 25 1.08 O.U, 0. 89

18" diam concrete 4 0.12 0.09 0.10

24" diam concrete 6 0.19 0.07 0.11 Increases as diameter increases

36" diam concrete 6 0.21 0.12 0.16

Group 18 0.21 0.07 0.12

ENTRANCE LOSS COEFFICIENT, FLUSH INLET

16" diam corrugated 7 0.60 0.25 0.42


36" diam corrugated 6 0.£>8 0.43 0.53

Group 20 O.ffl 0.25 0.49


24" corrugated pipe arch 0 Random


Group 11 0.59 0.33 0.49

18" diam concrete 7 0 • .1.3 0.05 0.08

24" diam concrete Increases as diameter increases

36" diam concrete 5 0.12 0.05 0.10

Group 12 0.13 0.05 0.09

4

?ABIA TI

SI'UMARI OF TEST RESUL$i - PIPES FLOUING PARTLY FULL

PlpeNo. c fTests

llaxinun l{ininun Average lVpe of Variatlon

!{ANNINC ROUGHNESS COEFSICIN'IT

]8rr dlan corrugated

2lrn dlan corrugated

J6r dLas corrugat€d

I

10

1L

0.0258

o.02LL

0.0211

0.02!8

0.023?

0.0228

o.0252

0.02[0

o.02)6

Randon

Group )2 o.o25B 0.0228 O.OZlr2

lStt corrugated pipe arch

2lrr! corrugated oipe arch

35r eorrugated pipe arch

10

?

I3

o.023)

0.0228

0.0230

0.02r.6

0.0213

0.0223

o.0220

o.0226

Randon

Group 2(' 0 .0233 0.0213 o.o22b

IEtl dlan concrete

2bt dian concrete

36f dlan concrete

t n

6

o.01to

0.0r08

0.oLo2

0.0102

0.0107

0.0101 Randon

Group IO 0.0110 0.0t02 0.0106

EN1RANCE IO.SS CoEFFICIENT, pRoJECTING INTET

l8tr dian ccrrugated

2hrr dian corrugated

36tt dian corrugated

L 0.77

o . 7 7

0.81

0.58

0.63

0.58

0.71

o.69

o.69

Randon

'Group 1 A 0 .8 r u. >o 0 .70

I8n corrugated pj.pe arch

2lrtr corrugated pipe areh

36r corrugated plpe arch (

0. 82o.96

0.51

0.1-!3

o.3LO.LI

u. o>

o.68

0.116

Randoro

0roup L5 0.96 0.31

l3't dian concrete

?lro dianr concrete

l6n dian eoncrete

8 o.20

o _"t

o. 13

o_0,

0. 16

o-* Randorn

0roup !u o,2) 0.02 o.L2

BNTRANC8 LoSS CoEFFICIET'IT, FLUSE INLET

18"

2Lnr(n

dian co"rugated

dian corrugated

dian corrugated

!

A

o.560.5bo.53

0.28

o.lQ

o. )7

0.1[0.1r8

0. L2

Randon

Oroup L> 0.56 o.28 u.llll

r8r

2ljr

Xe

corrugated pipe arch

corrugated pipe arch

corrugated pLpe erch b

0.b3 0 ' I 7

v . r ?

0.30

0.26

llandon

Group I I o.L3 0.15 0.28

IEr dlan concrete

2hr diar concrete

J5r dlan concret€

2 o-* o.06 0. lo

Group 0, 15 0.06 0.10

Randon

4

TABLE II

SUMMARY OF TEST RESULTS - PIPFS FLOWING PARTLY FULL

Pipe No. of Maximum IIinimum Average Type of Variation Tests

MANNING ROUGHNFSS COEFFICIENT

18" diam corrugated 8 0.025R 0.0248 0.0252

24" diaID corrugated 10 0.024L 0.0232 0.0240 Random

36" diam corrugated lL 0.0243 0.0228 0.0236

Gr oup 32 0.0258 0. 0228 0.0242


24" corrugated oipe arch 3 0.0228 0.0213 0.0220 Random


Group 26 0.0233 0.0213 0.0224

18" diam concrete 10 0.0110 0.0102 0.0107

2L" diam concrete 6 0. 0108 0.0102 0. 0104 Random

36" diam concrete

Gr oup 16 0.0110 0.0102 0.0106

ENTRANCE LOSS COEFFICIENT, PROJECTING INLET

18" diam corrugated 4 0.77 0.58 0. 71


36" diam corrugated 7 O.Sl 0.58 0.69

'Group 16 0.131 0.58 0.70

18" corrugated pipe arch 5 0.82 0. 43 0.65

24" corrugated pipe arch 3 0.96 0. 34 0.68 Random

36" corrugated pipe arch 7 0.5L 0.41 0.46

Group 15 0.96 0.34 0.57

18" diam concrete 8 0.20 0.13 0.16

24" diam concrete 6 0.23 0.02 0.08 Random

36" diam concrete

Group 14 0.23 0.02 0.12

ENTRANCE LOSS COEFFICIENT, FLUSH INLET

18" diam corrugated 4 0.56 0.28 0.41

24" diam corruga ted 5 0.54 0. 42 0.48 Random

36" diam corrugated 6 0.53 0.37 0.42

Group 15 0.56 0.28 0.44

18" corrugated pipe arch 5 0.43 0,17 0.30

24" corrugated pipe arch 0 Ilandom


Group 11 0.43 0.15 0.28

8" diam concrete 2 0.15 0.06 0.10 Random

24" diam concrete

36" diam concrete

Group 2 0.15 0.06 0.10

TABLE III

RECOMMENDED DESION COEFFICTENffi

FOR CORRUGATED METAL AND CONCRETE CULVERTS

Itern

.|tCorrugated ^ t+--

u;;; i-- con*ete

Manning coeff i -c ient, fu1l f low

Manning coeff ic ient, part ly ful l f low

Project ing inlet coeff ic ient, fuI1 f low

Project ing inlet coeff ic ient, part ly ful l f low

Flush inlet coeff ic ient, ful l f low

Flush inlet coeff ic ient, part ly ful l f low

v . v ( > v

0 .02L0

0 . 9 0

0 . 7 0

n q n

0. h0

0.0100

0.0110

U . I >

0 . 1 5

0 , 1 0

0 . 1 0

oTh" above recornmended values appty to nevr, straight pipe vrith no

obstruct ions, s ide openings, or other f low-disturbing features" I 'he Man-ning coefficj.ents for conugated rnetal apply to corrugations uith 1/2-in.heieht and 2 2/3-in. spacing" The Manning coefficients for concrete applyto pipe manufaetured by the cast-and-vibrated process in 6-ft lengths ofpipe and uith non-pressure rubber: ring joints.

As a culvert mater ial , corrugated metal is obviously much less ef-

ficient hydraulically than concretel detailed comparisons appear later in the

report" fn general , i t may be said that a culvert usual ly can, and should,

be designed to flow full under the given conditions of discharge and available

head. Such a design would usual ly be most economical, regardless of uhich

naterial is used. Howev-er, a concrete culvert flowing full has a much higher

hydraulic capacity than a cormgated culvert of the same dianeter. Therefore,

whenever hydraul ic eff ic iency is the control l ing design factor in a glven

culvert, concrete or other snooth-walled pipe is rmrch superior to corrugated

netal"

r1I" METHODS OF TESTLNG AND ANALYSIS

All of the pipes were tested in the nain testing channel of the

St. Anthony FaIIs Hydraulic taboratory. Each pipe was approxinatefy 193 ft

Iong and on a slope of approximately 0.002. Bulkheads were 1nstaIled near

the two ends of the pipe in order to form headnater and tailwater pools, the

general experimental installation is shown on Fig. I.

TABLE III

RECOMMENDED DESIGN COEFFICIENTS

FOR CORRUGATED METAL AND CONCRETE CULVERTS

Item

Manning coefficient, full flow

Manning coefficient, partly full flow

Projecting inlet coefficient, full flow

Projecting inlet coefficient, partly full flow

Flush inlet coefficient, full flow

Flush inlet coefficient, partly full flow

Corrugated Metal

0.0250

0.0240

0.90

0.70

0.50

0.40

* Concrete *

0.0100

0.0110

0.15

0.15

0.10

0.10

*The above recommended values apply to new, straight pipe wi th no obstructions, side openings, or other flow-disturbing features. 'l'he ManninG coefficients for corrugated metal apply to corrugations with 1/2-in. he ight and 2 2/3-in. spacing. The Manning coefficients for concrete apply to pipe manufactured by the cast-and-vibrated process in 6-ft lengths of pipe and with non-pressure rubber ring joints.

5

As a culvert material, corrugated metal is obviously much less ef

f ic ient hydraulically than concrete; detailed comparisons appear later in the

report. In general, it may be said that a culvert usually can, and should,

be designed to flow full under the given condi tions of discharge and available

head. Such a design would usually be most economical, regardless of which

rna terial is used. Howev_er, a roncrete culvert flowing full has a much higher

ydraulic capacity than a corrugated culvert of the same diameter. Therefore,

whenever hydraulic efficiency is the controlling design factor in a given

culvert, concrete or other smooth-walled pipe is much superior to corrugated

etal.

TIL METHODS OF TESTlNG AND ANALYSIS

All of the pipes were tested in the main testing channel of the

St. Anthony Falls Hydraulic Laboratory. Each pipe was approximately 193 ft

ong and on a slope of approximately 0.002. Bulkheads were installed near

he two ends of the pipe in order to form headwater and tailwater pools. The

general experimental installation is shown on Fig. 1.

F iq . l - 36 - i n Conc re te Cu l ;e i " i Tes t I ns to l l a t ron

6

Fig. 1- 36-in. Concrete Cul vert Test Installation

7

A large number of runs was nade in eaeh pipe for both fu1l and part-

fu11 flor condltions and for both projecting and flush inlets in an attenpt

to study as wj-de a range of flow conditions as facilities would pernit. The

false bulkhead used to sinmlate a flush entrance is shoyvn.in Fig. 2.

F ig. 2- F lush Heodwol l o t In le i to 36- in . Concrete Culver t

For each ntn, eareful measurements were made of the discharge, the

trydraulic grade 1ine, and the vrater temperature. The diseharge Tyas controlled

b5r gates at the entrance to the testing channeS- and was usually measure'd in

large vo}:metric tanks, although weighing tanks or a calibrated supply-line

7

A large number of runs was made in each pipe for both full and part

full flow conditions and for both projecting and flush inlets in an attempt

to study as wide a range of flow conditions as facilities would permit. The

false bulkhead used to simulate a flush entrance is shown in Fig. 2.

Fig. 2- Flush Headwall at Inlet to 36-in. Concrete Culvert

For each run, careful measurements were made of the discharge, the

ydraulic grade line, and the water temperature. The discharge was controlled

by gates at the entrance to the testing channel and was usually measured in

l arge volumetric tanks, although weighing tanks or a calibrated supply-line

B

meter were used for some runs. The tailwater 1eve1 was controlled by a weirgate at the dovirnstream end of the charu:e1 in order to adjust the hydraulicgrade 1ine. The latter was deternined by piezometric neasurements at j^ntervals

along the prpe, eaeh piezometer tap being connected to a eentral rnanometerboard, where simultaneous static pressure readings cor:Icl be observed for allreaehes of the pipe.

For details of the experinental apparatus and procedure, TechnicalPapers No. l+ and No. 5 of this series should be consulted. It is believedthat accurate and reliable results have been obt:Lined.

Froro the erperimental data, friction coefficients anC entrance eoef-fieients were eomputed for each run. Barrel friction losses were obtainedfrom the slope of the hydraulic gradient in the central reaches of the pipewhere the gradient was a strai-ght line. Entrance losses were obtained Wextending the straight-line portion of the hydraulic gradient back to theplane of the pipe in1et, adding the pipe velocity head and then deducting thetotal fron the headwater elevatlon.

In the part-fuI1 flow tests, a condition of approximately r:niformflowvras established for the particular depth and discharge, Thus, the hydrau-Iie gradient was equal or nearly equal to the eulvert s1ope. A view at theculvert outlet with part-fu11 flow in the barrel appears in Fig. l.

F i q 3 - O u t l e t o f 3 6 - i n( Flowing

Diometer Cor rugoted Cu lver tPort ly Ful l )

8

meter were used for some runs. The tailwater level was controlled by a weir

gate at the downstream end of the channel in order to adjust the hydraulic

grade line. The latter was determined by piezometric measurements at intervals

along the pipe, each piezometer tap being connected to a central manometer

board, where simultaneous static pressure readings could be observed for all

reaches of the pipe.

For details of the experimental apparatus and procedure, Technical

Papers No.4 and No.5 of this series should be consulted . It is believed

that accurate and reliable results have been obtained.

From the experimental data, friction coefficients and entrance coef

ficients were computed for each run. Barrel friction losses were obtained

from the slope of the hydraulic gradient in the central reaches of the pipe

where the gradient was a straight line. Entrance losses were obtained by

extending the straight-line portion of the hydraulic gradient back to the

plane of the pipe inlet, adding the pipe veloci ty head and then deducting the

t otal from the headwater elevation.

In the part-full flow tests, a condition of approximately uniform

f low was established for the particular depth and discharge. Thus, the hydrau

lic gradient was equal or nearly equal to the cuI v~rt slope. A view at the

culvert outlet with part-full flow in the barrel appears in Fig. 3.

Fig . 3 - Outlet of 36 - in. Diameter Corrugated Culvert

( Flowing Partly Full)

I

fn nost casesr this conditlon was also a tranquil flow eonditj-on.However, the critical slope for the )6-in. conerete pipe was so near the actuals)-ope of the pipe that near-critical flow uas obtained at nearly all clepthsin this pipe. The resultant excessive wavi.ness and vari-ability of the watersurface made it impossibl-e to deternine eoefficients for the r:niform part-fu11

flow condition j-n this pipe"

Reference rnay again be nade to Teehnical Papers No" lr ana No. 5 formore detailed e:iplanations of the conputational procedures euployed"

The experimental rating curves for all of the pipes are shovrn inFigs. L, 5, 6, and f,

rV" ANALYS$ A}ID DISCUSSION OF NESIIf,?S

A. General Analytic Relations

The general equation defining flow through ei culvert is

H = K * $ . * r * . * " * ( : )

In thls equation, !i is the diffe:'ence between tc'ral head j-n the headwater andtailwater pools. If the veloeity heads in the pool-s are sna11 or i-f they arenearly equaI, then H nay be takenas the difference in eletations between theheadyrater and tailwate:'pools. ?he aver&ge velocity of f1ow, I, i-s measuredin the cr:ntraI reacl:es of the pipe rhere the flow is unifei:'m. The normal baruelfriction loss, x, (v'i?c), is the loss whi*h would oceur in an interlor reaehof a very long hS4pothetir:al pipe of the same eross secti-oil and naterial, thereach having a length equal t,o the length of the actual culvert.

The entranee 1oss, Xu tvz/Ze)r 5-s the excess friction l*ss near thepipe inlet over the normal bamel frie:;.!-*n l-oss in that region" in the erqperl-ments elescribed in this paper' the entran*r* loss was o"r,"tained by extending thestraight-line portion of the hydraulie g::ade line to the pi-ane oj ti:e entrance,adding the unlform velocity head, snd d*ducling the totaj- j.}on the headwaterelevation. simiLarly, the outlet losi;, Ko 'r',:2,izr), was obiained by extendingthe hydrarrlic gradient linearly to the plane of th* outlet, adding the velocityheadr and subtracting the taibyater elevatir:n f,::orn the sun.

The entrance and outlet loss coeff,i*ients, K" and K*, are usuallyobtained eriperimentally for dlffereni Qrp*s of entranees and outle*;s, although

9

In most cases, this condition was also a tranquil flow condition.

However, the critical slope for the 36-in. concrete pipe was so near t he actual

slope of the pipe that near-critical flow was obta ined at nearly all depths

in this pipe. The resultant excessive waviness and variability of the water

surface made it impossibl e to determine coefficients for the uniform part-full

flow condition i n this pipe.

Reference may again be made to Technical Papers No . 4 and No. 5 for

more det ailed explanations of the computa t ional procedures employed.

The experimental rating curves for all of the pipes are shown in

Figs. 4, 5, 6, and 7. "

IV 4 ANALYSIS AND DISCUSSION OF RESULTS

A. General Analytic Relations

'I'he general equation defining flow through a culvert is

v2 V2 V2 H = K -- + K -- + K -- (3) e 2g f 2g 0 2g

In this equation, H i s the differ ence between t ot al head i n the headwater and

tailwater pools. If the velocity heads i n the pool s are small or if they are

nearly equal, then!! may be taken as the difference in elevations between the

headwater and tailwater pools. The average velocity of flow, Y." is measured

in the central reaches of the pi pe where the flow is uniform. The normal barrel

frict:i. on loss , Kf (V2/ 2g), is the loss which would occur in an interior reach

of a very long hypothetical pipe of t he same cross section and material, the

reach having a length equal t o the length of the actual culvert.

The entrance loss, K (V2/2g) , is the excess friction l oss near the

e pipe inlet over the normal bar rel fri ction l oss in that regi ono I n the experi-

ments described in this paper; the entrance loss was obtained by extending the

straight- line portion of the hydraulic grade l i ne to the plane of the entrance,

adding the uniform velocity head, and deduc ting the total from the headwater

elevation. Similarly, the outlet loss , Ko (V2/ 2g), was obt ained by extending

the hydraulic gradient linearly t o the plane of t he outlet, adding the ve l ocity

head, and subtracting the tai lwater eleva t i on from the sumo

The entrance and outlet loss coeff i cients , K and K , are usually e 0

obtained experiment a l ly for different types of entrances and outle t s , although

to

t . o o

o ,90

o.80

o.70

- o .40cQ)()L

^o o.30II

to.25

co; o.2oo(,

! o.roJ0

p

xo. ro

oll) o.o9oo o.oga

Dischorge i n c f s

Fig. 4- Exper imentol Rot ing Curves( Concrete Culverts Flowing Full )

-c: Q)

U

... Q)

a.. c

T-c: Q) .-'0 0 ... (!)

0 .-;:, 0 ... '0 >. :t:

.... 0

Q)

a. 0

(/)

1.00

0.90

0.80

0.70

0.60

0.50

0 .40

0.30

0 .25

0 .20

0 .15

0.10

0 .09

0.08

0.07

0.06

0 .05

0 .04

0 .03 3

I I

I V

/

4

1 ;1

I I J

f L ° Cb

/ .~ , / Q. /

..... Cb V-J ,Cb

/ <;:u I jJ ~t

.~

} V if

~ .~ / 0/

Q. V J ..... Cb / P ,Cb

~ <;:u I Cb

(J0 .~

j Q.

d Cb . ~' I r ~J ~ j ~ v (J0 1

J ·s· I V I I Co

I'f) I J

II J r

/ II

I /

V

5 6 7 8 9 10 15 20 25 30

Discharge in cfs

Fig. 4- Experimental Rating Curves

(Concrete Culverts Flowing Full)

/0

p

II d ~

/ i

if

i /

40 50 60

co()

o,(L

c.9oc'

(9

.93o

E

-

oQ'o.oa

2.OO

r . 5 0

| . 0 0o .90o . 8 0

o .70

0.60

o .50

o 4 0

o .30

o .23

0.20

o. l5

o. r00.09

o.o8

o.o7

o.06

o.o 5

o.o4

o.03

2 . 5 3 4 5 6 7 A 9 l O 1 5

D i s c h o r g e i n c f s

Fig. 5- Exper imentol Rot ing Curves( Corrugoted Metol Culverts Flowing Full )

II

/I

d tl , f

If t

I P t)

I I

{ / s e)I

Y

I I

- vCV

q (J\.(,

v /os\ -:"/=d

{

$l(,. \

:..r-c.

Q

o

lr:/ 7 / h

{

, // / f /

II

/

/ //

JI I t

lI

( PI

ot

d

/

/

I

(t

r . 5 2 5

II

2.00

p

,/ I. 50

1.00

0 . 90

0 . 80

0 . 70

0.60

0.50

0.40 -c CII u

0 . 30 ... CII

Cl. 0 . 25

c

- 0.20 c CII

"0 0

0 . 15 ... C)

u

I p l~ ~ ~~ :t l( 1/1 9

f j I / ~ ~ { r 'I If , I r ~

11 ! ~ / If; f f ( ~-,~ Q. / ,

/ / ~L ,c; If r ~-fJ~~ Q."-~t;~

~ ~ ~; ~ u ' °9 "-;!'I"

.... u

~V'~ <:r

.;/ 11 <I> ....... 0 I ~ .~ h~ Q. f:' /1 If Q. "J ~ ,~U

'ff (J ·r, , ()

'i' <0 . ~ ·r 'If. try'/; rf f P 7 f!J V ~.

<0 / <' try

'/ I II 1 I :; 0 ...

0.10 "0 >.

0.09 :r: - 0.08 0

CII 0.07

a. 0 0.06 (/)

0.05

l I I liP / / I I 1/ d

/ , f-" / / 'II ~ f

/ 0 I

lei /

/ 0 .04

/ , 0 .03

/ 'I

J c!

0.02

0.01 1.5 2 2.5 3 4 5 6 7 8 9 10 15 20 25 30 40

Discharge in cfs

Fig. 5- Experimental Rating Curves

( Corrugated Metal Culverts Flowing Full )

t2

\36" Ct

;ompule.l I\,ncrete Pip€lormol Disc rorgE

\I

24" Concrete i p e

Erperimenlol N(n : O . l

rmol) r o4

)ischrr r9e

\ t

tE" Concrete Pipe | | IExperimenlol Normol Dischorge / 2

.r[rcot ursnorgetor o 36" Pioe

---f---n . o:o106----.....

\ ,f| lrcor urScnofgrj for o 2o"eipo

I 4 1.Critlcol Dirchorg.

for on 18" Pip.,l '2.

{/, I

tr7

- o )

.g

'IL

o

f

c l

ooo

.5

I

f,

F

o=3

o

E

o

r o 2 0 3 0Dischorge in cfs

Fig . 6 - Exper imento l Rot ing Curves(Concrete Culverts Flowing Port iy Ful l )

0 l s c h o f g c i n c f s

Fig.7- Exper imentol Rot ing Curves

( Corrugoted Metol Culverts Flowing Portly Full )

36" Circulor Plp.n c O.O235

u l r c u p r r r P Cn = O.0 24O .r

36" Pipc Archn : 0 .0226

ls" Circulor Pipln = O.O253 /

24" Pipc Archn ' 0 .O220

d

. \ { {

tS" plpc arch ll

n ,O .OZ23 J{ /- j

) 7,r

r { I -g

,Ar' r

tuv I

3

I. 36" Concrele Pipe Computed Normal Discharge

n'O.OIO

i'--.

24" Concrele Pipe > V EKperimentol Normal Discharge V n'0.0 104 .-/

i /'" --.-/ --- .... , -

-= 2 ... c

,,/ - "'----s o u::

18 " Conc rete Pipe I J Experimental Normal Discharge " b;? --'

a. .. o

I

M If ,

o o

3

n ' 0 :0106

~

/ p ~ .J .', 0

{t; ~ / /

/

If' :"/

/

~ ~,:, ff./ ~ :'::, ----:.,

10

"-,, ? ~ .-~ V , - '

",,-Critical Discharge

" for a 24" Pipe

-- ............ Crit ical Discharo_ for on 18" Pipe

20 Discharge in cfs

30

Fig . 6- Experimental Rating Curves

(Concrete Culverts Flowing Partly Full )

\

\ )

/

--------rilicol Discharge

for a 36" Pipe

40

) 36" Circular Pipe

.z:;

-;;'1 .. o

o

IS" Circular Pipe n ' 0.0253

I IS Pipe ArChj n· 0.0223

PJ / I f ~ fd ~ "./'

/;; ~ V I/fZ / r o

n' 0.0 36

j.,/ "

./V 24 Circular Pipe

~ n ' 0.0240 '\ } V

../ ~ 36" Pipe Arch n • 0.0226

.I 24" Pipe Arch .............. /'

.............. V

n' 0 .0220

\ ./ ~

/ rP""

V- i / ./' ~

./ -r

..P"'" /'"

/' /

r

5 10 15 20

Discharge in cis

Fig . 7- Experimental Rating Curves

( Corrugated Metal Culverts Flowing Partly Full

12

-'

13

they nay be closely corryuted analybically in many cases from principles of

hydrodynamics.

The barrel friction loss coefficient, Kf, is usually expressed in

terns of one or nore of the various pipe-flcm foruru1as, The nost commonly

used fornulas of this type are the Darcy formula and the Manning formula. The

latter formula has already been given as Eq. (r). The Darcy forrnula is

(L)H ="f

The Darcy frietion factor, !, is related to the lbnning roughness coeffieient,

n, by the following:

4 - 1 1 ?I . - I I ' $)

tsotir the Mannlng coefficient and Darcy friction factor ean be computed fron

tlte measured discharge, cross-sectional dj-mensj-ons, and hydraulic graclient.

The friction factor is known to be a function of the Reynolds number

and the pipe naterial. The Reynolds nunber, Re, i-s defined by the expression

^ Lnvn e = i (5)

In this expression, the kinernatic viscosity, I./ , is a fluid property vrhich, for

a given fluid, varies with tenperature.

The Manning coefficient has corrnonly been supposed to be dependent

only on the pipe naterial for the usual design flows in engineering conduits.I{owever, the present studies have denonstrated that it j-s also dependent on

the Reynolds nr:mber, at least within the usual range of flows in conerete and

eorugated netal eonduits. This would also be found true w"ith the eoefficients

of the Scobeyr Hazen-Y{i11ians, and other enpirical pipe-flow fornulas.

B" Frietion Losses for Fu1l Flow

The Darcy friction factor, !, is known to depend upon the Reynolds

nunber, Re, and the pipe roughness. Forpipes of a given naterial, the absolute

roughness is presurned to be the sane, regardless of the pipe size. However,

the relative effect of a given tlrye of ra1I roughness on the flow should

decrease as the pipe size increases.

" . L u 2 = n t- ljR 29 "t 2e

2n

w

1)

they may be closely computed analytically in many cases from principles of

hydrodynamics.

The barrel friction loss coefficient, Kf , is usually expressed in

terms of one or more of the various pipe-flow formulas. The most commonly

used formulas of this type are the Darcy formula and the Manning formula. The

latter formula has already been given as Eq. (1). The Darcy formula is

L V2 V2 Hf = f LR 2g = Kf 2g (4)

The Darcy friction factor, f, is related to the Manning roughness coefficient,

~, by the following:

2 n

f = 117 :i73 R

(5)

Both the Manning coefficient and Darcy friction factor can be computed from

the measured discharge, cross-sectional dimensions, and hydraulic gradient.

The friction factor is known to be a function of the Reynolds number

and the pipe material. The Reynolds number, Re, is defined by the expression

Re = 4RV /I

(6)

In thi s expression, the kinematic viscosity, /I, is a fluid property which, for

a given fluid, varies with temperature. '

The Manning coefficient has commonly been supposed to be dependent

only on the pipe material for the usual design flows in engineering conduits.

However, the present studies have demonstrated that it is also dependent on

t he Reynolds number, at least within the usual range of flows in concrete and

corrugated metal conduits. This would also be found trup. with the coefficients

of t he Scobey, Hazen-Williams, and other empirical pipe-flow formulas.

B. Friction Losses for Full Flow

The Darcy friction factor, f, is known to depend upon the Reynolds

number , Re, and the pipe roughness. For pipes of a given material, the absolute

roughness is presumed to be the same, regardless of the pipe size. However,

the relative effect of a given type of wall roughness on the flow should

decrease as the pipe size increases.

rb

ft has becone conmon in recent years to use the ratio of equivalent

sand dianeter to pipe diameter as a neasure of the relative roughness of a

pipe. The equivalent sand dianeterr Kr, is understood to be the diameter of

uniform sand grains vihich could be coated on a smooth pipe of the same dianeter

as the pipe under consideration and would cause the same friction loss as

obtained in the actual pipe. The friction factor can then be written as a

funetion of the Reynolds number and relative roughness, thusl

Kf = fn 1ne, f,) ( 7 )

fn the laminar and partly turbulent regimes of flow, the wall rough-

ness has no persistent influence upon the flow strueture, and thus the friction

factor is a function of the Relmolds nunber onLy" the functional relation of

Eq. (Z) ls then e:oressible by the following equations for laminar and oartly

turbulent (smooth-pipe) flow, respectively:

, 5 Lrde

( 8 )

and

f - (e )

Equation (8) is the Poiseuil le equation for viscous f low" Equation (p) is

due to Nikuradse and is only one of several semi-enpirical equations vrhich

have been suggested by various authors to describe the partly turbulent regine,

though probably the most generally accepted of such equations"

In the regime of fuIl turbulence, the wall roughness predominates

and the friction factor does not vary uith increasing Reynolds number. The

Nikuradse equation for this regime is:

f o (10 )

(2 rog Re 1F - 0.8)2

K( t . r l r - z r o g f ) 2

The transition between the regines of partial and full turbulence

has been largely ignored in most hydraulic design practice heretofore" The

traditional empirical pipe design for:nulas have neglected the effect of vis-

cosity, which implicitly assumes fully turbulent conditions. An equation which

14

It has become COlmnon in recent years to use the ratio of equivalent

sand diameter to pipe diameter as a measure of the relative roughness of a

pipe. The equivalent sand diameter, K , is understood to be the diameter of s uniform sand grains which could be coated on a smooth pipe of the same diameter

as the pipe under consideration and would cause the same friction loss as

obtained in the actual pipe. The friction factor can then be written as a

function of the Reynolds number and relative roughness, thus:

K f = fn (Re, ;)

In the laminar and partly turbulent regimes of flow, the wall rough

ness has no persistent influence upon the flow structure, and thus the friction

factor is a function of the Reynolds numb~r only. The functional relation of

Eq. (7) is then e:xp ressible by the following equations for laminar and partly

turbulent (smooth-pipe) flow, respectively:

and

f

f _ 64 - Re

1

(2 log Re if _ 0.8)2

(8 )

(9)

Equation (8) is the Poiseuille equation for viscous flow. Equation (9) is

due to Nikuradse and is only one of several semi-empirical equations Ylhich

have been suggested by various authors to describe the partly turbulent regime,

though probably the most generally accepted of such equations.

In the regime of full turbulence, the wall roughness predominates

and the friction factor does not vary with increasing Reynolds number. The

Nikuradse equation for this regime is:

f • 1

K 2 (1.14 - 2 log ;)

(10)

The transition between the regimes of partial and full turbulence

has been largely ignored in most hydraulic design practice heretofore. The

traditional empirical pipe design formulas have neglected the effect of vis

cosi ty, which implici tly assumes fully turbulent conditions. An equation which

has been fairly extensively

brook and liilhite:

used for this transi-tional realm is

1 1 "L2

that of Cole-

Kl r . r l+ - 2 rog (* *L J

(11)

The Colebrook-'ll{hite curve is asln'nptotj-c to the Ni}uradse srnooth-pipe and rough-

pipe curves, as defined by Eqs. G) ana (10), and purports to represent the

transitional region of pipe flow as obtained on actual conmercial pi-pes.

The frietion factor - Reynolds number curves for the corrugated netal

and concrete pipes included in the experlments reported herein are shown in

Fig. B, along with the smooth-pipe curve. Both sets of experimental curves

indi-cate a functional dependence of the frietion factor.upon both the Reynolds

nurnber and t'he relative roughness, implying that the flow regine is transi-

tional- between partlal and fuIl turbulence.

n n r ' - 27 . ) > \ l

Re '[f J

. t 0

09

.08

.07

.06

4cyt-

ffi'l rpe-E\6 f

11|-\itcutor,

Cor ug o led 'ela / ipes

SrDor) th t i p e(Et

"-]oslr . \\\

t S )

Concre;rle Pipes--_l*lrcTr*:--_ 24" 3 6 " crr I ,Pes

tt iD t"-J--;

i-

; . o5o0u-

.04c.9' ih . 0 3

. o lr0o.ooo 2 O 0 . 0 o 0 - R V 5 0 0 ' 0 0 0

R e y n o l d s N u m b e r , A " = 3 ,

Fiq 8 - Comporison of Friction Foctors(Concrete ond Corrugoted Metol Culverts )

50, ooo r,0o0,o0o 2 , O 0 O , 0 O O

15

has been fairly extensively used for this transitional reaLll is that of Cole

brook and Whi te :

1 f = --------------~----------~ K 2

2 log (2. + 9.3~ l D Re -Vf J

(11)

The Colebrook-White curve is aSY1!lptotic to the Nikuradse smooth-pipe and rough

pipe curves, as defined by Eqs. (9) and (10), and purports to represent the

transitional region of pipe flow as obtained on actual commercial pipes.

The friction factor - Heynolds number curves for the corrugated metal

and concrete pipes included in the experiments reported herein are shown in

Fig. 8, along with the smooth-pipe curve. Both sets of experimental curves

indicate a functional dependence of the friction factor upon both the Reynolds

number and the relative roughness, implying that the flow regime is transi

tional between partial and full turbulence .

~

0

~ 0 u..

c 0

" ~

. 15

I

.10

09

.08 --

.07

.06

.05

.04

.03

r--.02 SmOOth -

P'Pe

.01 50,000

---~ --- t>.(c\'l - -" I'\\l_e

-I--~~I'\\le ~~....-C;(cu z ---:-: ~ t>.(c\'l ..

-- \8 ~I _____ -f4C\(CU\O~_ I--~

I~~ I'lpe 36" Ci(Culor

Corrugated Metal Pipes

-1--1-- - . Concrete Pipes

(8las' --::::::t:----t.~ 2 " IUS)

...... ClrcUlo ~, 36" Circu/ r

smOOlh~~ --r-. Pipes

Ipe (N ' r-- -Ikur __ fdSe

) r--r--_I----100,000 200,000 4 R V 500,000 1,000,000

Reynolds Number, Re = -v-

Fig. 8 - Comparison of Fr iction Factors

( Concrete and Corrugated Metal Culverts

r--

r--.. 2,000,000

1 6

Holuever, neither the curwes for the corrugated pipes nor those for

the eonerete pipes can be satisfactorily expressed in Lerms of the Colebrook

equation. The eorrrrgated pipes especially gave results eontradietory to those

that would be erpected from the Colebrook equation, slnee a definite increase

in friction factor with increasing Relmolds number was noted for each of then,

whereas the equation postulates a decreasing friction factor.

These curves seem to approach the horizontal at high lleynolds num-

bers, but they all show a rising characteristic throughout the experi-mental

range. Such a ri-sing eharacteristie was unexpected and is unique anong con-

mercial pipes, These results serve to ernphasize t'tre fact that pipes withrrregularrrpatterns of roughness nay behave quite dlfferently hydraulically fron

pipes of rrrandomrr roughness patterns, for whieh the Colebrook equation was

derived. the detailed hydrodynanics of friction losses in corrugated pipe is

still obscure and undoubtedly quite complex, but the essential faet of the

rising friction factor - Reynolds number cur:ve for this material is a signi-

ficant finding of these experiments.

2OO,OOO SOO,OOO sOO,@o

Reynolds Number, ne = 4$J(

Fiq. 9- Comporison of Roughness Coeff ic ients

(Concrete ond Corrugoted Metol Culverts )

o

.9

oo

o

o

o(ro,=co=

lS" Circulor Pipe 24'.Pipe Arch

Corr u g aled l4elo/ . Prpes

Concrele PiDes

16

However, neither the curves for the corrugated pipes nor those for

the concrete pipes can be satisfactorily expressed in terms of the Colebrook

equation . The corrugated pipes especially gave results contradictory to those

that would be expected from the Colebrook equation, since a definite increase

in friction fac tor with increasing Reynolds number was noted for each of them,

whereas the equation postulates a decreasing friction factor.

These curves seem to approach the horizontal &t high Reynolds num

bers, but they all show a rising characteristic throughout the experimental

range. Such a rising characteristic was unexpected and is unique among com

mercial pipes. These results serve to emphasize the fact that pipes with

"regular" patterns of roughness may behave quite differently hydraulically from

pipes of "random'l roughness patterns, for which the Colebrook equation was

derived. The detailed hydrodynamics of friction losses in corrugated pipe is

still obscure and undoubtedly quite complex, but the essential fact of the

rising fricti on factor - Reynolds number curve for this material is a signi

ficant f i nding of these experiments.

0 30

.025

c '" ~ ~ .020

U

'" '" '" " ~ '" g .015

0::

'" .= " " o ~

.010

. 0 0 •

-

.008 70,000

-IS" P i~ Arch IS " Circular !,ipe 24' Pipe Arch 36" Pipe ~rch 24'Ci r~ar Pipe 36" Circ~lar Pipe

f---:::: ~ -~ --

100,000

-Corruqated Metal Pipes

Concrete Pipes

S"C II . J 36" Circular Pipe

- I ,rcu a r P'Pj"" ~'" '2~" C irc,ular ji pe

200 ,000 300,000 500,000 700,000

Reynolds Number, Re : ~

Fig. 9- Comparison of Roughness Coeffic ients

(Concrete and Corrugated Metal Culverts)

1,000,000 ',500,000

t 17

The same type of varlati-on, though not so pronouneed, is evident

in ttre curve of experimental values of the Manning coefficient versus Reynolds

nunber for the corrugated pipes, as shown on Fig. t. Thus, the value of n to

be used in the design of a corrugated pipe depends upon both the pipe size

and the Reynolds nunber, and it is not a corstant as has been custornarily

assumed.

The friction factor - Reynolds number curves for the concrete pipes

show a falling characteristic, as would be implied from the Golebrook equation.

liowever, they will not yield a eonstant value of the equivalent sand dianeter,

K"r for concrete pipe. Rather, K" was found to increase with Relmolds nunber

for a given pipe and to increase with the size of pipe.

thus the Nikuradse and Colebrook equabions are inadequate to deseribe

the flow in the pipes studied in these tests, both concrete and corrugated

metal. The equivalent sand dianeter, Ku, does not appear to senre sati-sfac-

torily as a representative length parameter for flow in such pi,pes.

the l{anning coeffrcient, whlui has already been noted as varying

with Reynolds nurnber and with pipe size for the cormgated pipes, was never-

theless more nearly eonstant than the Darcy friction factor or than K" as

conputed from the Nikuradse or Colebrook equations. Similar1y, the Manning

coefficient showed some variation with Reynolds nurnber and pipe size for the

concrete pipes, but the variation was much less than the variatj-on in f or in

K-. For oractieal design use, the Manning coeffieient still seems to be thes

most nearly constant measure of surfaee roughness. Figure 9 shows the Manning

coefficient as a function of Relmolds nunber, giving experimental culves for

all the pipes tested.

The values of n for corrugated pipes obtained in the present tests

are considerably higher than the value of 0.021 which is conmonly used at

present. Further, it is inportant to recognize that, if the experimental

facilities had permitted the establishnent of flors of still higher iteynolds

number in the pipes, still higher values of n wouLd probably have been obtained

for such pipes. Consequently, it is strongly urged that n-values used in

corrugated pipe design should be selected fron the curves of Fig. 9, and that

if the design situation lies beyond the present experimental range, an n-value

of at least 0.025 be used,

'. 17

The same type of variation, though not so pronounced, is evident

in the curve of experimental values of the Manning coefficient versus Reynolds

number for the corrugated pipes, as shown on Fig. 9. Thus, the value of !! to

be used in the design of a corrugated pipe depends upon both the pipe size

and the Reynolds number, and it is not a constant as has been customarily

assumed.

The friction factor - Reynolds number curves for the concrete pipes

show a falling characteristic, as would be implied from the Colebrook equation .

However, they will not yield a constant value of the equivalent sand diameter,

K , for concrete pipe. Rather, K was found to increase with Reynolds number s s . for a v,iven pipe and to increas e with the size of pipe.

Thus the Nikuradse and Colebrook equations are inadequate to des cribe

the flow in the pipes studied in these tests, both concrete and corrugated

metal. The equivalent sand diameter, K , does not appear to serve satisfacs

torily as a r epresentative length parameter for flow in such pipes.

The Manning coeffi cient, whicn has already been noted as varying

with Reynolds number and with pipe size for the corrugated pipes, was never

theless more nearly constant than the Darcy friction factor or than K as s computed from t he Nikuradse or Colebrook equations. Similarly, the Manning

coefficient showed some variation with Reynolds number and pipe size for the

concrete pipes, but the variation was much less than the var iation in f or in

K. For practical design use, the Manning coefficient stil l seems to be the s

most nearly constant measure of surface roughne ss. Figure 9 shows the Manning

coefficient as a function of Reynolds number, giving experimental curves for

all the pipes tested.

The values of n for corrugated pipes obtained in the present tests

are considerably higher than the value of 0.021 which is commonly used at

present. Further, it is important to recognize that, if the experimental

facilities had permitted the establishment of flows of still higher Reynolds

number in the pipes, still higher values of !! would probably have been obtained

for such pipes. Consequently, it is strongl y urged that n-values used in

corruga ted pipe design should be selected from t he curves of Fig. 9, and that

if the design s i tua tion lies beyond the present experimental range, an n-value

of at least 0.025 be used.

r8

The values of n obtained for the concrete pipes, on the other hand,

rere lower than previously reconmended values. Also, a tendency for n todecrease was noted for increasing Reynolds nunbers. Consequently, a recon-

nended value of 0.0110, andpossibtyas lowas 0.0100, for n for new east-and-vibrated eonerete pipe seerns waranted by the present experiraental results.

the question as to how rnuch, if any, these reconnended n-values forboth concrete and corrugated metal should be increased to allow for deteriora-tion with age, for leakage, and other factors can be settled only on the basisof the individuaL conditlons under which a particular pipe will be senring andwill depend largely on the judgrnent of the designer.

C. Friction tosses for Part-Fu1l FIow

The Manning coefficient nas found to be very nearly constant for

the cond:ition of part-full, uniforn, tranqu.ir flow in a given type of pipe.

the small variations that were noted were of an order of magnj-tude correspond-

ing to possible random experimental variations.

For the corugated pipes, the average n for part-fuIl flow uas

0.0231r. No systenatic vari-ation with Reynolds number or with d.epth of flor

was apparent, although it is possible that sueh variations nay have existedbut tended to offset each other. A snall effect due to-shape of section wasnoted. The average n for the pipe arch sections was 0.02211 and for the cir-cuLar seetions was 0.O2b2. For the circular sections, the lfanning coefficientevidenced a slight deerease as the pipe dianeter increased.

For the concrete pipes, the average n for part-full flow was 0.0106

and there was a very small range of variation fron this average. For the

l8-in. piPer there seemed to be a slight systenatic decrease in n as the depth

of flow (and consequently the ReSmolds nunber) increased, but this tendency

was not observed on the 2L-in. pipe, perhaps because of the greater nagnitudes

of experinental variations on this pipe. It was not possi-ble to obtain part-

full flovr data on the 3Gin. pipe because of the proxinity of the pipe slopeto the critical slope for most di-scharges in the piper a fact which resulted

in troublesome waviness and instability on the water surface in the pipe andprecluded dependable neasurementso

For practical design purposes these snall variatlons nay be con-

sidered negligible. Reasonable reconmended values of n for uniforr tranquil

18

The values of n obtained for the concrete pipes, on the other hand,

were lower than previously recommended values. Also, a tendency for ~ to

decrease was noted for increasing Reynolds numbers. Cons equently, a recom

mended value of 0.0110, and possibly as low as 0.0100, for n for new cast-and

vibrated concrete pipe seems warranted by the present experimental results.

The question as to how much, if any, these recommended n-values for

both concrete and corrugated metal should be increased to allow for deteriora

tion with age, for leakage, and other factors can be settled only on the basis

of the individual conditions under which a particular pipe will be serving and

will depend largely on the judgment of the designer.

c. Friction Losses for Part-Full Flow

The Manning coefficient was found to be very nearly constant for

the condition of part-full, uniform, tranquil flow in a given type of pipe.

The small variations that were noted were of an order of magnitude correspond

ing to possible random experimental variations.

For the corrugated pipes, the average n for part-full flow was

0.0234. No systematic variation with Reynolds number or with depth of flow

was apparent, although it is possible that such variations may have existed

but tended to offset each other. A small effect due to · shape of section was

noted. The average ~ for the pipe arch sections was 0.0224 and for the cir

cular sections was 0.0242. For the circular sections, the Manning coefficient

evidenced a slight decrease as the pipe diameter increased.

For the concrete pipes, the average ~ for part-full flow was 0.0106

and there was a very small range of variation from this average. For the

18-in. pipe, there seemed to be a slight systematic decrease in ~ as the depth

of flow (and consequently the Reynolds number) increased, but this tendency

was not observed on the 24-in. pipe, perhaps because of the greater magnitudes

of experimental variations on this pipe. It was not possible to obtain part

full flow data on the 36-in. pipe because of the proximity of the pipe slope

to the critical slope for most discharges in the pipe, a fact which resulted

in troublesome waviness and instability on the water surface in the pipe and

precluded dependable measurements.

For practical design purposes these small variations may be con

sidered negligible. Reasonable recommended values of n for uniform tranquil

r9

flor appear to be O.02lr0 for corrugated pipes and 0.0110 for concrete pipes of

the tlpe tested, assunlng new, well-laid pipe without projecting elements.

D. Entrance Losses

The entrance loss is understood to be the excess of actual enerry

loss in the entranee region of a pipe over that which would be caused by normal

pipe friction over the sane length of pipe. The entrance loss is not confined

to a snall region right at the entrance, but it is spread over a length of

pipe of at least several dianeters. It is caused largely by re-expansion of

the contracted Jet of entering water. Much of the kinetic energy of the high-

velocity entering jet forms excessive rotational turbulence in the flow when

it approaches an adverse pressure gradient in expanding to fill the pipe.

this excess turb'rlence is gradually darnped out as the flow moves dovmstream.

Sinultaneously, development of the nonnal turbulent boundary layer is taking

olace frorn the pipe wall outward to its center.

ff the entranee loss is written as an entrance coeffieient multiplied

by the veloeity head of flow in the pipe, the most irnportant factor governing

the magnitude of the coefficient is the geonetry of the entrance Iip. the

form of entrance controls the amount of contraction and therefore the amount

of re-expansion and excess turbulence"

The chief item in the reducti-on of entrance loss is therefore the

design of the entrance to reduce the entrance contraction. this can be done

by rounding or beveling the entrance, or by providing some other approach

transition.

The contraction will be greatest rhen ttre pipe entrance projects

into the headwater pool and uLren the pipe thickness is snalI, that is, with

a sharp-edged entranee. This condition is approached at the entrance to a

comugated pipe rith a re-entrant inlet. The St. Anthony Falls Iaboratory

experinental values for the entrance coefficient for projecting corrugated pipe

inlets were close to the theoretical value of 1.00 for re-expansion loss in

such a situation. The average value obtained was 0"85. The slight rounding

of the entrance due to the initial comugation suffieed to cause the reduction

fron the theoretical value.

Ifhen a flush headnall inlet is used, the contraction is reduced.

The theoretical re-erpansion loss for a sharp-edged inlet is approxi:nately

19

flow appear to be 0.0240 for corrugated pipes and 0.0110 for concrete pipes of

the type tested, assuming new, well-laid pipe without projecting elements.

D. Entrance Losses

The entrance loss is understood to be the excess of actual energy

loss in the entrance region of a pipe over that which would be caused by nonnal

pipe friction over the same length of pipe. The entrance loss is not confined

to a small region right at the entrance, but it is spread over a length of

pipe of at least several diameters. It is caused largely by re-expansion of

the contracted jet of entering water. Much of the kinetic energy of the high

velocity entering jet fonns excessive rotational turbulence in the flow when

it approaches an adverse pressure gradient in expanding to fill the pipe.

This excess turbulence is gradually damped out as the flow moves downstream.

Simultaneously, development of the normal turbulent boundary layer is taking

olace from the pipe wall outward to its center.

If the entrance loss is written as an entrance coefficient multiplied

by the velocity head of flow in the pipe, the most important factor governing

the magnitude of the coefficient is the geometry of the entrance lip. The

form of entrance controls the amount of contraction and therefore the amount

of re-expansion and excess turbulence.

The chief item in the reduction of entrance loss is therefore the

design of the entrance to reduce the entrance contraction. This can be done

by rounding or beveling the en trance, or by providing some other a~proach

transition.

The contraction will be greatest when the pipe entrance projects

into the headwater pool and when the pipe thickness is small, that is, with

a sharp-edged entrance. This condition is approached at the entrance to a

corrugated pipe with a re-entrant inlet. The St. Anthony Falls Laboratory

experimental values for the entrance coefficient for projecting corrugated pipe

inlets were close to the theoretical value of 1.00 for re-expansion loss in

such a situation. The average value obtained was 0.85. The slight rounding

of the entrance due to the initial corrugation sufficed to cause the reduction

from the theoretical value.

"''hen a flush headwall inlet is used, the contraction is reduced.

The theoretical re-expansion loss for a sharp-edged inlet is approximately

20

O.I+I (V2 /2g) , and this could be e:rpected to decrease d.ue to the rounding at

the first corrugation, the anount depending somewhat on the pipe dianeter.

The St" Anthony Falls Laboratory tests for this condition indicated an average

coefficient of 0.1+9, which was higher than erpected. Honever, the data are

dependable, vrd-fhout exeessive scatter, and it appears necessary to recomend

about 0"50 for K" for cormgated pipes w'ith flush inlets" A value of K" of

about 0.90 should be used for corrugated pipes with projecting inl-ets"

Entrance loss coefficients for concrete pipes are considerably lower

than those for corrugated pipes" Conerete pipes are conmonly nade wittr either

bell-and-spigot or tongue-and-groove type joints, l-aid with the bell or groove

end upstream. This has the effect of an increased diareter at the culvert

entranee from which the contraetion is initiated, and therefore, less re-

expansion is required from jet dianeter to normal plpe diareter. The entrance

loss coefficient depends somewhat on pipe dia.ureter and the amount of widening

at the joint, but average values can be used with suffleient accuracy"

Furthernore, the pipe wall thickness is almost sufficient to serste

as a flush headwall when the pipe projects into the headnrater" Consequently,

the entrance loss coefficient for concrete pipe culverts is affected very 1itt1e

by whether the pipe has a projecting or flush inl-et. dn ihe basis of the

experimental results, a valrre of 0.1! has been recomrnended for projecting

eoncrete pipe inlets and 0.I0 for flush inlets"

lVhen the headnrater elevation drops below the inlet erowne a part

of the entering jet contraction is removed, eonstraint at the water surface

is removed, and therefore the entrance loss coefficient becomes snaller" Holv-

ever, the entrance coefficients for concrete pipe are so sna1l as to be subject

to large relative inaccuracies" The present experinental data do not appear

to warrant design values of K" less than C.15 and 0"10 fon projecting and flush

concrete pipe inlets, respectively, for part-fu11 flor conditions, even though

these are the same values reconmended for fuLl f1ow"

For coruugated pipes, however, a material reduction of the entrance

coefficients was obtaj-ned when the culvert flowed only partly fu1I" Reeormended

design values for this condition are 0.?0 and O"l+0 for projecting and flush

inletsr respectively.

20

0.41 (V2j2g), and this could be expected to decrease due to the rounding at

the first corrugation, the amount depending somewhat on the pipe diameter.

The St. Anthony Falls Laboratory tests for this condition indicated an average

coefficient of 0.49, which was higher than expected. However, the data are

dependable, ~~thout excessive scatter, and it appears necessary to recommend

about 0.50 for K for corrugated pipes with flush inlets. A value of K of e e about 0.90 should be used for corrugated pipes with projecting inlets.

Entrance loss coefficients for concrete pipes are considerably lower

than those for corrugated pipes. Concrete pipes are commonly made with either

bell-and-spigot or tongue-and-groove type joints, laid with the bell or groove

end upstream. This has the effect of an increased diameter at the culvert

entrance from which the contraction is initiated, and therefore, less re

expansion is required from jet diameter to normal pipe diameter . The entrance

loss coefficient depends somewhat on pipe diameter and the amount of widening

at the joint, but average values can be used with sufficient accuracy.

Furthermore, the pipe wall thickness is almost sufficient to serve

as a flush headwall when the pipe projects into the headwater. Consequently,

the entrance loss coefficient for concrete pipe culverts is affected very little .. bJr whether the pipe has a projecting or flush inlet. On the basis of the

experimental results, a value of 0015 has been recommended for projecting

concrete pipe inlets and 0 .10 for flush inlets.

When the headwater elevation drops below the inlet crown, a part

of the entering jet cont raction is removed, constraint at the water surface

i s removed; and therefore the entrance loss coefficient becomes smaller. How

ever, the entrance coeffic i ents for concrete pipe are so small as to be subject

to large relative inaccuracies. The present experimental data do not appear

to warrant design values of K less than G.15 and 0.10 for. projecting and flush e

concrete pipe inlets, respectively, for part-full flow conditions, even though

these are the same values recommended for full flow.

For corrugated pipes, however, a material reduction of the entrance

coefficients was obtained when the culvert flowed only partly full. Recommended

design values for this condition are 0.70 and 0.40 for projecting and flush

inlets, respectively.

2t

Ttre above entrance coefflclents apply only if the flowln the plpe ls

snrbcrltical. Supercritical. slopes and vel"ccities are :rcx:orPanied by nuch htgher

entrance eoefficients when applied to the nornal part-fulL flmr condltion.

E. Qrtlet Losses

Tleoretj-ca11y, the outlet loss for a pipe disctrarging into a rela-

tively quieseent tailwater pool ie equal to ttre velocity head of the flow in

the pipe at its exit, for both full and part-full flow.

UnCer cet'tain eondltions, part of this exit velocity head may be

consenred and converted into useful hearl in the outlet channel flow. This

rlll be true especially when the outlet channel is relatively narrorr as tas

ttre caae in the e:cperimental lnstallation.

The outlet loss coefflcient was founct to average about 0.90 for fuI1

flor Ln both concrete and cormgated pipes. Determinations of outlet Loss

rere not nade for the part-full conditlon, but they would undoubtedly be about

the sane, provided ttre coefficient was deterrnined with reference to the actuaL

exit velocity head.

For Cesign purposes the outlet coefficient norroally should be taken

equal to unity, unless a speciall]'designed, flared-outLet section is used.

F. Corparison of 5t. Anthony Falls Laboratory Results with Other Data

The test resrrlts reporte<l in this paper have considerably extended

previous lororledge on the {prlraulics of concrete and corrugated netal pipes.

T?rc nost dependable data on this subject prior to the new results were obtalned

ln a series of studieE conducted at the tlniversity of Iowa over a period of

sevcral years ending in 192L*. The lowa tests uere rnade on concrete and cor-

nrgated pipes 12, LB, 2b, and 30 inches in dianeter, ritb lengths varying fron

& to 36 ft.

Values of the [dannlng and Kutter roughness coefficients, as obtalned

ln ttrese tests# are given in Table fV.

*D. L. Yarnell, Ir. A. Nagler, and S. ll. Woodward, The Flou of Water

Through Cu1verts, (University of Iora Studles ln Engineeringr Bulletin I,-June, 1926).

tuia, p, ss,

21

The above entrance coefficients apply only if the flow in the pipe is

subcri tical. Supercri tical slopes and velocities are a~ompanied by much higher

entrance coefficients when applied to the normal part-full flow condition.

E. Outlet Losses

Theoretically, the outlet loss for a pipe discharging into a rela

tively quiescent tailwater pool is equal to the velocity head of the flow in

the pipe at its exit, for both full and part-full flow.

Under certain conditions, part of this exit velocity head may be

conserved and converted into useful head in the outlet channel flow. This

will be true especially when the outlet channel is relatively narrow, as was

the case in the experimental installation.

The outlet loss coefficient was found to average about 0.90 for full

now in both concrete and corrugated pipes. Detenninations of outlet loss

were not made for the part-full condition, but they would undoubtedly be about

the same, provided the coefficient was determined with reference to the actual

exit velocity head.

For design purposes the outlet coefficient normally should be taken

equal to unity, unless a specially designed, flared-outlet section is used.

F. Comparison of st. Anthony Falls Laboratory Results with Other Data

The ' test results reported in this paper have considerably extended

previous Imow1edge on the hydraulics of concrete and corrugated metal pipes.

The most dependable data: on this subject prior to the new results were obtainE~d

in a series of studies conducted at the University of Iowa over a period of

several years ending in 1924*. The Iowa tests were made on concrete and cor

rugated pipes 12, 18, 24, and )0 inches in diameter, with leneths varying from

24 to 36 ft.

Values of the Manning and Kutter roughness coefficients, as obtained

in these tests ** are given in Table IV.

*n. L. Yarnell, F. A. Nagler, and S. M. Woodward, The Flow of Water Through Culverts, (University of Iowa Studies in Engineering, Bulletin 1, June, 1926).

-M:*'Ibid, p. 55.

22

TABI,E

AVERAGE RolIcHt{ESS COEFFTCTENTS,

rvIOTTA TESTS OT CULVffiT PIPES

FipeDian\ 1 n " /

T2

1B

1 4

30

0.01u0.0121

0.0130

0.0127

0.0119

0,0121

0.0130

o"ot25

Kutter n

0"019,1+

0,0217

0"0216

o.0232

Manning n

o"a22B

0.02h8

o.0239

O"O25l1

Corrugated Metal Pipe

The Kutter coefficient, was conputed fron the Kutter forrnula

n

{E

r . r ( r ^ 0 ,00281 + 1 "811i . l l . o 2 t T

n (12)

r + ( l r t " 6 5 + 0 " 0 9 2 8 1 )

The lrlanning formula, whieh has largely superseded the Kutter formulat

was originally designed with the intent that its rrcughness coefficient would

be the same as the Kutter roughness coeffieient for a glven plpe or open-

channel rnaterial. As i-s evident fron Table IV, this interehangeability of

coeffieients is satisfaetory for the lowvalues of n associated with concrete

pipe -

For corrugated pipe, the ltranning n is eonsj-derably higher than the

Kutter n, so that they eannot be used interchangeably" Horever, i-t appears

that they were used interchangeably in subsequent design literature for eor-

rugated pipe" fhe average Kutter n for coruugated pipe is about 0"021 as

indicated by the lowa tests and also by other studies, whereas the average

Itranning ! n-as about 0"021+. Most corrugated culvert nanufacturers reeosnend

a Manning coefficient of not nore than 0"021 for use in design of corrugated

pipe culverts and ""rr'"t"o.

oFor "*"rp1e, Handbook of Culvert and Draina Practiee, by Amco Drainage

lEfffins Conpany, 19!7)

Q = A r l n s

Concrete Pipe

Kutter n Manning n

pp" 209-1J"

22

TABLE IV

AVERAGE ROUGHNESS COEFFICIENTS, IOWA TESTS rn CULVERT PIPES

,

Pipe Concrete Pipe Corrugated Metal Pipe Diam (in. ) Kutter n Manning n Kutter n Manning !!

12 0.0117 0.0119 0.0194 0.0228

18 0.0121 0.0121 0.0217 0.0248

24 0.0130 0.0130 0.0216 0.0239

30 0.0127 0.0125 0.0232 0.0254

The Kutter coefficient was computed from the Kutter formula

41.65 + 0.00281 + 1.811 Q = A iRS S n

1 + (41.65 + 0.00281) ~ S {R

(12)

The Manning formula, which has largely superseded the Kutter formula,

was originally designed with the intent that its roughness coefficient would

be the same as the Kutter roughness coefficient for a given pipe or open

channel material. As is evident from Table IV, this interchangeability of

coefficients is satisfactory for the lowvalues of n associated with concrete

pipe.

For corrugated pipe, the Manning!! is considerably higher than the

Kutter !!, so that they cannot be used interchangeably. However, it appears

that they were used interchangeably in subsequent design literature for cor

rugated pipe. The average Kutter E. for corrugated pipe is about 0.021 as

indicated by the Iowa tests and also by other studies, whereas the average

Manning !! was about 0.024. Most corrugated culvert manufacturers recommend

a Manning coefficient of not more than 00021 for use in design of corrugated

. 1 * plpe cu verts and sewers •

*For example, Handbook of Culvert and Drainage Practice, by Armco Drainage and Metal Products, Inc. (Indiana: R. R. Donnelley & Sons Company, 1947) pp. 209-13.

23

the St. Anthony Falls Laboratory tests confirm the fact that an n

of 0.021 for corrugated pi-pe is mueh too low. A value of n of at .l,east 0.A25

is reeonmended on the basis of present hnowledge.

Prevlously reeorunended values of n for eonerete pipe have, houever,

been higher than the values obtained i,n the St. Anthony Falls Laboratory tests.

Tfre Iowa tests indicated that n averaged about O.CL25 for concrete culverts

flowing full, whereas the St. Anthony Falls taboratory tests justify a value

as low as 0.0100 for new conerete pipe of the type tested. It is probable

that methods of manufacture of precast concrete pipe have sufficiently inproved

in the two decades that have elapsed since the fowa tests and other significant

tests on concrete eulvert pipe to produce surfaces of a higher degree of

stroothness and better joints than were then obtainable.

The Anerican Concrete Pipe Association, on the basis of previous

tests and recommendations by various authors, has until now reconmended an n

of 0.013 for use in the Kutter or Manning fornulas. In view of the nen results,

it aopears that this value is quite eonservative, unfess a considerable in-

erease in roughness wlth age of the euJvert is to be anticipated, or unless

the pipe rnanufacturing process enployed is such as to produce a materially

rougher surface than in the experimental pipes.

TLre Iowa tests, which were the most extensive bnd significant tests

available prior to the St. Anttrony Fal1s Laboratory tests, did not reveal the

very significant trends in friction factor and roughness coeffieient with

Reynolds number that the present tests have brought to light. No measurements

of water temperature were reported for the Iowa tests, so that it is not

possible to conpute accurate values of the Reynolds number for those tests"

In view of this fact, certain trends that might have been inferred from the

Iowa tests, sueh as variation of n with discharge or pipe diarneter, eannot be

substantiated.

Furtherrnore, the fowa investi-gations did not include a study of

part-full flow conditions in culverts" There have been a few tests reported,

however, on concrete pipes flowing partly fu11*. These have sometines indica-

ted that the friction factor or roughness coefficient is slightly greater for

part-full flow than for fuII flow, and that it usually exhibits a slight

oC. F. Johnson, nDeterrnination of Kutterrs n for Sewers Partly Fil}edrrl

I"rySgg^r., American Societyof Civil Engineersl vof . l09r (191+l+) t pp. 223-lJ7, Especial ly see discussion by T. R. Canp, R. G" Coulter, and C. E. Hamser.

23

The St. Anthony Falls Laboratory tests confirm the fact that an n

of 0.021 for corrugated pipe is much too low. A value of n of at least 0.025

is recommended on the basis of present knowledge.

Previously recommended values of !! for concrete pipe have, however,

been higher than the values obtained in the St. Anthony Falls Laboratory tests.

The Iowa tests indicated tnat !! averaged about 0.0125 for concrete culverts

flowing full, whereas the St. Anthony Falls Laboratory tests justify a value

as low as 0.0100 for new concrete pipe of the type tes ted.. It is probable

tha t me thods of manufacture of precast concrete pipe have sufficiently improved

in the two decades that have elapsed since the Iowa tests and other significant

tests on concrete culvert pipe to produce surfaces of a higher degree of

smoothness and better joints than were then obtainable.

The American Concrete Pipe Association, on the basis of previous

tests and recommendations by various authors, has until now recommended an n

of 0.013 for use in the Kutter or Manning formulas. In view of the new results,

it aopears that this value is quite conserva ti ve, unless a considerable in

crease in roughness with age of the culvert is to be anticipated, or unless

the pipe manufacturing process employed is such as to produce a materially

rougher surface than in the experimental pipes.

The Iowa tests, which were the most extensive and significant tests

available prior to the st. Anthony Falls Laboratory tests, did not reveal the

very significant trends in friction factor and roughness coefficient with

Heynolds number that the present tests have brought to light. No measurements

of water temperature were reported for the Iowa tests, so that it is not

possible to compute accurate values of the Reynolds number for those tests.

In view of this fact, certain trends that might have been inferred from the

Iowa tests, such as variation of n with discharge or pipe diameter, cannot be

substantiated.

Furthermore, the Iowa investigations did not include a study of

part-full flow co ndi tions in culverts. There have been a few tes ts reported,

however, on concrete pipes flowing partly full *. These have sometimes indica

ted that the friction factor or roughness coefficient is slightly greater for

part-full flow than for full flow, and that it usually exhi bi ts a slight

* C. F. Johnson, "Determination of Kutter's n for Sewers Partly Filled~" Transactions, American Society of Civil Engineers -; Vol. 109, (1944), pp. 223-Tif. Especially see discussion by T. R. Camp, R. G. Coulter, and C. E. Ramser.

2b

increase as the depth of uniforn flow decreases. A slight tendenc]' of this

kind was also noted on the 18-in. pipe in the present tests.

In considering this phenomenon one must recognize that, actually one

is corparing flow conditions wlij-ch are geometrieally dissiroilar and that the

arbitrary use of the hyd.rauU-c rad.ius as the linear dinension of comparison

is only an approxirnation whieh has been found to give acceptable results.

No part-fulI flow tests in cormgated pipes of the nature discussed

in tlis report, seem to have been published prevlously. A .few tests have been

reported on corrugated nretal flumes. li. E. Horton has given n-values for such

flunes rangtng fronr 0.0225 to 0.0100.

Acl<no'wledgment

The experimental progran described in this report wae sponsored by

the Aneriean Concrete Pipe Association and the Portland Cement Association.

A1l experiments were concLuctecl at the St. Anthony !-a1-1s Hydraulic laboratory

of the University of Minnesota, unCer the srrpervision of Dr. Lorenz G. Straubt

Dj-rector. Most of the e:rperimental observations were made rqr Thomas Timar.

l1yo of the pipes were tested by Onen Laraband f{illianDingrnn' Ilenry M. Morris

was Project Leader clurlng most of the stucly. Lois Fosburgh and Leona Schultz

edited and prepared the rnanuscript; illustrative material 'lrras arranged by

Loyal A. Johnson.

24

increase as the depth of uniform flow decreases. A slight tendency of this

kind was also noted on the IS-in. pipe in the present tests.

In considering this phenomenon one must recognize that actually one

is comparing flow conditions ~nuch are geometrically dissimilar and that the

arbitrary use of the hydraulic radius as the linear dimension of comparison

is only an approximation which has been found to give acceptable results.

No part-full flow tests in corrugated pipes of the nature discussed

in this report, seem to have been published previously. A ·few tests have been

reported on corrugated metal flumes. It. E. Horton has given n-values for such

flumes ranging from 0.0225 to 0.0300.

Acknowledgment

The experimental program described in this report was sponsored by

the American Concrete Pipe Association and the Portland Cement Association.

All experiments were conducted at the St. Anthony Falls Hydraulic Laboratory

of the University of Minnesota, under the supervision of Dr. Lorenz G. Straub,

Director. Most of the experimental observations were made ~J Thomas Tirnar.

1\vo of the pipes were tested by Owen Lamb and William Dj ngman. Henry M. Morris

was Project Le'ader during most of the study. Lois Fosburgh and Leona Schultz

edited and prepared the manuscript; illustrative material Vlras arranged by

Loyal A. Johnson.

25

g ! 9 q . q . g & r

A = Cross-sectional area of f1ow, sq ft

D = Pipe dianeter, ft

f = Darcy fricti.on factor

g = Acceleration of gravity = 32.16 ft/sec/see

H = Total head on culvert, ft

H_ = Entrance head 1oss, fte

H" = Friction head 1oss, ftI

K = Entrance loss coefficiente

Ko = Barrel friction loss coeffieientL

K = Ortlet loss coefficiento

K_ = Dianeter of sand grain of equivalent roughness, fts

ite = Reynolds nr:rnb"t = Llv

n = Marming roughness coefficient

a = Rate of f1ow, cfs

R = Hydraulic radius, ft

S = Slope of hydraulic gradient

V = Average velocity of fIow, fps

v = Kinematic viscosity, sq ft/sec

GLOSSARY

A = Cross-sectional area of flow, sq ft

D = Pipe diameter, ft

f Darcy fricti,on factor

g = Acceleration of gravity = 32.16 ft/sec/sec

H = Total head on culvert, ft

H = Entrance head loss, ft e

Hf = Friction head loss, ft

K = Entrance loss coefficient e

Kf = Barrel friction loss coefficient

K = Outlet loss coefficient o

K Diameter of sand grain of equivalent r..oughness, ft s

Re = Reynolds number = ~v

n = Manning roughness coefficient

Q = Rate of flow, cfs

R = Hydraulic radius, ft

S = Slope of hydraulic gradient

v = Average velocity of flow, fps

v = Kinematic viscosity, sq ft/sec

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