RESERVE
coPy
RTSERVE
COPY
\\ii)i~~;~U~L
ST.
ANTHONYFALLS
FALTSHYDRAULIC
HYDRAUTICLABORATORY
LABORATORY
sT.ANTHONY
g}$VERSITY OF
UNIVERSITY
MINNESOTA
OT MINNESOTA
;i:, :; :::ir; .".r n;,;
LORENZ
Director
TORENZG.
G. STRAUB,
STRAUB,Director
/'
Technical
Technical Paper
Pcper No.3,
Series B
No. 3, Series
Hydraulic Data
Data Comparison
Comparison
of Concrete
Concrete and Corrugated Metal
Culvert Pipes
Pipes
by
LORENZ
TONENZG.
STRAUB
G. STRAUB
and
cmd
HENRY
HENRYM.
M. MORRIS
MOBNIS
July,
1950
IulY, 1950
Minneapolis,
Minnecpolis, Minnesota
Minnesotq
1851
l85l •.
UNIVERSITY
I'NIVERSITYOF
OF MINNESOTA
MINNESOTACENTENNIAL
CENTENNIAI •.
1951
I95I
COpy
UNIVERSITY OT
OF MINNESOTA
MINNESOTA
I'!{TVEBSITY
ST. ANTHONY
ANTHONY TAttS
FALLS HYDRAI'LIC
HYDRAULIC LABORATORY
LABORATORY
ST.
LORENZ G.
G. STRAUB,
STRAUB, Director
Director
tOnENZ
Technical Poper
Paper No.
No.3,
Series B
3, Series
Technicql
Hydraulic Data
Data Comparison
Hydraulic
Comparison
of Concrete
Concrete and Corrugated Metal
Culvert Pipes
Pipes
by
LORENZ
TORENZG.
STRAUB
G. STRAUB
and
cmd
HENRY
M.
MORRIS
M.
HENRY MONRIS
July,
1950
IulY, 1950
Minneapolis,
Minnesotq
Minnecpolis, Minnesota
1851
CENTENNIAT •.
I'NIVEBSITY OF MINNESOTA CENTENNIAL
l85l •. UNIVEFI.SITY
l95l
1951
CONTENTS
C O N T E N T S
Page
Page
List
L
i s t o f of
f l l u sIllustrations
trations
.
I.
r.
II.
rI.
III.
NT.
IV.
rV.
o c .
c r
c c
.
.
.
.
.
..
•
c o .
•
. ...........
0
•
iii
iii
•
INTRODUCTION
rNmoDuclToN.o ..
RESUME
RESUIIEOF
PROGRAM
EXFER,IUts,ITAI.
OF EXPERIMENTAL
PROGRAII
A.
A . Scope
S c o pofe Tests
o f T e •s •t s• . •. c . .
oo .• . • . •
•c .• . •
c . .
. c
B.
B . Summary
S u r u n aof
r y Results
R
o fe s u l t s•
" • • •. c c . . . . , .
..
.
o. o
ME'rnODS
TESTING
M E T T O DOF
SO
F T E S TAND
I N GANALYSIS
ANDANALYSIS....O
.
. ' C ' O
"
ANALYSIS
ANALYSIS AND
AND DISCUSSION
DISCUSSION OF
OF RESULTS
8E.SUtlE . . O '
O '
A.
A . General
G e n e r aAnalytic
l A n a l y t iRelations
c R e l a t i - •o n• s . .
o..
o c o
....
Friction
B. Friction
Losses for
Full Flow o .
for Full
Friction
Part-Full
C. Friction
Losses for
Flow
FIow •. •. • •
for Part-Full
Entranee Losses • • • • • • • • •
D.
D" Entrance
c
E. Outlet
E.
Outlet Losses
Losses •••
Falls Laboratory
F. Comparison
St" Anthony Falls
Comparison of
of St.
Iaboratory Results
Results
with
• • • •. o
• •
• ••
w i t h O tOther
h e r D a tData
a
o.
o o
Acknowledgment
Aeknowledgnent
c o o o o . . . . c c . . c . . c c . o . o c . "
•
0
G
Glossary
1 o s
so
0
a
•
r
•
y • c•
o
0
0
o
0
o 0 c0
.
o
•
•
o
ii
It
0
.
•
•
o
•
.
•
•
.
0
0
•
•
•
•
c
•
o
.
.
•
,
•
•
•
•
0
•
•
•
•
o•
.•
.0
.0
•
0
o
•
•
•
0
•
c•
0
r
1I
1
I
1
1
2
S
5
99
9
13
13
18
18
L9
19
21
2L
21
2L
zLI
24
2 2S5
OFI
!LIST
r9r 9
tILLUSTRATIONS
!!!qrSarr9gg
Page
Page
6
. o . . c
Figure
Figure
1I
36-in. Concrete
Concrete Culvert
Culvert Test Installation
Installation
35-in.
2
Flush Headnall
Headwall at
at fnlet
Inlet to
Culvert .• .
to 36-in..
36-in. Concrete
Concrete Culvert
17
3
Outlet
Outlet of
of 3Gin.
36-in. Diam Corrugated
Corrugated Culvert
Culvert (Flowing
Partly
Full)
PartlyFull)
. o
,.
· · · · ·. . · ·c
8
······ · ········
(Comugated Metal
Curves (Corrugated
Experimental
Experimental Rating Curves
Culverts
C u l v e r t sFlowing
F l o w i nFull)
gFull)
· · · · · · · · ·. . · · · · · ·. . · · · ·o o·
Experimental
Experirnental Rating
Rating Curves
Culverts
Curves (Concrete Culverts
Flowing
F l o r i n gPartly
P a r t lFull)
yFull)
· · · · · · · · · · ·. . ·. . ·. . · · · · · · · ·
Experimental
etal Culverts
Rating Curves
Experinental Rating
Meta1
Culverts
Curves (Corrugated M
Flowing Partly Full)
····· ··········
(Concrete and
Comparison
Friction Factors (Concrete
and Corrugated
Conparison of
Corrugated
of Friction
Metal Culverts)
····
···
(Concrete and
Comparison
RoughnessCoefficients
and
Corryarison of Roughness
Coefficients (Concrete
Corrugated Metal Culverts)
··· ···· ·······
t0
10
b
5
6
7
·
....·······
Experimental
Rating Curves
Culverts
Experinental Rating
Curves (Concrete Culverts
Flowing
Full)
FlowingPull)
..
c c. !..
...····
FlowingPartlyFull)
8B
MetalCulverts) ,
99
,
0
.
..
..
ComugatedMetalCulverts).
iii
l-]-I
a.
..
o o
o.
c.
c o o
.
c
0
11
12
..
r
12
o.
0
o
15
c.
o
16
gHYDRAULIC
I!E4q!Ig
9 g I A E I g 9 { 9OFE
!DATA
A T A gCOMPARISON
AND
CORRUGATED
METAL
gCONCRETE
. 9 r g . & q ra
sr q g
. q B & g q . { r sg
9E L ! !
R Tr . IPIP
sC U
g L! Vr rE E
I l s E! S
I.
I.
INTRODUCTION
INTRODUCTION
Full-scale tests
tests were eonducted
conducted at
at the
the St"
st. Anthony Fa1ls
Falls lfydraulic
Hydraulic
F\r11-scale
Laboratory of
of the University
University of
of Minnesota primarlly
primarily for
for the purpose of
of obtainobtainIaboratory
ing pipe
pipe friction
friction and entranee
entrance loss
loss coefflci-ents
coefficients for
for concrete
concrete and corrugated
corrugated
ing
metal culvert
culvert pipes,
pipes, i*rich
which would be mor
moree aecurate
accurate and
and dependable
dependable than those
netal
currently recommend.ed
recommended in
in culvert
culvert design literature.
literature.
eurrently
Comparison
of these test
test
Compariion of
is presented
presented in
in this
this paper and
and reconmendations
recommendations are given
given for
for design
design values
values
data is
of the coeffieients
coefficients under
under various
various flow
flow conditi-ons"
conditions.
of
all
which
The
all of
of which
The experimental
made on new culverts,
culverts,
studies were
were made
e><perinental studies
'were installed
were
and maintained
with excellent
excellent alignment.
aligrunent.
installed
and
maintained with
A high
degree of
high degree
A
of
accuracy was
possible in
of the
the culverts.
eulverts.
was possible
in these
all of
these tests
tests for
for all
to
Sizes
Sizes up to
33 ft
investigated.
in diameter were
were investigated"
ft in
Analytical
obtained from
Analytical studies
fron the experiexperiof the
data obtained
were made
made of
ttre data
studies were
where
mental observations
to
basic pipe
pip e flow
theory where
flow theory
obsenrations which
whi-ch are significant
to basic
significant
systematic
consideration.
i.rto*consideration.
forrn roughness and large
large diameters
dianeters come
"orn" into
systenatie form
II.
RESUME
PROCfi.AM
II.
OF EXPERIMENTAL
RESU}EOF
EXPffiIMENTA1PROGRAM
A.
Scope
T.ests
of ~ests
Scope of
18 inches
A total
in size
ranging in
total of
of nine culverts
were tested,
tested, ranging
size from 18
culverts were
of approxiapproxiin
an overall
length of
in diameter
in diameter,
overall length
dianeter to
diameter, each
with an
to 36
each with
36 inches in
groups as
mately
The
as follows:
The culverts
nately 193
193 ft.
ft.
culverts fall
fal1 into
into three
three groups
followsl
(a)
Circular
Circular concrete
eoncrete pipes
(U)
(b)
Circular
Cireular corrugated
netal pipes
eorrugated metal
(")
(c)
Corrugated
arches
Corrugated metal pipe arches
inches, 24
2! inches,
lnehesl
In
of 18
18 inches,
fn each
rnade with
each group, tests
tests were
were made
with pipe diameters of
and
and 36
36 inches.
di-mension
In
identifying dimension
In the case
case of the pipe arch sections,
sections, the identifying
periphery.
refers
refers to aa circular
circular section
section of equal periphery.
partly
pipe was
rhen flowing
flowing partly
Each
and also when
Each pipe
was tested
when flowing
flowing full
fu11 and
tested when
nain flow
flor
full,
nas used
for each
two main
ftlll, and
and aa wide range
range of discharges
diseharges was
used for
each of these two
22
eonditions.
condi
tions.
Friction and
Friction
and entrance
entrance loss
loss determinations
deterninations were
madefor
rere made
for all
all runs.
runs.
For the
partly full
the partly
full flow
flow condition,
For
condition, uniform
uniform subcritical
subcritical flow
flow was
was established
established
as the
the basis
basis for
for measurements.
measurements"
as
Technical Papers
Papers No.
No. 4lr and
Technical
and No.5,
No. 5r Series
B, respectively,
Series B,
respectively, describe
describe
in detail
detail the
the hydraulic
irydrauU-e tests
tests on
in
on the
pipes and
the concrete
concrete culvert
culvert pipes
and the
the corrugated
corrugated
pi-pes separately.
netal culvert
eulvert pipes
metal
separately.
Horuever, the
However,
the salient
salient test
test results
results for
for both
both
(Technical Paper
tlpes of
of cul¥erts
presented in
culuerts are
are presented
paper (Technical
in this
types
this paper
Paper No.3).
No. 3) "
pipe, with
Each pipe,
with the
the exception
Each
exception of the
2,h-in. concrete
pipe and
the 24-in.
eoncrete pipe
and the
the
2l+-in. corrugated pipe arch, was
24-in.
vras tested
tested under
under.' two
two types of entI"'al'lCe
entrsrce condicondi(f)
tionsl namely,
projecting 2 ft
nanely, (1) inlet
int-et projecting
tions;
into the headwater
fI into
headwaterpool, and
ana (2) inlet
inlet
flush with
with the headwall.
headnrall-" The
The two
flush
oned as
two pipes menti
mentioned
as exceptions
exeeptions were
were tested
tested
projecting inlets.
inlets"
only with projecting
B.
Sr:unary
Summar~y
of Results
of
The main
quantities
main quantities
The
determined
determlned for
for use
use in
in culvert
culvert design were
were the
Manning roughness
roughness coefficient
coefficiett
Manning
n*
, which
ro and
and the entrance
entranee loss coefficient,
coeffici-ent, K
K"r
e
are defined in
in terms
terms of Eqs.
Eqs. (1) and
and (2) respectively:
respectivelyl
a=+$*z/t,t/z
,
H
e
)
v2
rtv
= Ke z-2gg
=
K
((1)
r)
((2)
2)
For
For the pipe
pipe flowing
flowing ful1n
full , the test
test results
results are sumlarized
summarized j-n
in Table
I.
I. This tabulati-on
tabulation shows
shows maxirnum,
maximum, mlnimum,
minimum, and
and average values
values of
of n and K"
K for
for
e
each
each pipe.
pipe. The
The unnner
manner in
in rvhich
which the coefficj-ents
coefficients varied
varied is
is also
also indicated"
indicated.
A
A sinilar
similar sunmary
summary tabulation
tabulation for
for the
the partly
partly full
full flow
flow condition
condition
appears
appears in
in Table If.
II.
the
The significance
significance to
to be
be attached
attached to
to the
the indicated
indicated variations
variations in
in the
the
coufficients
cOl.-fficients is
is discussed later
later in
in this
this report"
report. For aceurate
accurate analysis
analysis or
or
design,
design, these
these variations
variations must
must be
be properly
properly considered"
considered. However,
However, for
for the
the usualusual
eulvert
culvert design
design this
this degree
degree of
of accuracy
accuracy would
would not
not be
be warranted.
warranted. Reeonrnended
Recommended
design
design values,
values, assuming
assuming new,
new, straight
straight pipe.,
pipe, are
are given
given in
in Table
Table rlr,
III, based
based on
on
the
the results
results of
of the
the studies
studies deseribed
described in
in this
this report.
report.
*A11
*All synbols
symbols are
are defined
defined in
in the
the Glossary
Glossary on
on page
page Zl.
23.
33
TABI.ErI
TABLE
SUUIIARTOF
TESTRESULTS
SUlO4ARY
OFnsT
NESUL1S-. PIPES
FIXtrIilG FULL
FI,jI,L
PIPES FWIUNG
No. of
of
No.
?estc
Tests
Pipe
Pipe
Uaxinu!
l!aximum
llinimum
lIinimlD
Average
Average
Type
Tlpe of
Veliatlon
of Variation
UANilI}.IGROUGHNESS
ROUGHNESS
COEFflICTENT
MANNING
COEFFICIENT
18i diam
dian
18"
ZLn
dian
24" diam
dian
36tr diam
36"
Lt
13
L'
12
0.0251
0.0251
o.o25?
0.0252
o.o2b7
0.0247
o.0222
0.0222
0.0228
0.0228
0.0216
0.0216
0.0242
o.o2\2
0.0242
0.o2tQ
0.0232
o.o2J2
36
36
o.0252
0.0252
0.@16
0.0216
0.0239
o.o2t9
23
23
77
9t
o.0255
0.0255
0.0215
0.0245
O.g2.h0
0.021i0
0.0210
0.0210
0.0217
0.0217
0.0216
0.0215
0.0239
o.0239
0.02)6
o.0?]6
0.0232
o.0232
i9
39
0.0255
0.0255
0.02)'0
0.0zlo
0.J237
0.0237
L2
12
99
u
11
0.0108
0.ot08
0.0104
0.0rol
0.0108
0.0108
0.0091
0.0091
o.oorJ
0.0093
0.0103
0.0103
0.0097
0.009?
0.0100
0.0100
0.0106
0.0106
32
t2
0.0t08
0.0108
0.0091
0.0091
0.0101
o.0ro1
corrugated
corrugated
corrugeted
corrugated
corrugated
corrugated
t l
11
Group
Group
18tt corrugated
plpe arch
corrugated pipe
arch
18"
plpe arch
2!n corrugated
corrugated pipe
erch
24"
pipe arch
corrugated pipe
arch
J6n corrugated
36Group
Group
I8n diam
dlan concrete
concret€
18"
2lrtr diam
dlen concrete
concrete
24"
dlan concrete
concret€
36n diam
36"
Group
Group
Increases
Increaees as
as
Decreases
Decreages as
as
Reynolds
Reynolds
diameter
dianeter
No.
No. increases
increaseo
increases
lncreeses
Increases
lteynolds No.
Increases as
as Reynolds
t'lo. increases
Lncreaaeg
Decreases
Decreasee as
as diameter
dleneter increases
lncroaaes
Decreases
Decreaees as
tbynotde No.
as rteynolds
}{o. increases
lncr€sgea
Increases
Increeseg as
as diameter
dianeter increases
lncreaaea
EN]RANCELOSS
ENTRANCE
IOSS COEFFICIENT,
COEFFICIENT, PROJECTING
'ROJECIINO INLET
I}ILET
I8r
18"
2lrrl
24"
36n
36"
dj,an corrugated
corrugated
diam
diarn corrugated
conugated
diam
dlan corrugated
corrugated
diam
4Il
6
6
0.89
89
0.
0.88
0.88
0.85
0.8£-
0.63
0.63
0.78
0.78
0.62
o.62
0.79
o.79
n Ar
0.81
0.75
0.75
Group
I6
16
0.89
0.89
0.62
o.62
0.78
0. ?8
L2
12
6
7
r.08
1.08
o.96
0.96
r.03
1.03
0.72
o.72
0.66
0.66
0.76
o.76
0.90
0.90
0.89
0.89
0.88
0.88
25
25
r.08
1.08
O.U,
o.6(
0.. 8
899
0
2Li
concrete
24" diam concrete
b
4
8
6
35n
diam concrete
concrete
36" dian
A
6
0.
0.12
12
o.19
0.19
0
.2r
0.21
0.09
0.09
0.07
0
.0?
0.12
o.
12
0.11
o.
rl
0.16
o.16
I6
18
00.21
.21
00.07
.07
00.12
. 12
XBr
18"
ZLn
24"
J6r
36"
corrugated
corrugated
corrugated
corrugated
corrugated
corrugated
pipe
arch
pipe arch
plpe
arch
pipe arch
pipe
pipe alch
arch
Group
Group
18tr dlan
concrete
diam concrete
18"
Oroup
Group
Random
Randon
Random
Randou
0.10
Increases as diact€r
diameter ii.lcreases
increases
Increases
ENIIIANCE
ENTRANCE IOSS
LOSS CoEFFICIEXT,
COEFFICIENT, FLUSI{
FLUSH INLET
18n
16" dian
diam corrugated
corrugated
0.60
0.60
0.56
0.56
0.68
0.£>8
o0.25
.25
0.50
0.50
o.
0.43
L3
0.42
v.
ua
J6r
diam corrugat€d
corrugated
36" dian
7I
7
66
0roup
Group
20
20
0.68
O.ffl
o0.25
,25
0.49
O.lr9
99
0
22
00.59
.59
0.42
o.tp
0.51
o.5r
u.4)
0.45
o0.33
.33
o0.39
.39
11
o0.59
,59
0.t3
0.33
0.49
o.t9
7
00.•1.1.33
0.05
0.05
0.08
0.08
5
0.12
0.12
0.05
0.05
0.10
L2
12
0.]3
0.13
0.05
0.05
00.09
.09
2lrr
diam corrugat€d
corrugated
24" dlan
18r
corrugated plpe
pipe erch
arch
16" eorrugated
2Ln
corrugated plp€
pipe arch
arch
24" corrugated
35tr
corrugated pipe
pipe arch
arch
36" corrugated
Group
Group
l,8n
concrete
diam concrete
18" dian
II
o0.53
.53
Random
Randon
ZLn
diam concrete
concrete
24" dlan
16r
diam concr€te
concrete
36" dtan
Grop
Group
Random
Ibndorn
n0.53
<a
Increases aB
as dlaDoter
diameter increasea
increases
Increaaes
4
TABLE
II
?ABIA TI
SUMMARY
FLOUINGPARTLY
TEST RESULTS
RESUL$i - PIPFS
PIPES FLOWING
PARTLYFULL
FULL
SI'UMARI OF
OF TEST
No.
N o . of
cf
Tests
Tests
Pipe
Plpe
Maximum
llaxinun
IIinimum
l{ininun
Average
Average
Type
lVpe of
Variatlon
of Variation
MANNING
COEFFICIENT
!{ANNINCROUGHNFSS
ROUGHNESS
COEFSICIN'IT
18"
]8rr diam
dlan corrugated
corrugated
2lrn diaID
24"
dlan corrugated
corrugated
36"
dLas corrugated
corrugat€d
J6r diam
8I
10
10
lL
1L
0.025R
0.0258
0.024L
o.02LL
0.0243
0.0211
0.0248
0.02!8
0.0232
0.023?
0.0228
0.0228
0.0252
o.0252
0.0240
0.02[0
0.0236
o.02)6
G
r oup
Group
32
)2
0.0258
o.o25B
0.
0228
0.0228
0.0242
O.OZlr2
10
3?
I3
13
0.0233
o.023)
0.0228
0.0228
0.0230
0.0230
0.0216
0.02r.6
0.0213
0.0213
0.0221
0.0223
0.0223
0.0220
o.0220
0.02
26
o.0226
26
2('
0.0233
0.0233
0.0213
0.0213
0.0224
o.o22b
tn
10
6
0.0110
o.01to
0.
0108
0.0r08
0.0102
0.oLo2
0.0102
0.0102
0.0107
0.0107
0.
0104
0.0101
16
IO
0.0110
0.0110
0.0102
0.0t02
0.0106
0.0106
lStt corrugated pipe arch
18"
2lrr! corrugated
corrugated oipe
arch
24"
oipe arch
pipe arch
eorrugated pipe
arch
36"
35r corrugated
Group
Group
18"
IEtl diam
dlan concrete
concrete
dian concrete
2bt diam
2L"
36"
dlan concrete
concrete
36f diam
G
r oup
Group
Random
Randon
Randon
Random
Random
Randon
pRoJECTINGINLET
ENTRANCE
LOSS
EN1RANCE
IO.SSCOEFFICIENT,
CoEFFICIENT, PROJECTING
INTET
18"
l8tr diam
dian corrugated
ccrrugated
2hrr diam
dian corrugated
corrugated
24"
dian corrugated
corrugated
36"
36tt diam
'Group
'Group
18"
I8n
24"
2lrtr
36"
36r
4L
5
7
0.77
0.77
o.77
0.77
O.Sl
0.81
0.
0 .58
58
0.63
0.63
0.58
0.58
0.
0 .71
71
o.69
0.69
o.69
0.69
1A
16
0.131
0.8r
0.58
u. >o
0.70
0.70
5
3
7(
0.82
0. 82
0.96
o.96
0.51
0.5L
0.
43
0.1-!3
o .34
3L
0.
0.41
O.LI
0.65
u. o>
0.68
o.68
0.46
0.116
15
L5
0.96
0.96
0.31
0.34
0.57
88
6
0.20
o.20
0.23
o
_"t
0.13
o. 13
0.02
o_0,
0.16
0. 16
0.08
o-*
14
!u
0.23
o,2)
0.02
0.02
0.12
o.L2
corrugated
pipe arch
corrugated pj.pe
arch
corrugated
pipe arch
areh
corrugated pipe
plpe ar
corrugated
ch
corrugated pipe
arch
Group
0roup
18"
l3't diam
dian concrete
concrete
dianr concrete
24"
?lro diam
36"
eoncrete
dian concrete
l6n diam
Group
0roup
Random
Randon
Randoro
Random
Random
Randorn
ENTRANCE
LOSS
BNTRANC8
CoEFFICIET'IT,FLUSH
FLUSEINLET
LoSS COEFFICIENT,
INLET
0.56
o.56
0.54
0.5b
0.53
o.53
0.28
0.28
0.
42
o.lQ
o.)7
0.37
0.41
0.1[
0.48
0.1r8
0.42
0. L2
L>
15
0.56
0.56
0.28
o.28
u.llll
0.44
5
0
6b
0.43
0.b3
0,17
0'I7
0.30
0.30
0.33
0.15
v. r?
0.26
0.26
11
0.43
o.L3
0.15
0.15
0.28
0.28
2
0.15
o-*
0.06
o.06
0.10
0.lo
2
0, 15
0.15
0.06
0.06
0.10
0.10
18"
18" diam
dian corrugated
co"rugated
ted
24"
2Ln diam
dian corruga
corrugated
r(n diam
dian corrugated
36"
corrugated
4!
5
6A
Group
Oroup
18"
r8r corrugated
pipe arch
corrugated pipe
arch
pipe arch
24"
2ljr corrugated
corrugated pipe
arch
pipe arch
corrugated pLpe
erch
36"
Xe corrugated
Group
Group
8" diam
IEr
dlan concrete
concrete
24"
2hr diam
diar concrete
concrete
dlan concrete
concret€
36"
J5r diam
Group
Group
II
Random
Randon
Ilandom
llandon
Random
Randon
5
TABLE
TABLEIII
III
RECOMMENDED
DESIGN
DESIONCOEFFICIENTS
RECOMMENDED
COEFFICTENffi
FOR CORRUGATED
FOR
METAL
CULVERTS
ANDCONCRETE
CORRUGATED
METALAND
CONCRETE
CULVERTS
Corrugated
Corrugated
-Metal
u;;;i--
Itern
Item
.|t
*
t+
^
*
Concrete
con*ete
Manning coefficient,
fu1l flow
flow
Manning
coeffi-cient, full
0.0250
v.v(>v
0.0100
0.0100
partly full
Manning
partly
Manning coefficient,
full flow
flow
coefficient,
0.0240
0.02L0
0.0110
0.0110
Projecting
full
Projecting inlet
flow
inlet coefficient,
coefficient,
fuI1 flow
0.90
0.90
0.15
U.I>
Projecting inlet
inlet coefficient,
partly full
full flow
Projecting
partly
coefficient,
flow
0.70
0.70
0.15
0.15
Flush inlet
full
inlet coefficient,
coefficient,
full flow
flow
n q n
0.50
0.10
0,10
partly full
flow
Flush inlet
partly
inlet coefficient,
coefficient,
full flow
0 .h 0
0.40
0.10
0.10
oTh"
*The above recommended
pipe
th no
recornmended values
pipe wi
values apply
nevr, straight
vrith
no
appty to new,
straight
obstructions,
obstructions,
side
features.
'l'he
flow-disturbing
features"
I'he ManManside openings, or other
other flow-disturbing
ningG coefficients
for corrugated
nin
for
coefficj.ents
rnetal apply
apply to
to corrugations
conugated metal
corrugations with
uith 1/2-in.
1/2-in.
heieht
and
2
2/3-in.
he ight
2/3-in. spacing.
The
for
spacing"
The Manning coefficients
coefficients
for concrete
concrete apply
apply
pipe manufactured
to pipe
to
process in
manufaetured by the
process
the cast-and-vibrated
6-ft lengths
cast-and-vibrated
in 6-ft
lengths of
of
pipe
uith non-pressure
non-pressure rubber
rubber: ring
pipe and with
joints.
ring joints.
As aa culvert
As
obviously much
culvert material,
material, corrugated
corrugated metal
metal is
is obviously
much less
less efefficient
hydraulically
than concrete;
f ic ient hydraulically
than
detailed comparisons appear
concretel detailed
appear later
later in
in the
the
report"
rep
ort.
general, it
In
may be said
fn general,
it may
that a culvert
said that
culvert usually
usually can, and should,
should,
be designed
designed to
flow full
given conditions
to flow
full
under the
condi tions of
under
the given
discharge and available
of discharge
available
head.
Such a design would usually
Such
economical, regardless
of uhich
which
usually be most
most economical,
regardless of
naterial
is used.
rna terial is
Howev-er,
Howev_
er, a concrete
roncrete culvert
culvert flowing
flowing full
full
has a much
higher
much higher
hydraulic
than a corrugated
ydraulic capacity
the same
same dianeter.
diameter.
capacity than
cormgated culvert
culvert of
of the
Therefore,
Therefore,
whenever
whenever hydraulic
hydraulic efficiency
efficiency is
is the
controlling design factor
factor in
in a given
glven
the controlling
culvert,
concrete
culvert,
concrete or
or other
other snooth-walled
smooth-walled pipe
pipe is
is rmrch
much superior
superior to
to corrugated
corrugated
netal"
etal.
TIL
r1I"
METHODS OF
OF TESTLNG
TESTlNG AND
AND ANALYSIS
ANALYSIS
METHODS
All
All of
of the
the pipes
pipes were tested
tested in
in the
the nain
main testing
testing channel
channel of
of the
the
St. Anthony
St.
An thony FaIIs
Falls Hydraulic
Hydraulic taboratory.
Laboratory.
Each pipe
pipe was
was approxinatefy
approximately 193 ft
ft
Iong
ong and on a slope
slope of
of approximately
approximately 0.002.
0.002.
installed near
near
Bulkheads were 1nstaIled
the
he two ends of
of the
the pipe
pipe in
in order
order to
to form
form headnater
headwater and tailwater
tailwater pools,
pools.
general
general experimental
experimental installation
installation is
is shown
shown on Fig.
Fig. I.
1.
The
the
6
Fig.
F i q . 1l-
T e s t Installation
36-in.
3 6 - i n Concrete
C o n c rtee Cul
Instollatron
C u vert
l ; e i " iTest
7
pipe for
partA large
and partwas made
nade in
in each
for both
both full
fu1l and
large number
numberof runs was
eaeh pipe
projecting and
full
and for
for both projecting
and flush
inlets in
in an
fu11 flow
flor conditions
condltions and
flush inlets
an attempt
attenpt
pernit.
to study as
would
as wide
wj-de aa range
as facilities
would permit.
range of flow
flow conditions
conditions as
facilities
The
The
false
in Fig.
flush entrance is
is shown
false bulkhead used
used to simulate
sinmlate aa flush
shoyvn.in
Fig. 2.
Fig. 2
Fig.
2at
36-in.
Concrete
Culvert
F l u s h Headwall
H e o d w o lo
l t IInlet
n l e i ttoo 3
- Flush
6-in. C
o n c r e t eC
ulvert
For each
each ntn,
run, eareful
careful measurements
measurements were
were made
made of
of the discharge,
discharge, the
the
trydraulic
ydraulic grade 1ine,
line, and
and the vrater
water temperature.
temperature.
The
The diseharge
discharge Tyas
was controlled
controlled
b5r
by gates at
at the
the entrance
entrance to
to the testing
testing channeSchannel and was
was usually
usually measure'd
measured in
in
large
l arge vo}:metric
volumetric tanks,
tanks, although
although weighing
weighing tanks
tanks or
or a calibrated
calibrated supply-line
supply-line
8B
meter were
were used
used for
for some
someruns.
runs. The
The tailwater
meter
tailwater level
1eve1was
was controlled
controlled by
by aa weir
weir
gate at
at the
the downstream
dovirnstreamend
end of
of the
the channel
gate
charu:e1in
in order
order to
adjust the
to adjust
the hydraulic
hydraulic
grade line.
j^ntervals
1ine. The
Thelatter
latter was
piezometric
wasdetermined
grade
etric measurements
deternined by
by piezom
neasurementsat
at intervals
along the
prpe, each
the pipe,
piezometer tap
eaeh piezometer
along
tap being
being connected
connected to
to aa central
eentral manometer
rnanometer
board, where
where simultaneous
simultaneous static
pressure readings
board,
static pressure
readings could
cor:Iclbe
be observed
observed for
for all
all
pipe.
reaehes of
of the
the pipe.
reaches
For details
details of
of the
For
the experimental
experinental apparatus
procedure, Technical
apparatus and
and procedure,
Technical
Papers
No.
l+
and No.5
No. 5 of
of this
this series
Papers No.4 and
series should
be consulted
should be
consulted.. It
It is
is believed
believed
that accurate
accurate and
and reliable
reliable results
results have
that
have been
been obtained.
obt:Lined.
Frorothe
the experimental
erperimental data,
From
data, friction
friction coefficients
coefficients and
anCentrance
entrance coefeoeffieients were
were computed
eomputedfor
for each
ficients
losses were
each run. Barrel
Barrel friction
friction
were obtained
obtained
from the slope of the hydraulic
hydraulic gradient
gradient in
in the central
central reaches
reaches of the pipe
where the gradient
gradient was
was aa straight
where
strai-ght line.
line.
Entrance losses were
were obtained by
W
extending
the
portion
straight-line
extending
straight-line portion of the hydraulic
hydraulic gradient
gradient back
back to the
plane of the pipe inlet,
in1et, adding the pipe veloci
plane
velocityty head
head and
and then deducting the
fron the headwater
headwater elevation.
ttotal
otal from
elevatlon.
In the part-full
part-fuI1 flow
flow tests,
In
uniform
tests, aa condition
condition of approximately
approximately r:niform
flowvras
established for
for the particular
f low was established
particular depth and
Thus,
and discharge.
discharge,
Thus, the hydrauhydraugradient
Iie
was equal or nearly
nearly equal to
lic gradient was
to the cuI
v~rt slope.
view at
eulvert
s1ope. A view
at the
culvert
culvert outlet
outlet with
with part-fu11
part-full flow
flow in
in the barrel
barrel appears
appears in
in Fig.
Fig. l.
3.
FFig
i q. 33 -- O
Outlet
Diameter
Corrugated
Culvert
u t l eoof
t f 336
6 -- iin.
n D
i o m e t eC
r o r r u g o t eC
du l v e r t
(( FFlowing
Full))
l o w i n gPPartly
o r tlyFull
9I
fn most
nost cases,
casesr this
this condition
In
conditlon was
was also
also aa tranquil
tranquil flow
flow condition.
eonditj-on.
However,the
the criti
critical
slope for
for the
the 36-in.
However,
cal slope
he actual
pipe was
conerete pipe
wasso
near tthe
)6-in. concrete
so near
actual
of the
pipe that
s)-ope of
the pipe
that near-critical
near-critical
slope
flow
ined at
flow was
uas obta
obtained
at nearly
nearly all
all depths
clepths
in this
pipe.
this pipe.
in
The resultant
resultant exces
The
sive wavine
ss and
excessive
wavi.ness
vari-ability of
and variability
of the
the water
water
made
surface
it
impossibl-e
surface made it impossibl e to
to determine
deternine coefficients
eoefficients for
part-fu11
r:niform part-full
for the
the uniform
j-n
flow condition
condition i n this
pipe"
this pipe.
flow
Reference may
rnayagain
again be
Reference
cal Papers
. 4lr and
bemade
nade to
Teehnical
to Techni
Papers No
No"
ana No.
No. 55 for
for
more
detailed
e:iplanations of
of the
more det
ailed explanations
t ional procedures
the computa
procedures employed.
conputational
euployed"
The experimental
experimental rating
rating curves
The
curves for
for all
pipes are
all of
of the
the pipes
are shown
in
shovrnin
"
Figs. 4,
6, and
and 7.
L, 5, 6,
Figs.
f,
rV"
IV
4
A.
A.
ANALYS$ AND
A}ID DISCUSSION
ANALYSIS
DISCUSSIONOF
OF RESULTS
NESIIf,?S
General Analytic
Analytic Relations
General
The general
general equation
equation defining
'I'he
fl
ow through
defining
flow
through aei culvert
culvert is
is
v2
2
V
2
V
H==KeK-* +$K.f *-r +* K.0 *-"
H
2g
2g
2g
*
In this
thls equation,
equation, !iH iiss the differ
diffe:'ence
In
ence between
between ttc'ral
ot al head
n the headwater
head ij-n
tailwater pools.
If the velocity
veloeity heads
tailwater
pools. If
pool s are sna11
small or
heads iinn the pool-s
or if
i-f they
they
nearly
equaI,
then
H nay
nearly e qual, then!!
may be takenas
taken as the difference
difference in
in eletations
eleva tions between
(3)
(:)
and
and
are
the
headyrater
headwa ter and
and tailwate:'pools.
tailwater pools. ?he
The aver&ge
avera ge velocity
velocity of
of f1ow,
flow, I,
Y." i-s
is measured
measured
in
in the cr:ntraI
central reacl:es
reac hes of
of the pipe
pi pe rhere
where the flow
flow is
is unifei:'m.
uniform. The
The normal baruel
barrel
2
friction
frict:i. on loss,
loss , x,
K (v'i?c),
(V / 2g), is
is the loss
loss whi*h
which would oceur
occur in
in an interlor
interior reaeh
reach
f
of
of a very
very long
long hS4pothetir:al
hypotheti cal pipe
pipe of
of the
t he same
same eross
cross secti-oil
section and naterial,
material, the
the
reach
reach having
having a length
length equal
equ al t,o
t o the length
length of
of the
the actual
actual culvert.
culvert.
2
The
The entranee
entrance 1oss,
loss, Xu
K tvz/Ze)r
(V /2g) , 5-s
is the
the excess
excess friction
friction l*ss
l os s near
near the
the
e
pipe
inlet
pipe inlet over
over the
the normal
normal bamel
bar rel frie:;.!-*n
fri ction l-oss
l oss in
in that
that region"
regi ono in
I n the
the erqperlexperiments
ments elescribed
described in
in this
this paper'
paper; the
the entran*r*
entrance loss
loss was
was o"r,"tained
obtained by
by extending
extending the
the
straight-line
straight- line portion
portion of
of the
the hydraulie
hydraulic g::ade
grade line
l i ne to
to the
the pi-ane
plane oj
of ti:e
the entrance,
entrance,
adding
adding the
the unlform
uniform velocity
velocity head,
head, snd
and d*ducling
deduc ting the
the totajtotal j.}on
from the
the headwater
headwater
2
'r',:2,izr),
elevation.
elevati on. simiLarly,
Similarly, the
the outlet
outlet losi;,
los s , Ko
Ko (V / 2g), was
was obiained
obt ained by
by extending
extending
the
the hydrarrlic
hydraulic gradient
gradient linearly
linearly to
t o the
the plane
plane of
of th*
t he outlet,
outlet, adding
adding the
the velocity
ve l ocity
headr
head, and
and subtracting
subtracting the
the taibyater
tai lwater elevatir:n
eleva t i on f,::orn
from the
the sun.
s umo
The
The entrance
entrance and
and outlet
outlet loss
loss coeff,i*ients,
coeff i cients , K"
K and
and K*,
K , are
are usually
usually
e
0
obtained
obtaine d eriperimentally
experiment a l ly for
for dlffereni
different Qrp*s
types of
of entranees
entrances and
and outle*;s,
outle t s , although
although
/0
to
1
t.oo
1.00
;1
o,90
0.90
o.80
0.80
I
o.70
0.70
I
J
f
/
0.60
Cb
.~
Q.
/
0.50
.....Cb
,Cb
J
.40
- 0o.40
cc
:
Q)
...
^o
a..
Q)
II
ct
o.30
0.30
~
.~
Q.
0o.25
.25
c
c:
o
.;'0
Q)
0o
(,...
. ~'
I
~
Cb
.~
Q.
j
d
Cb
~
>.
x:t:
o
.r o
0.10
I
o.o9
0 .09
ll)
Q)
oa.
o0 o.og
0.08
·s· I
V
I
J
II
V
J
r
/
0.06
I
I
Co
I'f)
I
a(/)
0.07
I
1
(J0
J
...
i
/
~J
r
v
J
;:,
0
0
p
'0
/
~
if
J
~ j
.15
.!0 0o.ro
i
P
(J0
(!)
....o0
V
I
<;:u
0o.2o
.20
d
i0/f
/
.....Cb /
,Cb
T-
II
.~
V
}
L
V-
<;:u
jJ
Q)
()
U
p
/
I
~t
/
-
,L °
/
II
0 .05
I
/
V
0 .04
0 .03
3
4
5
6
7
8
9
10
15
20
25
Discharge
n ccfs
D
i s c h o r g e iin
fs
FFig.
i g .44- EExperimental
xper imentol
Rating Cur
Curves
Roting
ves
((Concrete
ConcreteCulverts
Culverts Flowing
Flowing Full
Full))
30
40
50
60
II
2.OO
2.00
pI
50
I.r .50
,/I
Ip
l~ ~
:tl
80
0o. .80
d t
~~
l(
ff j
70
0o. .70
r{
0.60
0.60
~
...o,
30
0o..30
CII
(L
Cl.
{
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F i g. .66 - Experimental
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RotingCurves
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13
they may
nay be
be closely
they
closely computed
in
principles of
corryuted analytically
analybically
in many
many cases
cases from
from principles
of
hydrodynamics.
hydrodynamics.
The barrel
barrel friction
The
K
friction loss
loss coefficient,
Kf,, is
is usually
coefficient,
usually expressed
in
expressed in
f
of one
one or
terns of
or more
nore of
of the
the various
various pipe-flow
pipe-flcm formulas.
terms
foruru1as, The
The most
nost commonly
commonly
used formulas
fornulas of this
this type
type are the Darcy formula and
used
and the
the Manning
Manning formula.
formula.
(r).
latter formula has
already been
latter
The
has already
been given as
Eq. (1).
The Darcy
Darcy formula
as Eq.
is
forrnula is
H
"f
H
LL V
u2 2= "tn Vt 2
"f- .LR
2g = K 2g
=
f =
ljR 29
The
The
(L)
(4)
f 2e
Darcy friction
The Darcy
frietion factor,
The
factor, f,
is related
lbnning roughness
related to the Manning
roughness coefficient,
coeffieient,
!, is
n, by the following:
following:
~,
4
-
1 1 ?
II'
fI . =- 117
22
n
:i73
n
w
(5)
$)
R
tsotir the Manning
Mannlng coefficient
coefficient
Both
and
factor
and Darcy friction
friction
factor can
ean be
be computed
computed from
fron
tlte measured
measured discharge, cross-sectional
the
cross-sectional dimensions,
dj-mensj-ons,and
graclient.
and hydraulic
hydraulic gradient.
The friction
friction
is known
The
factor
factor is
knownto
to be
Reynolds number
be aa function
function of
of the Reynolds
number
and the pipe material.
The Reynolds
and
naterial.
The
Reynolds number,
nunber, Re,
i-s defined
Re, is
defined by the expression
^n e == 4RV
Lnv
Re
i
(6)
(5)
/I
In
In this
thi s expressi
on, the kinernatic
kinematic viscosity,
/I,, is
is aa fluid
fluid property
property vrhich,
which, for
for
expression,
viscosity, I./
a given
given fluid,
fluid, varies
varies with
with tenperature.
temperature. '
The
coefficient has
has corrnonly
commonly been
been supposed
supposed to
to be dependent
dependent
The Manning
Manning coefficient
only
only on the pipe
pipe naterial
material for
for the
the usual
usual design
design flows
flows in
in engineering
engineering conduits.
conduits.
I{owever,
However, the present
present studies
studies have denonstrated
demonstrated that
that it
it j-s
is also
also dependent
dependent on
the
number, at
at least
least within
within the usual
usual range of
of flows
flows in
in conerete
concrete and
and
t he Reynolds nr:mber,
eorugated
corrugated netal
metal eonduits.
conduits.
This would also
also be found true
trup. w"ith
with the eoefficients
coefficients
This
of
of the
t he Scobeyr
Scobey, Hazen-Y{i11ians,
Hazen-Williams, and
and other
other enpirical
empirical pipe-flow
pipe-flow fornulas.
formulas.
B"
B.
Frietion
Friction Losses
Losses for
for Fu1l
Full Flow
The
The Darcy friction
friction factor,
factor, !,
f, isis known
known to
to depend
depend upon
upon the
the Reynolds
nunber,
number , Re, and the
the pipe
pipe roughness. Forpipes
For pipes of
of a given
given naterial,
material, the
the absolute
absolute
roughness
roughness is
is presurned
presumed to
to be the
the sane,
same, regardless
regardless of
of the
the pipe
pipe size.
size.
However,
However,
the
the relative
relative effect
effect of
of a given
given tlrye
type of
of ra1I
wall roughness
roughness on the
the flow
flow should
should
decrease
decrease as the
the pipe
pipe size
size increases.
increases.
rb
14
It
recent years to use
use the ratio
of equivalent
equivalent
in recent
ratio of
ft has
has become
becone COlmnon
conmonin
sand
pipe diameter as
roughness of
relative roughness
of aa
dianeter to pipe
as aa measure
neasure of the relative
sand diameter
pipe.
pipe.
The
The equivalent
understood to
to be
be the diameter of
of
Kr,, is
is understood
equivalent sand
dianeterr K
sand diameter,
s
uniform
grains which
uniform sand
vihich could
on aa smooth
of the same
same diameter
dianeter
could be
be coated on
smooth pipe of
sand grains
as
loss
friction
loss as
as
as the pipe under
under consideration
and would
would cause
cause the same
same friction
consideration and
obtained in
pipe.
actual pipe.
in the actual
The
factor
The friction
factor can
be written
written as
as aa
friction
can then be
function
funetion of
and relative
relative roughness, thus:
thusl
of the Reynolds
Reynolds number
number and
K
K
= fn
ff =
(Re,
fn 1ne, ;)
(7)
f,)
In
partly turbulent
wall roughlaminar and
turbulent regimes
regimes of
of flow,
flow, the wall
fn the laminar
and partly
ness
persistent influence
friction
ness has
has no
no persistent
upon the flow structure,
strueture, and
and thus the friction
influence upon
the functional
factor
numb~r only.
factor is
Relmolds nunber
relation of
of
function of
of the Reynolds
onLy" The
functional relation
is aa function
(Z) is
Eq. (7)
Eq.
ressible by the following
partly
following equations for
for laminar
ls then e:xp
e:oressible
laminar and
and oartly
turbulent
turbulent (smooth-pipe) flow,
flow, respectively:
respectively:
_ 64
f, -5 ReL
rde
( 8))
(8
and
f -
1
(e)
(9)
- 0.8)2
(2
(2 log
r og Re
Re if
0.8) 2
1F _
Equation (8) is
Equation
for viscous
viscous flow.
is the Poiseuille
Poiseuille equation
equation for
flow"
(p) is
Equation
Equation (9)
is
due
equations
due to Nikuradse and
and is
only one
vrhich
is only
one of
of several
several semi-empirical
equations Ylhich
semi-enpirical
have
have been
various authors to describe the partly
been suggested
partly turbulent
suggested by various
turbulent regime,
regine,
though
generally accepted
though probably the most
most generally
accepted of such
equations"
such equations.
In the regime of
of full
fuIl turbulence,
turbulence, the wall
wall roughness
roughness predominates
The
and
friction factor
factor does
Reynolds number.
and the friction
does not vary with
uith increasing
number. The
increasing Reynolds
Nikuradse
Nikuradse equation for
for this
this regime
regime is:
is:
ff o•
1
K
K
(10 )
(10)
2
( t . r l r- -2z log
r o g ;)
f)2
(1.14
The transition
The
between
transition
partial and
between the regimes
regines of
of partial
and full
full turbulence
has
has been
been largely
largely ignored in
practice heretofore.
in most
most hydraulic
hydraulic design practice
heretofore"
The
The
traditional
traditional
empirical
empirical pipe design formulas
for:nulas have
vishave neglected the effect
of viseffect of
cosi
ty, which implici
cosity,
implicitlytly assumes
assumesfully
fully turbulent
turbulent conditions.
conditions.
An
An equation which
15
11"
L2
has been fairly
fairly extensively
extensively used
used for
for this
this transi-tional
transitional realm
reaLll is
is that
that of
of ColeColebrook and liilhite:
Whi te :
brook
1
((11)
11)
f = --------------~----------~
K
n n r ' - 22
7
. ) > \ll
(
*
log
(2.
+
9.3~
*
2
r
o
g
lr.rl+
'[f
D
Re
-V f JJ
L
J
The Colebrook-'ll{hite
Colebrook-White curve is
is asln'nptotj-c
aSY1!lptotic to
to the
the Ni}uradse
Nikuradse srnooth-pipe
smooth-pipe and
and roughThe
as defined
defined by Eqs.
Eqs. G)
(9) ana
and (10),
(10), and
and purports
purports to
to represent
represent the
pipe curves, as
transitional region
region of
of pipe
pipe flow
flow as obtained
obtained on actual
actual conmercial
commercial pi-pes.
pipes.
transitional
The
The frietion
friction factor
factor - Reynolds
Heynolds number
number curves for
for the corrugated
corrugated netal
metal
and concrete
concrete pipes
pipes included
included in
in the experlments
experiments reported
reported herein
herein are shown
shown in
in
and
Fig. 8,
with the smooth-pipe curve.
curve.
Fig.
B, along with
sets of
of experimental
experimental curves
Both sets
indicate a functional
functional dependence
dependence of
of the frietion
friction factor.upon
factor upon both the Reynolds
Reynolds
indi-cate
number and
the relative
relative roughness, implying
that the flow
is transiimplying that
and t'he
flow regime
regine is
nurnber
transitional between
between partlal
partial and
and full
turbulence .
fuIl turbulence.
tional. 15
I
.10
.t0
4
" I'\\l_e
09
09
--
.08
.08
.07
.07
~
-I-- ~~I'\\le
C;(c u
-- \8
\6
---
cyt-
ffi'l
~I
---
t>.(c\'l
-
-
~~....z
---:-: ~
t>.(c\'l
..
rpe-E
f
-f4C\(CU\O~_
I-- ~
_____
I~~
36" Ci(Culor
I'lpe
11|-\itcutor,
.06
.06
~
0;
'ela
Corrugated
ipes
Cor ugo led Metal/ Pipes
.05
.o5
~
o
00
u..
uc
.04
.04
0
.9
"
'i
~
h .03
.03
.02
r-SrDor
SmOOth
)th
-t i p e
"-]
P'Pe -1--1-\\\ (Et
8l o s l r .
( as'
IUS)
tS) - -
Concrete
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Concre;rlePipes
.
--_l*lrcTr*:--_
::::::t:----t.~
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"
~,
......
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36"
crrI r
ClrcUlo
,Pes
- - r - . Pipes
smOOlh~~
tt Ipe
iD
(N '
r--
fi-
Ikur
t"-J--;
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dSe
)
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.ol
50,000
50, ooo
100,000
r0o.ooo
4- RRVV
3 ,v Reynolds
N u m b e r Re
,A " == R e y n o l d sNumber,
Fiq. 88 -Fig
2O0.0o0
200,000
r--r--_I--
500'000
500,000
Comparison
of
iction Factors
Comporison
of Fr
Friction
Foctors
o n cre te
((C
Concrete
and
Metal
o n d Corrugated
M etolCulverts
C or r ugoted
Culver ts
)
- r--
--
1,000,000
r,0o0,o0o
r--..
2,O0O,0OO
2,000,000
166
1
However, neither
neither the
the curwes
curves for
for the
the corrugated
corrugated pipes
pipes nor
nor those for
for
Holuever,
the eonerete
concrete pipes can be satisfactorily
satisfactorily expressed
expressed in
in Lerms
terms of
of the Colebrook
Colebrook
equation .
equation.
The eorrrrgated
corrugated pipes especially
especially gave
gave results
results eontradietory
contradictory to
to those
The
that would be erpected
expected from the Colebrook equation,
equation, slnee
since a definite
definite increase
increase
that
in friction
friction factor
fa c tor with
with increasing
increasing Relmolds
Reynolds number
number was
was noted for
for each
each of
of then,
them,
in
whereas the equation postulates
postulates a decreasing friction
friction factor.
factor.
whereas
These curves seem
seem to
to approach
approach the horizontal
horizontal at
&t high
high lleynolds
Reynolds numnumThese
bers, but
but they all
all show
show a rising
rising characteristic
characteristic throughout
throughout the experi-mental
experimental
bers,
Such a ri-sing
rising eharacteristie
characteristic was
was unexpected
unexpected and
and is
among concomSuch
is unique anong
mercial pipes,
pipes.
These results
results serve
serve to
to ernphasize
emphasize t'tre
the fact
fact that
that pipes with
with
These
mercial
rrregularrrpatterns
"regular"
patterns of
of roughness
roughness nay
may behave
behave quite
quite dlfferently
differently hydraulically
hydraulically fron
from
range.
pipes
pipes of
of rrrandomrr
"random'l roughness
roughness patterns,
patterns, for
for whieh
which the Colebrook equation
equation was
was
derived.
derived.
the
The detailed
detailed hydrodynanics
hy drodynamics of
of friction
friction losses
losses in
in corrugated
corrugated pipe
pipe is
is
still
obscure and
and undoubtedly quite
quite complex,
complex, but the essential
essential fact
of the
faet of
obscure
still
rising
Reynolds number
curve for
material is
is aa signinumber cur:ve
for this
this material
signifrictionon factor
factor - Reynolds
rising fricti
ficant
i nding of
of these
ficant ffinding
these experiments.
0 30
IS" P i ~ Arch
.025
co
'"
~.9
~o
U
o
'"'"o
'""
'"oo
g
.020
--
--- ~
f---::::
IS
lS"" Circular
Pipe
Circulor!,ipe
24'
Pipe Arch
24'.Pipe
Arch
36" Pipe ~rch 24 'Ci r~ar Pipe 36" Ci rc~lar Pipe
~
Corruqated
l4elo/ . Pipes
Prpes
Corr u g aled Metal
~
(r
0::
.015
o
'"
,=
.=
""o
Concrete
Concrele Pipes
PiDes
c
=
~
-
.010
.0 0
S"C
II
. J
I
,rcu a r P'Pj" "
36" Circular Pipe
~'"
'2~" Circ,ular ji pe
•
.008
70,000
100,000
200
, 000
2OO,OOO
300,000
SOO,OOO
500,000
sOO,@o
700,000
4$J(
Reynolds
ReynoldsNumber,
ne := ~
Number, Re
icients
Fig
of
Coeffic
ients
Coeff
of Roughness
Roughness
F i q. 9.9 - Comparison
C o mp o ri son
(C o n cre te
M etolCulverts)
(Concrete
and
Metal
Culver ts
o n d Corrugated
C or r ugoted
)
1,000,000
',500,000
'.
t
17
17
The
pronouneed, is
evident
The same
varlati-on, though not
not so
is evident
of variation,
so pronounced,
same type of
in
Reynolds
Manning coefficient
ttre curve of
values of
of the Manning
coefficient versus Reynolds
in the
of experimental
experimental values
number
nunber for
for the corrugated pipes,
pipes, as shown
Fig. 9.
shown on
on Fig.
t.
Thus,
Thus, the value of
n to
of !!
be used
be
used in
depends upon
size
in the design of
of aa corrugated pipe depends
upon both the pipe size
and
Reynolds number,
has been
been customarily
and the Reynolds
not aa constant
as has
custornarily
nunber, and
and it
corstant as
it is
is not
ass
umed.
assumed.
The friction
The
factor
friction
Reynolds number
for the concrete pipes
factor - Reynolds
number curves
curves for
show
be implied
falling characteristic,
Golebrook equation
show aa falling
would be
equation..
characteristic, as
as would
implied from the Colebrook
liowever,
H
owever, they will
yield aa constant
dianeter,
will not
not yield
equivalent sand
sand diameter,
eonstant value of the equivalent
Relmolds number
K
to increase with
K"r
for concrete pipe.
pipe. Rather, K
nunber
K"
was found
with Reynolds
s , for
s was
.
given pipe and
for
e with
for aa v,iven
and to increas
with the size of pipe.
increase
Thus
cribe
thus the Nikuradse
and Colebrook
equabions are inadequate
deseribe
Nikuradse and
inadequate to des
Colebrook equations
the flow
flow in
these tests,
tests, both concrete and
and corrugated
in the pipes studied
studied in
in these
The
The equivalent
does not appear
appear to
to serve
dianeter, K
senre satisfacsati-sfacequivalent sand
Ku,, does
sand diameter,
s
torily
epresentative length
uch pipes.
parameter for
pi,pes.
torily as
for flow
flow in
as aa rrepresentative
length parameter
in ssuch
metal.
The
cient, whic
varying
the Manning
has already
been noted as varying
whluin has
already been
coeffrcient,
l{anning coeffi
with
Reynolds number
pipe size
pipes, was
with Reynolds
with pipe
for the corrugated
cormgated pipes,
was nevernevernurnber and
and with
size for
theless
factor
Darcy friction
friction
as
theless more
eonstant than the Darcy
factor or than K
K" as
more nearly
nearly constant
s
computed
he Nikuradse or
Similarly,
Manning
conputed from tthe
equations.
or Colebrook equations.
Similar1y, the Manning
Reynolds number
coefficient
and pipe size
for the
size for
variation with
with Reynolds
nurnberand
coefficient showed
showedsome
some variation
concrete pipes,
iation in
pipes, but
variatj-on
but the variation
variation was
was much
muchless than the var
in f or in
in
K.
be the
Manning coefficient
K-. For practical
oractieal design use, the Manning
coeffieient stil
seems to be
still l seems
ss
most
s s. Figure 9 shows
Manning
most nearly
roughness.
shows the Manning
nearly constant measure
measureof surface
surfaee roughne
giving experimental curves
Relmolds number,
for
coefficient
function of Reynolds
culves for
as aa function
nunber, giving
coefficient as
all
tested.
all the pipes tested.
The
The values of n for
tests
for corrugated
corrugated pipes obtained in
in the present tests
are considerably
higher than the value of
considerably higher
of 0.021 which is
used at
at
is commonly
conmonly used
present.
present.
Further, it
Further,
that, iiff the experimental
it is
is important
inportant to recognize that,
iteynolds
facilities
had
higher
permitted the establishment
facilities
had permitted
flors of
higher Reynolds
establishnent of
of flows
of still
still
number
numberin
n would
have been
been obtained
obtained
in the pipes, still
still higher
higher values of
of !!
wouLd probably have
for
for such
pipes.
such pipes.
Consequently,
used in
in
that n-values used
Consequently, it
is strongl
it is
stronglyy urged that
corruga
ted pipe design should be
he curves
and that
that
corrugated
fron tthe
curves of
of Fig.
Fig. 9, and
be selected
selected from
if
i tua tion lies
present experimental
n-value
lies beyond
beyond the present
experimental range, an n-value
if the design ssituation
of at
at least
least 0.025
0.025 be
be used.
used,
18
r8
The values
values of
The
of nn obtained
obtained for
for the
the concrete
pipes, on
concrete pipes,
the other
on the
other hand,
hand,
rere lower
lower than
previously recommended
than previously
were
reconmendedvalues.
values. Also,
Also, aa tendency
tendency for
for ~n to
to
decrease was
was noted
noted for
for increasing
Reynolds numbers.
decrease
equently, aa recomincreasing Reynolds
nunbers. Cons
Consequently,
reconnendedvalue
value of
of 0.0110,
0.0110, and
mended
possibly as low
as 0.0100,
andpossibtyas
lowas
0.0100, for
for nn for
for new
new cast-andeast-andvibrated concrete
eonerete pipe
pipe seems
vibrated
seernswarranted
waranted by
by the
the present
present experimental
experiraental results.
results.
the question
question as
The
as to
to how
howmuch,
rnuch, if
if any,
any, these
these recommended
reconnendedn-values
n-values for
for
both concrete
concrete and
and corrugated
both
corrugated metal
metal should
should be
be increased
increased to
to allow
allow for
for deterioradeterioration with
with age,
age, for
for leakage,
leakage, and
tion
and other
other factors
factors can
be settled
can be
settled only
only on
the basis
on the
basis
of the individual
individuaL conditions
conditlons under
under which
particular pipe
which aa particular
pipe will
will be
be serving
and
senring and
will depend
judgrnent of the designer.
depend largely
largely on
will
on the judgment
C.
c.
Friction Losses
tosses for
for Part-Full
Friction
FIow
Part-Fu1l Flow
The Manning
was
The
Manning coefficient
coefficient
nas found to be
be very
very nearly
nearly constant
for
constant for
cond:ition of
part-full,
of part-full,
the condition
uniform,
uniforn, tranquil
tranqu.ir flow
flow in
in aa given type of pipe.
pipe.
the small
small variations
variations that
The
that were
were noted were
were of
of an
an order
order of
of magnitude
magnj-tude correspondcorrespondpossible random
random experimental variations.
ing to possible
variations.
For the corrugated
flow
pipes, the average
corugated pipes,
average n for
for part-full
part-fuIl
flow was
uas
0.0231r. No
No systematic
systenatic variation
0.0234.
vari-ation with
Reynolds number
with Reynolds
number or with
with depth
d.epth of
flor
of flow
was apparent, although it
was
is possible
possible that
such variations
it is
that sueh
variations may
nay have
have existed
existed
but tended
tended to offset
offset each
each other.
other. A snall
small effect
due to-shape
to · shape of
of section
effect due
section was
was
noted.
The
The average
average n
~ for
for the pipe
pipe arch sections
sections was
was 0.02211
0.0224 and for
for the circircuLar
cular seetions
sections was
was 0.O2b2.
0.0242. For the circular
circular sections,
sections, the lfanning
Manning coefficient
coefficient
evidenced a slight
slight deerease
decrease as the pipe
pipe dianeter
diameter increased.
increased.
For the concrete pipes,
pipes, the average
average n
~ for
for part-full
part-full flow
flow was
was 0.0106
and there
there was
was a very
very small
small range of
of variation
variation fron
from this
this average. For
For the
l8-in.
18-in. piPer
pipe, there
there seemed
seemed to
to be a slight
slight systenatic
systematic decrease
decrease in
in n
~ as the depth
of
of flow
flow (and consequently the ReSmolds
Reynolds nunber)
number) increased,
increased, but
but this
this tendency
tendency
was
was not
not observed
observed on the 2L-in.
24-in. pipe,
pipe, perhaps
perhaps because
because of
of the greater
greater nagnitudes
magnitudes
of
of experinental
experimental variations
variations on this
this pipe.
pipe.
It was
was not
not possi-ble
possible to
to obtain
obtain partpartIt
full
full flovr
flow data
data on the
the 3Gin.
36-in. pipe
pipe because
because of
of the
the proxinity
proximity of
of the
the pipe
pipe slope
slope
to
to the
the critical
critical slope
slope for
for most
most di-scharges
discharges in
in the
the piper
pipe, aa fact
fact which
which resulted
resulted
in
in troublesome
troublesome waviness
waviness and
and instability
instability on
on the
the water
water surface
surface in
in the
the pipe
pipe and
and
precluded
precluded dependable
dependable neasurementso
measurements.
For
For practical
practical design
design purposes
purposes these
these snall
small variatlons
variations nay
may be
be conconsidered
sidered negligible.
negligible.
Reasonable
Reasonable reconmended
recommended values
values of
of nn for
for uniforr
uniform tranquil
tranquil
r9
19
flow
for concrete pipes of
of
for corrugated pipes and
0.0110 for
flor appear
appear to be
be 0.0240
O.02lr0 for
and 0.0110
projecting elements.
elements.
the type
without projecting
tlpe tested,
tested, assuming
new, well-laid
well-laid pipe without
assunlng new,
D.
D.
Entrance
Losses
Entrance Losses
The
understood to be
excess of actual
actual energy
enerry
The entrance loss
be the excess
loss is
is understood
normal
loss
be caused
which would be
caused by nonnal
loss in
that which
entranee region of aa pipe over that
in the entrance
pipe friction
pipe.
friction over the same
sane length
length of
of pipe.
The entrance loss
loss is
The
is not confined
to aa small
length of
of
right at
but it
it is
is spread
spread over aa length
snall region right
at the entrance, but
pipe of
of at
least several
dianeters.
at least
several diameters.
It
largely by re-expansion of
of
It is
is caused
caused largely
the contracted
jet of entering
the highhighkinetic energy
energy of the
contracted Jet
Muchof the kinetic
entering water. Much
velocity
jet fonns
when
in the flow when
velocity entering
forms excessive rotational
rotational turbulence in
entering jet
gradient in
fill
it
the pipe.
pipe.
expanding to fill
it approaches
approaches an
an adverse
adverse pressure gradient
in expanding
this excess
This
gradually damped
turb'rlence is
as the flow
moves downstream.
dovmstream.
excess turbulence
flow moves
is gradually
darnpedout
out as
Simultaneously,
Sinultaneously, development
layer is
taking
development of
turbulent boundary
boundary layer
is taking
of the normal
nonnal turbulent
olace from
frorn the pipe wall
wall outward
outward to its
its center.
center.
If
multiplied
as an
an entrance coefficient
coeffieient multiplied
ff the entrance
entranee loss is
is written
written as
by the velocity
veloeity head
pipe, the most
head of
flow in
factor governing
of flow
in the pipe,
most important
irnportant factor
the magnitude
geonetry of the entrance lip.
Iip.
magnitude of the coefficient
coefficient is
is the geometry
the
The
form of
and therefore
therefore the amount
of entrance controls
controls the amount
amount of
of contraction
contraction and
amount
of
of re-expansion and
turbulence"
and excess
excess turbulence.
The
therefore the
The chief
loss is
reducti-on of entrance loss
is therefore
chief item in
in the reduction
design of
reduce the entrance contraction.
of the entrance to reduce
contraction.
this can
be done
This
done
can be
by rounding or beveling
trance, or by providing
beveling the en
providing some
other a~proach
approach
entrance,
some other
transition.
transition.
projects
The
greatest when
The contraction
rhen the
ttre pipe entrance projects
will be
be greatest
contraction will
into
is, with
with
headwater pool and
that is,
into the headwater
and when
uLrenthe pipe thickness
thickness is
is small,
snalI, that
aa sharp-edged
sharp-edged entrance.
entranee.
This condition
approached at
is approached
at the entrance to aa
condition is
corrugated
aa re-entrant
inlet.
pipe with
rith
comugated pipe
re-entrant
inlet.
The
The St.
Falls Laboratory
Iaboratory
St. Anthony Falls
experimental
projecting corrugated pipe
experinental values for
for the entrance coefficient
for projecting
coefficient for
loss in
inlets
were close to the
in
the theoretical
theoretical value
value of
for re-expansion loss
inlets were
of 1.00 for
such
situation.
such aa situation.
The
The average
average value obtained was
was 0.85.
0"85.
The
The slight
slight rounding
of
corrugation
reduction
of the entrance due
due to the initial
cause the reduction
initial
suffieed to cause
comugation sufficed
from
fron the theoretical
theoretical value.
value.
Ifhen aa flush
flush headwall
"''hen
headnall inlet
inlet is
is reduced.
is used, the contraction
contraction is
The theoretical
The
theoretical re-expansion
re-erpansion loss
loss for
for aa sharp-edged
approxi:nately
inlet is
is approximately
sharp-edged inlet
20
2
0.41 (V2
(V /2g)
j2g),, and
and this
this could
could be e:rpected
expected to
to decrease d.ue
due to
to the rounding
rounding at
at
O.I+I
first corrugation,
corrugation, the
the anount
amount depending
depending somewhat
somewhat on the pipe
pipe dianeter.
diameter.
the first
The St"
St. Anthony
Anthony Falls
Falls Laboratory
Laboratory tests
tests for
for this
this condition
condition indicated
indicated an
an average
average
The
coefficient of
of 0.1+9,
0.49, which was
was higher
higher than erpected.
expected.
coefficient
Honever,
However, the data are
dependable, vrd-fhout
~~thout exeessive
excessive scatter,
scatter, and
and it
it appears
appears necessary
necessary to
to recomend
recommend
dependable,
0.50 for
for K"
K for
for cormgated
corrugated pipes w'ith
with flush
flush inlets"
inlets. A value of
of K"
K of
of
about 0"50
e
e
used for
for corrugated
corrugated pipes with
with projecting
projecting inl-ets"
inlets.
about 0.90 should be used
Entrance loss
loss coefficients
coefficients for
for concrete pipes are considerably
considerably lower
Entrance
for corrugated
corrugated pipes"
pipes.
than those for
Concrete pipes
pipes are conmonly
commonly nade
made wittr
with either
either
Conerete
bell-and-spigot or
or tongue-and-groove
tongue-and-groove type joints,
joints, l-aid
laid with
with the bell
bell or
or groove
groove
bell-and-spigot
end upstream.
upstream.
end
at the culvert
has the effect
effect of
of an increased diareter
diameter at
culvert
This has
entrance from which the contraetion
contraction is
is initiated,
initiated, and
and therefore,
therefore, less
less rereentranee
expansion is
is required
required from jet
jet dianeter
diameter to
to normal
normal plpe
pipe diameter
diareter. .
expansion
The
The entrance
entrance
of widening
widening
and the amount
loss coefficient
depends
somewhat on
pipe diameter
amount of
on pipe
dia.ureter and
loss
depends somewhat
coefficient
accuracy"
at
joint, but average
average values can
can be used
used with
with suffleient
sufficient accuracy.
at the joint,
to serve
Furthermore,
thickness is
is almost sufficient
Furthernore, the pipe wall
sufficient to
serste
wall thickness
Consequently,
as
projects into
into the headwater.
headnrater" Consequently,
as aa flush
whenthe pipe projects
flush headwall when
1itt1e
the entrance loss coefficient
affected very little
coefficient for
for concrete pipe culverts
culverts is affected
bJr whether
projecting or flush
inl-et.
flush inlet.
by
whether the pipe has
has aa projecting
.
of the
On
dn the
ihe basis of
projecting
experimental results,
valrre of
for projecting
of 0015
0.1! has
has been
been recommended
recomrnendedfor
results, aa value
concrete
.10 for
inlets and
and 00.I0
inlets"
eoncrete pipe inlets
for flush
flush inlets.
part
inlet crown,
When
erowne aa part
lVhen the headwater
headnrater elevation
elevation drops below the inlet
at the water surface
of the entering
jet cont
raction is
is removed,
eonstraint at
entering jet
contraction
removed, constraint
iiss removed;
becomessmaller.
snaller"
loss coefficient
and therefore
coefficient becomes
removed, and
therefore the entrance loss
HolvHow-
as to be
ever, the entrance coeffic
i ents for
be subject
subject
so small
sna1l as
coefficients
for concrete pipe are so
to large
ies.
large relative
inaccuracies"
relative inaccurac
appear
The
The present experimental
do not appear
experinental data do
projecting
and flush
to warrant design values of
c ting and
0"10 for.
flush
C.15 and
and 0.10
fon proje
of K
K" less than
than G.15
e
part-fu11 flow
concrete pipe inlets,
even though
though
inlets, respectively,
flor conditions,
conditions, even
respectively, for
for part-full
these are the same
fuLl flow.
f1ow"
same values recommended
reconmendedfor
for full
pipes, however,
of the entrance
For corrugated
material reduction
however, aa material
reduction of
coruugated pipes,
partly full.
Reeormended
coefficients
only partly
fu1I" Recommended
obtaj-ned when
whenthe culvert
coefficients was
was obtained
culvert flowed only
projecting and
and flush
flush
O"l+0for
for projecting
design
0.?0 and
and 0.40
for this
this condition
condition are 0.70
design values for
inlets,
inletsr respectively.
respectively.
2t
21
The above
above entrance
entrance coefflclents
coefficients apply
apply only
only ifif the
the flowln
flow in the
the plpe
pipe ls
is
Ttre
subcri tical. Supercritical.
Supercri tical slopes
slopes and
and vel"ccities
velocities are
are :rcx:orPanied
a~ompanied by
by nuch
much htgher
higher
snrbcrltical.
entrance eoefficients
coefficients when
when applied
applied to
to the
the nornal
normal part-fulL
part-full flmr
flow condltion.
condition.
entrance
E.
E.
Outlet Losses
Losses
Qrtlet
Theoretically, the
the outlet
outlet loss
loss for
for a pipe
pipe disctrarging
discharging into
into aa relarelaTleoretj-ca11y,
tively quieseent
quiescent tailwater
tailwater pool
pool ie
is equal
equal to
to ttre
the velocity
velocity head
head of
of the
the flow
flow in
in
tively
the pipe
pipe at
at its
its exit,
exit, for
for both
both full
full and part-full
part-full flow.
flow.
the
Under cet'tain
certain eondltions,
conditions, part
part of
of this
this exit
exit velocity
velocity head
head may
may be
UnCer
conserved and converted
converted into
into useful
useful hearl
head in
in the
the outlet
outlet channel flow.
flow. This
This
consenred
will be true
true especially
especially when
when the
the outlet
outlet channel
channel is
is relatively
relatively narrorr
narrow, as tas
was
rlll
the caae
case in
in the
the e:cperimental
experimental lnstallation.
installation.
ttre
The outlet
outlet loss
loss coefflcient
coefficient was
was founct
found to
to average
average about 0.90 for
for fuI1
full
The
Determinations
now Ln
in both
both concrete
concrete and cormgated
corrugated pipes.
pipes.
Detenninations of
of outlet
outlet Loss
loss
flor
were not
not nade
made for
for the
the part-full
part-full conditlon,
condition, but
but they
they would
would undoubtedly
undoubtedly be about
about
rere
to the actuaL
reference to
provided ttre
the coefficient
coefficient was
determined with
actual
with reference
was deterrnined
sane, provided
the same,
exit
velocity head.
exit velocity
taken
norroally should be taken
For design
normally
coefficient
outlet coefficient
Cesign purposes the outlet
is used.
section is
flared-outLet section
equal to unity,
designed, flared-outlet
speciall]'designed,
unity, unless aa specially
F.
with Other Data
Results with
Laboratory Results
Comparison
Falls Laboratory
Corparison of
of st.
5t. Anthony Falls
extended
considerably extended
have considerably
The
in this
this paper have
reporte<l in
The' test
resrrlts reported
test results
pipes.
netal pipes.
and corrugated
corrugated metal
previous
previous Imow1edge
on the hydraulics
lororledge on
{prlraulics of concrete and
obtalned
prior to the new
were obtainE~d
new results
results were
The
on this
this subject
subject prior
data on
nost dependable data:
T?rcmost
period of
of
Iowa over aa period
of Iowa
in
tlniversity of
conducted at the University
studieE conducted
ln aa series
series of studies
and corcorconcrete and
rnadeon
on concrete
uere made
several
The Iowa
lowa tests
tests were
192L*. The
in 1924*.
sevcral years ending in
varying from
fron
lengths varying
ritb leneths
rugated
in diameter,
dianeter, with
and )0
inches in
2b, and
12, 18,
LB, 24,
nrgated pipes 12,
30 inches
24
ft.
& to 36
36 ft.
as obtained
obtalned
coefficients,
Values
as
roughness coefficients,
Kutter roughness
and Kutter
[dannlng and
Values of
of the
the Manning
in
given in
fV.
in Table
Table IV.
are given
tests#** are
ttrese tests
ln these
*D.
*n.
Water
of Water
The Flow
Flou of
Woodward, The
ll. Woodward,
L.
and S.
S. M.
A. Nagler,
Nagler, and
Ir. A.
L. Yarnell,
Yarnell, F.
I,
(University
Bulletin
Engineeringr
ln
Culverts,
(University
of
Iowa
Studies
in
Engineering,
Bulletin
1,
Through
Studles
of
Iora
-Through Cu1verts,
June,
1926).
June, 1926).
-M:*'Ibid,
p, 55.
tuia, p.
ss,
22
22
TABLE rv
IV
TABI,E
AVERAGE RolIcHt{ESS
ROUGHNESS COEFFTCTENTS,
COEFFICIENTS, IOTTA
IOWA TESTS
TESTS OT
rn CULVffiT
CULVERT PIPES
PIPES
AVERAGE
,
Metal Pipe
Corrugated Metal
Concrete Pipe
Pipe
Fipe
Diam
Dian
\(in.
1 n " /)
Kutter n
Kutter
Manning n
Manning
12
T2
0.0117
0.01u
0
.0119
0.0119
18
1B
0.0121
0
.0121
244
1
300
3
Kutter n
Kutter
Manning
Manning !!
n
0.0228
o
"a22B
0.0121
0
,0121
0"019,1+
0.0194
0.0217
0,0217
0.0130
0
.0130
0.0130
0
.0130
0.0216
0"0216
0.0127
0
.0127
0.0125
o"ot25
0.0232
o.0232
o.0239
0.0239
O"O25l1
0.0254
0.02h8
0.0248
The Kutter
Kutter coefficient,
coefficient was
was conputed
computed from
Kutter forrnula
formula
The
fron the Kutter
iRS
(r
r..lr.l o 2 t +
^T
i41.65
0 , 0 0 2 8 1+
"811
0.00281
1.811
+ 1
n
Q
S
n
Q = AA r l n s
n
1r ++( l(41.65
r t " 6 5 ++ 00.00281)
" 0 9 2 8 1~
)
S
( 12)
(12)
{R
{E
Kutter formula,
The
has largely
The Manning
lrlanning formula,
whieh has
largely superseded
superseded the Kutter
formulat
formula, which
was originally
designed with
roughness coefficient
would
intent that
its rrcughness
coefficient
with the intent
that its
was
originally
glven plpe
be the same
pipe or openas the Kutter
Kutter roughness
openroughness coefficient
coeffieient for
for aa given
be
same as
channel material.
rnaterial.
As
of
of
As is
i-s evident
this interchangeability
interehangeability
fron Table IV, this
evident from
coefficients
with concrete
is satisfactory
lowvalues of
of n associated with
for the lowvalues
coeffieients is
satisfaetory for
pipe.pipe
pipe, the Manning!!
For corrugated
ltranning n is
is considerably
eonsj-derably higher
higher than the
corrugated pipe,
i-t appears
appears
Kutter
However,
Horever, it
interchangeably"
Kutter !!,
n, so
that they cannot
eannot be
be used
used interchangeably.
so that
that
for
literature
for coreorinterchangeably in
in subsequent
that they were
were used
used interchangeably
subsequent design literature
pipe"
rugated pipe.
pipe is
as
The
is about 0.021
0"021 as
average Kutter
Kutter E.
fhe average
n for
for corrugated
coruugated pipe
average
indicated
lowa tests
other studies,
whereas the average
indicated by the Iowa
tests and
and also by other
studies, whereas
Manning
nanufacturers recommend
reeosnend
Itranning !!
0"021+. Most
Most corrugated
culvert manufacturers
n-as about 0.024.
corrugated culvert
! was
aa Manning
of
of corrugated
corrugated
in design of
of not
not more
nore than 00021
0"021 for
for use
use in
Manning coefficient
coefficient
.
1 verts and
*•
plpe
cu
pipe
and sewers
culverts
""rr'"t"o.
oFor
Practiee, by Armco
Draina
Drainage
*For example,
Practice,
Culvert and
and Drainage
Amco Drainage
Handbook of
of Culvert
"*"rp1e, Handbook
19!7)
Conpany,
and Metal Products, Inc. (Indiana: R. R. Donnelley
&
Sons
Company,
1947)
lEfffins
pp.
pp" 209-13.
209-1J"
23
23
The
Anthony Falls
Falls Laboratory
Laboratory tests
that an
an n
the St.
St. Anthony
fact that
tests confirm
confirm the fact
of
pi-pe is
of 0.021
0.021 for
for corrugated pipe
muehtoo low.
is much
A value of
.l,east 0.025
0.A25
of n of at
at least
is
reeonmendedon
is recommended
hnowledge.
on the basis of present knowledge.
houever,
Previously
Prevlously recommended
have, however,
reeorunendedvalues of
of !!
n for
for concrete
eonerete pipe have,
been
been higher than the values obtained in
Falls Laboratory
Laboratory tests.
tests.
Anthony Falls
i,n the St. Anthony
Tfre Iowa
The
Iowa tests
tests indicated
about 0.0125
for concrete culverts
indicated tnat
that !!
n averaged
averaged about
O.CL25 for
culverts
flowing full,
Anthony Falls
Falls Laboratory
flowing
justify aa value
full, whereas
taboratory tests
whereas the St.
St. Anthony
tests justify
as
ted..
as low as
0.0100 for
for new
new concrete
as 0.0100
conerete pipe of
of the type tes
tested.
It
It is
is probable
thatt me
methods
tha
thods of manufacture
precast concrete pipe have
improved
manufacture of precast
have sufficiently
sufficiently
inproved
in
two decades
decades that
that have
elapsed since the Iowa
tests and
in the two
have elapsed
fowa tests
and other
other significant
significant
tests on
on concrete culvert
produce surfaces of
tests
of
eulvert pipe to produce
higher degree
degree of
of aa higher
smoothness
better joints
joints than were
stroothness and
and better
were then obtainable.
obtainable.
The American
The
Anerican Concrete
Concrete Pipe Association,
Association, on
on the basis of previous
tests and
and recommendations
recommendationsby various
tests
various authors,
reconmendedan
authors, has
has until
until now
now recommended
an n
0.013 for
of 0.013
for use
use in
Kutter or Manning
Manningformulas.
fornulas.
in the Kutter
In view of
results,
of the new
nen results,
it aopears
aopears that
quite conserva
that this
this value is
it
ti ve, unless
inis quite
unfess aa considerable ineonservative,
crease
be anticipated,
erease in
in roughness
roughness with
wlth age
age of
of the culvert
euJvert is
anticipated, or unless
is to be
the pipe manufacturing
process employed
rnanufacturing process
produce aa materially
as to produce
materially
enployed is
is such
such as
rougher surface than in
pipes.
in the experimental pipes.
The
and significant
tests
TLreIowa
tests
Iowa tests,
tests, which were
were the most
most extensive bnd
significant
available prior
prior to the st.
available
Anttrony Falls
Fal1s Laboratory
Laboratory tests,
tests, did
did not reveal the
St. Anthony
significant
very significant
trends in
factor
with
friction
factor and
with
in friction
and roughness
roughness coefficient
coeffieient
Reynolds number
Heynolds
number that
that the present
present tests
have brought to light.
tests have
light.
No
No measurements
measurements
of water temperature
temperature were
of
were reported
reported for
for the Iowa
tests, so
that it
it is
is not
Iowa tests,
so that
possible to compute
possible
Reynolds number
tests"
conpute accurate values of the Reynolds
number for
for those tests.
In view of this
this fact,
fact, certain
In
have been
certain trends that
that might have
been inferred
inferred from the
tests, such
Iowa
Iowa tests,
variation of
sueh as
as variation
be
of n with
with discharge or pipe diameter,
eannot be
diarneter, cannot
substantiated.
substantiated.
Furtherrnore, the Iowa
Furthermore,
fowa investigations
investi-gations did
did not include
include aa study of
part-full
flow co
part-full
flow
ndi tions in
conditions
in culverts.
culverts"
There
ts reported,
There have
have been
reported,
been aa few
few tes
tests
*.
however, on
however,
partly full
on concrete pipes flowing
flowing partly
fu11*.
These
have sometimes
These have
sometines indicaindica-
that the friction
friction
greater for
ted that
factor
factor or roughness
for
roughness coefficient
coefficient is
is slightly
slightly greater
part-full
part-full
flow than for
bi ts aa slight
for full
fuII flow,
flow, and
and that
usually exhi
slight
that it
it usually
exhibits
*oC.
C.
nDeterrnination of Kutter's
F. Johnson,
Johnson, "Determination
Kutterrs n for
Fil}edrrl
for Sewers
Sewers Partly
Partly Filled~"
(191+l+)
American
Transactions,
American
Society
of
Civil
Engineers
-;
Vol.
109,
(1944),
pp.
223Engineersl
vof
l09r
223Societyof
Civil
.
t
I"rySgg^r.,
Hamser.
Tif.
lJ7, Especially
Especially see
see discussion by T.
T. R.
R. Camp,
Canp, R.
G" Coulter,
and C.
C. E.
E. Ramser.
Coulter, and
R. G.
224b
increase as
as the
the depth
depth of
of uniforn
uniform flow
flow decreases.
decreases. AA slight
slight tendenc]'
tendency of
of this
this
increase
kind was
was also
also noted
noted on
on the
the 18-in.
IS-in. pipe
pipe in
in the
the present
present tests.
tests.
kind
In considering
considering this
this phenomenon
phenomenon one
one must
must recognize
recognize that,
that actually
actually one
one
In
is corparing
comparing flow
flow conditions
conditions wlij-ch
~nuch are
are geometrieally
geometrically dissiroilar
dissimilar and
and that
that the
the
is
arbitrary use
use of
of the
the hyd.rauU-c
hydraulic rad.ius
radius as
as the
the linear
linear dinension
dimension of
of comparison
comparison
arbitrary
is only
only an
an approxirnation
approximation whieh
which has
has been
been found
found to
to give
give acceptable
acceptable results.
results.
is
No part-fulI
part-full flow
flow tests
tests in
in cormgated
corrugated pipes
pipes of
of the
the nature
nature discussed
discussed
No
in tlis
this report,
report, seem
seem to
to have
have been
been published
published prevlously.
previously. A
A .few
·few tests
tests have
have been
been
in
reported on corrugated
corrugated nretal
metal flumes.
flumes. li.
It. E.
E. Horton
Horton has
has given
given n-values
n-values for
for such
reported
flumes rangtng
ranging fronr
from 0.0225 to
to 0.0100.
0.0300.
flunes
Acknowledgment
Acl<no'wledgment
experimental progran
program described
described in
in this
this report
report wae
was sponsored by
by
The experimental
The
the Aneriean
American Concrete Pipe Association
Association and
and the Portland
Portland Cement
Cement Association.
Association.
the
All experiments
experiments were concLuctecl
conducted at
at the
the St.
Falls Hydraulic
Hydraulic laboratory
Laboratory
St. Anthony !-a1-1s
A1l
G. Straub,
Straubt
of Dr. Lorenz
of the University
University of
Minnesota, under
supervision of
Lorenz G.
unCer the srrpervision
of Minnesota,
of
rqr
Timar.
ThomasTirnar.
made ~J Thomas
were made
Director.
Most
observations were
of the experimental
Most of
e:rperimental observations
Dj-rector.
M. Morris
Morris
Ilenry M.
f{illianDingrnn'
1\vo
and William
Dj ngman. Henry
Laraband
Onen Lamb
were tested
tested by Owen
l1yoof
of the pipes were
and Leona
Leona Schultz
Schultz
Fosburgh and
Lois Fosburgh
was
a der during
of the study.
most of
stucly. Lois
clurlng most
Leader
Project Le'
was Project
'lrrasarranged by
by
material Vlras
edited
material
illustrative
rnanuscript; illustrative
and prepared the manuscript;
edited and
Loyal A. Johnson.
Johnson.
25
25
g
!9q.q.g&r
GLOSSARY
Cross-sectional area
area of
A == Cross-sectional
of flow,
f1ow, sq ft
ft
D == Pipe diameter,
dianeter, ft
ft
= Darcy fricti,on
fricti.on factor
factor
f
= Acceleration
= 32.16
Acceleration of
gravity =
g =
of gravity
ft/sec/see
32.16 ft/sec/sec
= Total
H =
Total head
head on
on culvert,
culvert, ft
ft
H
H_ == Entrance
Entrance head
head loss,
1oss, ft
ft
ee
= Friction
H
H" =
Friction head
head loss,
1oss, ft
ft
fI
= Entrance loss
K =
loss coefficient
coefficient
ee
= Barrel
Ko =
Barrel friction
K
friction loss coefficient
coeffieient
fL
Ko == Outlet
Ortlet loss coefficient
coefficient
Dianeter of
K
grain of
K_ = Diameter
of sand
of equivalent
sand grain
equivalent r..oughness,
roughness, ft
ft
ss
Llv
Re
ite == Reynolds number
nr:rnb"t == ~v
= Manning
Marming roughness
n =
roughness coefficient
coefficient
Q
of flow,
f1ow, cfs
cfs
a == Rate of
R == Hydraulic
Hydraulic radius,
radius, ft
ft
S == Slope of
gradient
hydraulic gradient
of hydraulic
vV
= Average
Average velocity
=
velocity of
of flow,
fIow, fps
fps
v
= Kinematic viscosity,
=
viscosity, sq ft/sec
ft/sec