ENGINEERING F L E D MANUAL
CHAPTER 3
Compiled by:
William 3
Oregon
.
. Urquhart.
HYDRAULICS
C i v i l Engineer. SCS. Portland.
Contente
Page
b m r e r s i o n o f Units
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Hydroetatice
Pressure-Density-Weight Relationships
Piemmeter
Forces on Submerged Plane Surfaces
Resaure Diagrams
Buoyancy and F l o t a t i o n
Buoyancy
Flotation
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Hydrokinetics . . . . . . . . . . . . . . . . . . . . . . . . .
FlowContinuity . . . . . . . . . . . . . . . . . . . . . .
Conservation of Energy . . . . . . . . . . . . . . . . . . .
P o t e n t i a l Energy . . . . . . . . . . . . . . . . . . . .
Pressure Energy . . . . . . . . . . . . . . . . . . . . .
Kinetic Energy . . . . . . . . . . . . . . . . . . . . . .
Bernoulli P r i n c i p l e . . . . . . . . . . . . . . . . . . .
Hydraulic and Energy Gradients . . . . . . . . . . . . .
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F r i c t i o n Lose . . . . . . . . . . . . . . . . . . . . . .
Manning's Equation . . . . . . . . . . . . . . . . . .
Hazen-Williams Equation . . . . . . . . . . . . . . .
Other Losses . . . . . . . . . . . . . . . . . . . . . .
Hydraulics of P i p e l i n e s . . . . . . . . . . . . . . . . . .
Hydraulic e of Culverts . . . . . . . . . . . . . . . . . . .
Culverts Flowing With I n l e t Control . . . . . . . . . . . .
Pipe Flow
Laminar and Turbulent Flow
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Culverts Flawing With Outlet Control
Erosive Culvert E x i t V e l o c i t i e s
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Open Channel Flow
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Types of Channel Flow . . . . . . . . . . . . . . . . . . .
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Steady Flow and Unsteady Flow
Uniform Flow and Nonuniform Flow
Channel Croas-Section Elements
Manningf's Equation
C o e f f i c i e n t of Roughness. n
Physical Roughness
Vegetation
CrossSection
Channel Alignment
S i l t i n g o r Scouring
Obstructions
S p e c i f i c Energy i n Channels
C r i t i c a l Flow Conditions
General Equation f o r Critical Flow
C r i t i c a l Discharge
C r i t i c a l Depth
C r i t i c a l Velocity
C r i t i c a l Slope
S u b c r i t i c a l Flow
S u p e r c r i t i c a l Flow
I n s t a b i l i t y of C r i t i c a l Flow
Open Channel Problems
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Weir Flow
Basic Equation
Contractions
VelocityofApproach
Weir C o e f f i c i e n t s
Submerged Flow
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Water Measuring
Open Channels
Orif i c e s
Weirs
Rectangular Contracted Weir
Rectangular Suppressed Weir
C i p o l l e t t i Weir
900V-Notchweir
P a r s h a l l Flume
Trapezoidal Flume
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CurrentMeter
Water-Stage Recorder
Measurements by F l o a t s
Slope-Area Method
Velocity-HeadRod
Pipe Flow
O r i f i c e Flow
C a l i f o r n i a P i p e Method
Coordinate Method
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Figures
Figure 3-1
Figure 3-2
Figure 3-3
Figure 3-4
Figure 3-5
Figure
Figure
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Figure
Figure
Figure
Figure
Figure
Figure
Figure
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Figure
Figure
Figure
Figure
3-6
3-7
3-8
3-9
3-10
3-11
3-12
3-13
3-14
3-15
3-16
3-17
3-18
3-19
3-20
3-21
3-22
3-23
3-24
3-25
3-26
Figure
Figure
Figure
Figure
3-27
3-28
3-29
3-30
Figure 3-31
Table3-1
Table 3-2
Table 3-3
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R e l a t i o n s h i p between p r e s s u r e and head
Piezometer tube i n a pipeline
P l o t t i n g d i f f e r e n t i a l .l e n g t h piezometer
data i n t h e d e t e m i n a t i o n of e q u i p o t e n t i a l
pressure l i n e s
Pressure on submerged s u r f a c e s
R e l a t i o n s h i p between energy forms i n p i p e
and open channel flow
Pipe flow energy r e l a t i o n s h i p s
Culverts w i t h i n l e t c o n t r o l
Culverts w i t h o u t l e t c o n t r o l
Culvert water depth r e l a t i o n s h i p s
Various types o f open-channel flow
Channel energy r e l a t i o n s h i p s
The s p e c i f i c energy diagram
Sharp-crested w e i r
Broad-crested w e i r
Submerged weir
Flow through an o r i f i c e
Submerged o r i f i c e
Types of w e i r s
P r o f i l e of a sharp-crested w e i r
Rectangular c o n t r a c t e d w e i r
Suppressed weir i n a flume drop
Cip~lle~tiweir
90° V-notch w e i r
P a r s h a l l flume
Trapezoidal flume
Stage-discharge curve f o r unlined
irrigationcanals
Pipe o r i f i c e
Orifice coefficients
Measuring f l o w by the C a l i f o r n i a p i p e method
Required measurements t o o b t a i n flow
fromverticalpipes
Required measurements t o o b t a i n flow
from h o r i z o n t a l p i p e s
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ValuesofManningls. n
Values of Hazen-Williams C
Entrance l o s s c o e f f i c i e n t s
Exhibits
Ekhibit 3-1
Exhibit 3-2
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Water volume, weight and flow e q u i v a l e n t e
Pressure diagrams and methods of computing
,
h y d r o s t a t i c loads
E x h i b i t 3-3
Required thickness of flashboards
Head l o s s c o e f f i c i e n t s f o r c i r c u l a r and
E x h i b i t 3-4
square conduit8 flowing f u l l
E x h i b i t 3-5
Discharge of c i r c u l a r p i p e s flowing f u l l .
Manning's n
,
Solution of Hazen-Williams formula f o r
round p i p e s
F r i c t i o n head l o s s i n semirigid p l a s t i c
E x h i b i t 3-7
irrigationpipelines
Head l o s s c o e f f i c i e n t s f o r p i p e e n t r a n c e s
E x h i b i t 3-8
and bendaj
Exhibit 3-9
Headwater depth f o r c o n c r e t e p i p e c u l v e r t s
,
with i n l e t control
E x h i b i t 3-10 Headwater depth f o r CM p i p e c u l v e r t s with
i n l e t control
Exhibit 3-11 &ad f o r concrete p i p e c u l v e r t s flowing
f u l l with o u t l e t control
E x h i b i t 3-12 Head f o r CM p i p e c u l v e r t s flowing f u l l
with o u t l e t control
E x h i b i t 3-13 Elements of channel s e c t i o n s
E x h i b i t 3-14 S o l u t i o n of Manning's formula f o r
uniform flow
Exhibit 3-15 Discharge f o r c o n t r a c t e d r e c t a n g u l a r w e i r s
Exhibft 3-16 Discharge f o r C i p o l l e t t i weirs
M i b i t 3-17 Discharge f o r 9
0' V-notch w e i r s
E x h i b i t 3-18 Discharge from c i r c u l a r p i p e o r i f i c e s
w i t h f r e e discharge
Exhibit 3-19 Flow of water from v e r t i c a l p i p e s
E x h i b i t 3-20 Flaw of water from h o r i z o n t a l p i p e s
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Page
ENGINEERING FIELD MANUAL
CHAPTER 3.
I.
HYDRAULICS
GENERAL
This chapter presents the hydraulic principles t h a t apply t o the
design and operation of s o i l and water conservation measures. It w i l l
help the technician t o develop a b e t t e r understanding of hydraulics and
t o use the equations and exhibits contained herein.
The chapter contains sections on conversion of u n i t s , principles of
water a t r e s t (hydrostatics), and principles of water i n motion
(hydrokinetics). It discusses the application of these p r i n c i p l e s t o the
flow of water i n pipes, i n open channels, and through weirs. Lastly, the
more cormnon methods of measuring the flow of water i n open channels and
pipes a r e covered.
2.
CONVERSION OF UNITS
Valid equations must be expressed i n corresponding u n i t s . That i s ,
i n a t r u e equation there must be equality between both u n i t s and numbers.
The chance of making conversion e r r o r s can be g r e a t l y reduced by forming
the h a b i t of thinking i n terms of equality of unite a s w e l l a s t h e i r r e l a t i v e numerical values.
The foot-pound-second system i s used i n t h i s chapter unless otherwise
specified. Sometimes, however, it i s n e c e s s a r y t o convert t o other u n i t s ,
which involves the use of numerical conversion constants. Some frequently
used constants a r e given i n Exhibit 3-1.
EXAMPLE 3-1
It i s desired t o build a stock water tank with a capacity i n cubic
feet t h a t w i l l contain one day's flow from a spring t h a t flows a t the rate
of three gallons per minute.
3 gallons per minute day
Y cubic feet
Since cubic f e e t can not be d i r e c t l y equated t o gallons, some u n i t
factor having numerical value must be introduced i f the expression i s t o
be made a v a l i d equation.
The expression 3 g a l l o n s per minute p e r day i s a f r a c t i o n a l express i o n that c,an be w r i t t e n :
-3
.
- min. 9 =
3 g a l . -- 3 g a l .
.
min
day
Analysis shows t h a t :
aal.,
min
day
min.
Note t h a t a l l u n i t s on the l e f t cancel except cubic f e e t , t h u s leaving
the same u n i t s on each s i d e of t h e equation. The r e s u l t i s t h e following
g e n e r a l equation f o r conversions between g a l l o n s per minute per day and
cubic f e e t . If 3 gal/mi'n/day equals 577.5 c u . f t . , one gaf/min/day equals
192.51 cu.ft.
Then:
1 9 2 . 5 1
1 gpm day
gpn day
cu,ft,
* cu*ft.
EXAMPLE 3-2
1 a c r e f o o t per hour = Y g a l l o n s p e r minute
Step by s t e p a n a l y s i s results i n a v a l i d conversion equation c o n s i s t e n t i n both u n i t s and dimensions:
1 ad.&.
W-
,43,560
WSf.
1 H=
1 bu:
60min.
7.48 g a l . = 5431 g a l .
Id.=.
min.
5431 gal.
min.
EXAMPLE 3-3
1 cubic f o o t p e r second day = Y acre f e e t
Analysis r e s u l t s i n :
I f t h i s approach t o conversion problems, i s used, t h e r e s u l t s w i l l
be:
1. Freedom from conversion e r r o r s .
2.
Savings i n time i n both o r i g i n a l and "check"
computations.
3.
Accuracy of conversion f a c t o r s e l e c t i o n from standard
t a b l e s and other sources.
3.
HYDROSTATICS
The s u b j e c t of h y d r o s t a t i c s ( f l u i d s t a t i c s ) deals with problems i n
which t h e f l u i d i s motionless or a t r e s t .
PRESSURE-DENSITY-HEIGm RELATIONSHIPS
The fundamental equation of f l u i d s t a t i c s r e l a t e s pressure, density,
and depth. Unit pressures i n a f l u i d vary d i r e c t l y with t h e depth and t h e
u n i t weight of the f l u i d and a r e expressed by the equation:
p=wh
where p
w
h
or
h e E
W
(Eq. 3-1)
i n t e n s i t y of pressure per unit of area
u n i t weight of t h e f l u i d
= depth of submergence, or head.
=
=
Equation 3-1 shows that: pressure a t any point i n a l i q u i d of given
d e n s i t y depends s o l e l y upon t h e height of t h e l i q u i d above t h e point.
This allows t h e v e r t i c a l height, o r ''head," of t h e l i q u i d t o he used a s an
i n d i c a t i o n of pressure. Thus, pressure may be quoted i n such u n i t s a s
"inches of mercury" and "feet of water." The r e l a t i o n s h i p c.£ pressure and
head i s i l l u s t r a t e d numerically i n t h e 'hanometer" and "piezometer columns"
of Figure 3-1.
-
Mercury
Figure 3- 1 Relationship between pressure and head
I f t h e tank i s f i l l e d w i t h water u n t i l t h e p r e s s u r e gage reads
10 p . s . i . , t h e h e i g h t of t h e water s u r f a c e i n t h e piezometers and t h e
mercury i n t h e manometer can be c a l c u l a t e d from Equation 3-1.
Example 3-4
10 lb.
Water :
h =
4 = 6:ILl;iyia
x 144 sq.in.
,23.1
feet
1 sq.ft.
Mercury ( u n i t weight of 849 pounds per cubic f o o t ) :
10 lb.
h = sq.in.
849 l b .
cu.ft.
144 s q . i n . x 12 in. = 20.35 inches
1 sq.ft.
1ft.
Piezome ter
Figure 3-2 shows a p i e z m e t e r tube connected t o a pipe i n which t h e
l i q u i d i s under p r e s s u r e , The h e i g h t hl i s a measure of p r e s s u r e a t the
w a l l of the pipe i f t h e opening i s a t r i g h t angles t o t h e w a l l and f r e e
of any roughness o r p r o j e c t i o n i n t o t h e moving l i q u i d . The p r e s s u r e a t
the w a l l of t h e p i p e i s : pl = whl and t h a t a t t h e c e n t e r l i n e p = wh.
Figure 3-2 Piezometer tube in a p i p e l i n e
Piemmeters a r e used t o measure water p r e s s u r e i n drainage i n v e s t i g a t i o n s and e a r t h dam foundation s t u d i e s . Such a piezometer i s an unperfor a t e d small-diameter p i p e , so designed and i n s t a l l e d t h a t a f t e r i t has
been d r i v e n i n t o t h e s o i l t h e underground water cannot flow f r e e l y along
t h e o u t s i d e of the. p i p e and can e n t e r it only a t t h e bottom end. The
piezometer i s s o d r i v e n t h a t i t s lower end i s i n t h e stratum o r a t t h e
l e v e l where the p r e s s u r e i s t o be read. The h e i g h t t h a t water rises above
t h e bottom of t h e p i p e i s t h e p r e s s u r e head.
A piezometer should n o t be confused w i t h an observation w e l l which i s
used t o determine t h e l e v e l of t h e water t a b l e . The w e l l permits water t o
e n t e r t h e h o l e a t any l e v e l , thus connecting t h e v a r i o u s water b e a r i n g
s t r a t a i n t h e s o i l p r o f i l e . The p r o p e r l y i n s t a l l e d piezometer permits
water t o e n t e r only a t t h e bottom end and from only t h a t l e v e l i n t h e s o i l
profile.
A t y p i c a l example of t h e manner i n which piezometers of d i f f e r e n t
l e n g t h s may be used i n sets t o determine whether a c a n a l i s l e a k i n g i s
i l l u s t r a t e d i n Figure 3-3. I n t h i s example, sets of f o u r piezometers 5,
10, 15 and 20 f e e t i n l e n g t h have been i n s t a l l e d on a l i n e a t r i g h t angles
t o t h e a x i s of t h e c a n a l a t d i s t a n c e s of 15, 60, .and 100 f e e t from t h e cenThe f i r s t o b j e c t i v e i s t o o b t a i n hydrot e r l i n e of t h e c a n a l (Diagram A).
s t a t i c p r e s s u r e s a t a l a r g e number of p o i n t s under t h e water t a b l e a d j a c e n t
t o the canal.
In Diagram B, which r e p r e s e n t s t h e same c r o s s s e c t i o n shown i n A, t h e
small c i r c l e s i n d i c a t e t h e p o s i t i o n , o f t h e bottom end of each piezometer.
On t h e right-hand s i d e of t h e sketch, t h e number b e s i d e each c i r c l e i s t h e
water level e l e v a t i o n i n each piezometer. On t h e l e f t s i d e t h e numbers a r e
t h e e l e v a t i o n s of t h e bottom ends of t h e piezometers. Note t h a t t h e water
l e v e l e l e v a t i o n s a r e g r e a t e r than t h e e l e v a t i o n s of t h e bottoms of t h e c o r responding piezometers. The water s u r f a c e e l e v a t i o n i n t h e piezometer i s
w r i t t e n a t t h e p o i n t i n t h e p r o f i l e where t h e bottom of t h e piezometer i s
l o c a t e d , n o t where t h e water s u r f a c e i s located.
The t h i r d s t e p i s t o draw contours of equal h y d r o s t a t i c p r e s s u r e s , a s
i n Diagram C. These p r e s s u r e l i n e s are drawn i n t h e v e r t i c a l plane i n much
t h e same manner a s ground s u r f a c e contours are drawn i n t h e h o r i z o n t a l plane.
Water moves through t h e s o i l f r o m h i g h t o l o w p r e s s u r e s a n d i n a d i r e c t i o n
a t r i g h t angles t o t h e p r e s s u r e contours. This example i n d i c a t e s seepage
from t h e canal.
I f an a r t e s i a n p r e s s u r e c o n d i t i o n e x i s t e d i n t h e s o i l p r o f i l e , t h e
deep piezometers would show h i g h e r . water s u r f ace e l e v a t i o n s t h a n t h e s h o r t e r
piezometers, and t h e ground water contours would i n d i c a t e upward water pressure.
FORCES ON SUBMERGED PLANE SURFACES
The c a l c u l a t i o n of t h e s i z e , d i r e c t i o n , and l o c a t i o n of t h e f o r c e s on
submerged s u r f a c e s i s e s s e n t i a l i n t h e design of dams, bulkheads, water
control gates, etc.
,
D
D-
For a submerged h o r i z o n t a l p l a n e , t h e c a l c u l a t i o n of u n i t and t o t a l
p r e s s u r e s i s simple because t h e p r e s s u r e i s uniform over t h e a r e a . For
v e r t i c a l ' and i n c l i n e d p l a n e s the'p r e s s u r e v a r i e s w i t h depth, a s shown by
Equation 3-1, producing t h e t y p i c a l p r e s s u r e diagrams and t h e r e s u l t a n t
forces of Figure 3-4.
Figure 3-4
Pressure on submerged surfaces
The shaded a r e a , when m u l t i p l i e d by a u n i t of l e n g t h equals volume,
which i s known a s t h e "pressure volume," The r e s u l t a n t f o r c e , F, i s equal
t o t h e p r e s s u r e volume and p a s s e s through i t s c e n t e r of g r a v i t y (c.g.).
The r e s u l t a n t f o r c e a l s o p a s s e s through a p o i n t on t h e plane defined a s
the "center of p r e s s u r e " (c.p.).
Pressure Diagrams
The a n a l y s i s of s t r u c t u r e s under p r e s s u r e u s u a l l y w i l l be s i m p l i f i e d
by use of p r e s s u r e diagrams. Since u n i t p r e s s u r e v a r i e s d i r e c t l y with
head, diagrams showing t h e v a r i a t i o n of u n i t p r e s s u r e i n any plane take
t h e form of t r i a n g l e s , t r a p e z o i d s , o r r e c t a n g l e s .
I n s o l v i n g problems of f o r c e due t o water p r e s s u r e , t h e magnitude,
d i r e c t i o n , and p o s i t i o n of t h e f o r c e must be considered. The t o t a l f o r c e
r e p r e s e n t e d by t h e p r e s s u r e diagram can, f o r some problems, be r e p r e s e n t e d
by a s i n g l e f o r c e arrow through t h e p r e s s u r e c e n t e r a c t i n g i n t h e same
d i r e c t i o n a s the u n i t pressures.
E x h i b i t 3-2 g i v e s t h e most commonly used p r e s s u r e diagrams and methods
of computing t h e h y d r o s t a t i c load and c e n t e r of p r e s s u r e .
Example 3-5
A flashboard type of dam i s b u i l t with six 3 x 12-inch flashboards.
What i s (a) t h e load per foot on the bottom board, (b) the t o t a l load on
the bottom board i f it i s s i x f e e t long, and ( c ) the load per foot on the
top board ?
First draw the pressure diagram, remembering t h a t a
finished 12-inch board is 11.5-inches or 0.96-foot wide.
Solution:
Then from Equation 3-1:
p
Pi
pg
p,
=
=
=
= unit weight of water x depth of water
62.4 ( 7 . 5 )
62.4 (7.5
= 62.4
=
wh
62.4
- 0.96)
(1.74 + 0 . 9 6 )
(1.74)
=
=
=
=
468.0
408.1
168.5
108.6
lbs.
lbs.
lbs.
lbs.
per sq. E t .
per sq. ft.
per sq. f t .
per sq. f t .
And from Figure 3-4:
The hydrostatic load, F
= whA
=
pA
= unit preesure x area
then
(a)
=
(b)
=
(c)
=
x
0.96
= 420.5 l b s . per f t .
2523 l b s .
x
0.96
=
133.0 l b s . per f t .
The s o l u t i o n would be the same for etoplogs i n a water control
structure
.
D
Example 3-6
What i s t h e t o t a l water load, F, on t h e headgate shown i f i t i s
36-inches wide by 24-inches high, and hl i s 9 f e e t ?
Solution :
{Gate. lift
Water
Surfoca
h
I
Pressure diagram
o f load on
haodga.e
.t
F
h2
=
=
whl
f
wh2
area
2
9
+2
=
11 f e e t
Example 3-7
This s k e t c h shows t h e c r o s s
s e c t i o n of a c o l l a p s i b l e f l a s h board w i t h water a t t h e maximum
allowable e l e v a t i o n . Determine
t h e p o s i t i o n of t h e c e n t e r of
p r e s s u r e and t h e p i v o t under t h e
c o n d i t i o n s shown. Experience has
shown t h a t t h e pivot on t h e g a t e
must be 617 of t h e d i s t a n c e , from
t h e bottom of t h e flashboard t o
t h e c e n t e r of p r e s s u r e f o r t h e
board t o c o l l a p s e .
Pressure
Diagram
Solution :
A s d e f i n e d , t h e c e n t e r of p r e s s u r e i s t h e p o i n t where a perpendicular
through t h e c e n t e r of g r a v i t y of t h e p r e s s u r e prism s t r i k e s t h e a r e a under
p r e s s u r e . U s e E x h i b i t 3-2 f o r t h e s o l u t i o n of t h i s problem.
F i r s t draw t h e p r e s s u r e diagram:
h1
=
3 f t . and p 1
h2
=
3
d
=
6 ft.
+6
=
=
62.4(3)
9 and p2
9
=
62.4(9)
187.2 l b s / s q . f t .
=
= 561.6 l b s / s q . f t .
a
=
b
t h e n from E x h i b i t 3-2
-
5616.0
2246.6
=
2.50 ft.
= c e n t e r of p r e s s u r e
and
Example 3-8
It i s r e q u i r e d t o determine t h e maximum t h i c k n e s s of f l a s h b o a r d s
needed i n a f lashboard dam. The f l a s h b o a r d s w i l l impound water t o a depth
of 7 f e e t , have a 6-foot span, and be of Coast Region Douglas F i r .
This can be solved by t h e use of E x h i b i t 3-3.
From c h a r t , A , thicknese
From c h a r t B, c o r r e c t i o n
=
3.40 inches
= 1.15
Flashboard t h i c k n e s s = 3.4 (1.15) =
U s e nominal 4 x 12-inch flashboarda
3.91 inches
BUOYANCY AND FLOTATION
The f a m i l i a r p r i n c i p l e 8 of buoyancy and f l o t a t i o n are u s u a l l y s t a t e d ,
respectively :
1.
A body submerged i n a f l u i d is buoyed up by a f o r c e e q u a l t o
t h e weight of f l u i d d i s p l a c e d by the body.
2.
A f l o a t i n g body d i s p l a c e s i t s own weight of t h e f l u i d i n which
it f l o a t s
.
B
BUOYancy
A submerged body i s a c t e d on by a v e r t i c a l , buoyant f o r c e equal t o
t h e weight of t h e d i s p l a c e d water.
FB
= VW
(Eq. 3-2)
buoyant f o r c e
= volume of t h e body
= u n i t weight of water
FB
=
v
W
I f t h e u n i t weight of t:he body i s g r e a t e r than t h a t of water, t h e r e
i s an unbalanced downward f o r c e equal t o t h e d i f f e r e n c e between t h e weight
of t h e body and t h e weight of t h e water displaced. Therefore, t h e body
w i l l sink.
Flotation
I f t h e body has a u n i t weight l e s s than t h a t of water, t h e body w i l l
f l o a t w i t h p a r t of i t s volume below and p a r t above t h e water s u r f a c e i n a
position so t h a t :
(Eq. 3-3)
W = V w
W
V
w
weight of t h e body
volume of the body below the
water s u r f a c e ; i . e , , t h e volume
of t h e d i s p l a c e d water
= u n i t weight of water
=
=
A check should be made of t h e s t a b i l i t y of h y d r a u l i c s t r u c t u r e s a s
they w i l l be a f f e c t e d by submergence and whether t h e weight of t h e s t r u c t u r e w i l l be adequate t o r e s i s t f l o t a t i o n .
Porous m a t e r i a l s , when submerged, have d i f f e r e n t n e t
ing upon whether t h e voids a r e f i l l e d w i t h a i r o r water.
v a r i a t i o n i n t h e p o s s i b l e n e t weight of one cubic f o o t of
t u r a l timber weighing 55 pounds under average atmospheric
t i o n s and having 30 p e r c e n t v o i d s :
1 cu. f t . of s t r u c t u r a l
timber, 30 percent v o i d s
W
=weight i n a i r , lb.
FB
= buoyant f o r c e when
.
submerged, l b
W-FB = weight when submerged i n water
(net weight), l b .
After
Saturation
Be£o r e
Saturation
55
62.4
55
- 62.4=
55
-7.4
weights dependNote t h e wide
treated strucmoisture condi-
+
73.72
(0.30 x 62.4) = 73.72
62.4
-
62.4 = 11.32
The degree t o which t h e f a c t o r s discussed above a r e capable of
a f f e c t i n g t h e n e t o r s t a b i l i z i n g weight of a s t r u c t u r e i s i l l u s t r a t e d by
t h e following example:
Example 3-9
Assume a .timber c r i b d i v e r s i o n dam s u b j e c t t o complete submergence
under normal flood flows. M a t e r i a l s , weights and volumes a r e :
Percent of
Unit Weights
lbs./cu. f t .
Volume of the Dam
Material
55 i n air
73 s a t u r a t e d
150 s o l i d s t o n e
Timber
Timber
Loose stone,
30 percent
voids
Determine t h e n e t weight of one cubic yard of t h e dam when
1) not submerged, 2 ) submerged but timber n o t s a t u r a t e d , and
3) submerged w i t h timber s a t u r a t e d ,
1.
Compute cubic f e e t of timber, s o l i d s t o n e , and voids per
cubic yard of dam:
a.
b.
c.
2.
0.12 x 27 = 3.24 cu. ft.
0.7 x 0.88 x 27 = 16.63 cu. f t .
0.3 x 0.88 x 27 = 7.13 cu. ft.
Timber
Solid s t o n e
Voids
Compute the n e t weights of one cubic yard of dam:
Net Weights of Materials i n Pounds per Cubic Yard of Dam
Submerged
Material
--
Not submerged
Timber
Stone
_
3.24 x 5 5
1 6 . 6 3 x 150
E f f e c t i v e or s t a b i l i z ing weight o f dam p e t
c u b i c yard
Timber not saturated
178
2494
2672
3.21(55
16.63(150
- 62.4)
- 62.4)
-
-24
1457
1433
1
Timber saturated
3.24(73
- 62.L
-
34
1457
149 1
D
Example 3-10
A box i n l e t drop spillway f o r a 4 x &foot highway c u l v e r t i s t o
be constructed. The box i n l e t has been designed as shown. Determine i f
it i s s a f e from f l o t a t i o n with a s a f e t y f a c t o r of 1.5 and i f n o t , d e t e r mine t h e s i z e of spread f o o t i n g required. Design assumptions a r e a s
follows :
1.
The s o i l i s s a t u r a t e d t o t h e l i p of t h e ,box and has
a buoyant weight of 50 pounds per cubic f o o t .
2.
There i s no f r i c t i o n a l r e s i s t a n c e between t h e w a l l s
of the box and t h e surrounding s o i l .
3.
Unit weight of concrete
4.
Unit weight of water
-
-
150 pounds per cubic foot,
62.4 pounds per cubic foot.
F i r s t determine the weight (W) of the box.
End w a l l = 4 ' x 4' x 0.67'
2 sidewalls = 4 ' x 8.67'
x 150
x 0.67' x 150 x 2
Floor a l a b = 5.33 x 8.67 x 0.75 x 150
=
1,608 lba.
-
6,907
=
5,199
Next determine t h e buoyant f o r c e (FB) a c t i n g on t h e box by
Equation 3 -2 :
FB
=
Vw
= (5.33 x 4.75 x 8.67)
62.4
=
13,697 l b s .
Worn Equation 3-3, f l o t a t i o n w i l l occur i f W i s less t h a n or equal
(FB has been s u b s t i t u t e d from Equation 3-2 f o r Vw):
t o FB
13,714 l b s . i s g r e a t e r than 13,697 l b s . , t h e r e f o r e , t h e box will not
f l o a t , b u t t h e r e q u i r e d s a f e t y f a c t o r of 1.5 has n o t been accomplished.
bquired weight of box:
W
=
1.5 FB = 1.5 (13,697)
Additional weight t o be added t o box = 20,546
= 20,546 l b s .
- 13,714 = 6,832
lbs.
This a d d i t i o n a l weight w i l l be provided w i t h a spread f o o t i n g around
t h r e e s i d e s of t h e box, and t h e weight of t h e e a r t h load on t h e f o o t i n g .
Weight p e r square f o o t of spread f o o t i n g
+ 0.75(150 -
60u yant soil
62.4)
ws
=
200
-1-
65.7
= 265.7 l b s .
Required a r e a of f o o t i n g
= -6832
265.7
I
= SO I V c u . f t.
I =&I
t
A
7
- 25.7 sq. f t .
I f a one f o o t wide spread footing is provided, the f o o t i n g area
would be 2(8.67)
7,33 = 24.7 s q . f t . and provide 24.7(265.7) = 6550 l b s .
of a d d i t i o n a l weight. The safety f a c t o r a g a i n s t u p l i f t would be:
+
S i m i l a r l y , a spread f o o t i n g 1'-3" wide would produce a s a f e t y f a c t o r
of 1.57. By i n t e r p o l a t i o n , a f o o t i n g 1'-1" wide would meet t h e f a c t o r of
s a f e t y requirement.
4.
HYDROKINETICS
Hydrokinetics i s t h e s o l u t i o n of f l u i d problems i n which a change of
motion occurs as t h e r e s u l t of t h e a p p l i c a t i o n o f a f o r c e t o t h e f l u i d
body (water i n motion).
D :
PUkl CONTINUITY
When the discharge through a given cross section of a channel or
pipe is constant, the flow ie steady. If steady flow occure at a l l sections in a reach, the flow is continuous. This ie known as continuity
of flow and is expressed by the equation:
Q = alvl =
a2v2 = a3v3
-
%vn
(Eq. 3 - 4 )
where Q a discharge in cubic feet per second
a = cross-.sectionalarea in square feet
v = mean velocity of flow in feet per second
1, 2, 3, n = subsc~iptsdenoting different cross
aections
Most of the hydraulic problems handled by field technicianr deal
with caaee of continuous flow.
10 cfrr of water flows through the tapered pipe ahbelow. Calculate the average velocities at eectione 1 and 2 with dismeters of 16 and
8 inches respectively.
from Equation 3-4
Q
=
a16V16 = agvg
10
= 3.1416(1.333)?
4
= 7.16 fps
v,
=
L
=
10
a
28.64 fpe
o r , based on the ratio of crosa-sectional areas
-
7 . 1 6 ( ~ 2 = 28.64 f p s
CONSERVATION OF ENERGY
Three forms of energy a r e normally conaidered i n the analysis of
Potential o r elevation energy, pressure energy,
problems i n water flow:
and k i n e t i c energy.
Potential Enerav
Potential energy i s t h e a b i l i t y t o do work because of the elevation
of a mass of water with respect: t o erne d a t m . A masr of weight, w, a t
an elevation e f e e t , has p o t e n t i a l energy mounting t o w s f o o t pounds with
respect t o the datum. The elevation head, e , expresses not only a l i n e a r
quantity i n f e e t , but a l e o energy i n f o o t pounds per pound.
Reaeure energy i r acquired by contact with other masses and is
tranmnitted t o o r through the l i q u i d mas8 under consideration. A mass
of water, aa such, does not have preesure energy. Pressure energy may
be supplied by a preesure pump o r through same other applied force. The
pressure head (h 2 ) aleo expresses energy i n f o o t pounds pet pound.
W
Kinetic E n e r a
Kinetic energy exista because of a v e l o c i t y of motion and amounts
to:
where W = weight of the water
v = v e l o c i t y i n f e e t per second
g = acceleration due t o g r a v i t y
'
When W equals one pound, the kinetic energy has a value of
2.
2g
This expression i a c a l l e d the velocity head. In other worde, i f the
i t , i s poaeible t o compute the
velocity of a stream of water i s kn&,
head which ie converted from presaure energy o r p o t e n t i a l energy t o c r e a t e
k i n e t i c energy. This p r i n c i p l e is extremely important i n hydraulics.
Under c e r t a i n caaditione, the three forms of energy are interchangeable. The r e l a t i o n s h i p between t he three forme of energy i n pipe and
channel flow i s ehmm by Figure 3-5.
Figure 3-5
Relationehip between energy forms i n pipe and
open channel flow
The t o t a l head, HI, is a v e r t i c a l distance and represents the value
of the t o t a l energy i n the eystem a t Section 1. This i s made up of the
velocity head which i a equivalent t o the k i n e t i c energy, the preseure head
which i s equivalent t o the energy due t o pressure, and the elevation head
which i s equivalent t o the energy due t o poeition.
In the case of channel f l w , the v e l o c i t y head i s t h e difference i n
elevation between the energy line and the watex surface.
In the case of pipe f l a u , the v e l o c i t y head i s the difference between
the elevation of the energy line end the elevation t o which watex would
r i s e i n a piezometer tube. In pipe flow the pipe may be lowered o r r a i s e d
within the zone of the elevation and the pressure heads without changing
the conditions of flow. I f the entrance end of the pipe i s lowered, the
elevation head i s reduced, but the p r e e s w e head is increased a corresponding amount. Conversely, i f the entrance end of the pipe i a raised, the
elevation head is increased and the pressure head is decreased, I f t h e
quantity of flaw and dirrmeter of pipe did not change, then t h e v e l o c i t y
head w i l l remain the same.
Bernoull i Pr i n c i p l e
Bernoulli ' a p r i n c i p l e i s the a p p l i c a t i o n of the law of conservation
of energy t o f l u i d flow. It may be s t a t e d a s follows: In f r i c t i o n l e s s
f l o w , t h e sum of t h e k i n e t i c energy, pressure energy, and e l e v a t i o n energy
i a equal a t a l l s e c t i o n s along t h e stream, This means t h a t i f w e meaeured
t h e v e l o c i t y head, t h e pressure head, and t h e e l e v a t i o n head a t one e t a t i o n i n a pipe or open channel c a r r y i n g flowing water without f r i c t i o n , we
would f i n d t h a t t h e t o t a l would be equal t o t h e t o t a l of t h e v e l o c i t y head,
t h e pressure head, and t h e e l e v a t i o n head a t a second s t a t i o n downstream
i n t h e same pipe or open channel, Figure 3-5. This i s t h e o r e t i c a l , but
t h e p r i n c i p l e i e used t o work out p r a c t i c a l s o l u t i o n s . In p r a c t i c e , f r i c tion and all other energy loseee must be conaidered and t h e energy equation
becomes :
L
w
+ P I + " l m V 2L
v
1
2g
where v
p
w
g
z
h
sub
h8
1,
+q+q
+hf
+hl
(Eq. 3-5)
2s
= mean v e l o c i t y of flow
= u n i t pressure
u n i t weight of water
= a c c e l e r a t i o n of g r a v i t y
= e l e v a t i o n head
= all l o s s e s of head other than by f r i c t i o n between
S t a t i o n s 1 and 2 such a s bends
= head l o s s by f r i c t i o n between S t a t i o n s 1 and 2
denotesupstreaniand d m s t r e a m s t i t i o n s , respectively
The energy equation and the equation of c o n t i n u i t y (Q = a 1 v l = a2 v 2 )
a r e the two b a s i c , simultaneous equations used i n solving problems i n
water flow.
Hydraulic and E n e r ~ yGradients
The hydraulic gradient i n open-channel flow i s t h e water s u r f a c e , and
i n pipe flow it connects t h e e l e v a t i o n s t o which the water would r i s e i n
piezmneter tubes along t h e pipe. !Che energy g r a d i e n t i s above t h e hydraul i c g r a d i e n t , a d i s t a n c e equal t o t h e v e l o c i t y head. I n both open-channel
and pipe flow, the f a l l (or s l o p e ) of t h e energy g r a d i e n t f o r a given
length' of channel or pipe r e p r e s e n t s the l o s s of energy by f r i c t i o n . When
considered together, t h e hydraulic g r a d i e n t and t h e energy g r a d i e n t r e f l e c t
not only t h e loss of energy by f r i c t i o n , but a l s o t h e conversions between
t h e t h r e e forms of energy. See Figure 3-5.
Pipe flow e x i e t s when a closed conduit of any form i s flowing f u l l .
In pipe flow, the croee-sectional area of flow i s fixed by the cross
section of the conduit and t h e water surface i s not exposed t o the atmosphere. Ihe i n t e r n a l pressure within a pipe may be equal t o , greater
than, o r lees than the l o c a l atmospheric preeeure.
The principles of pipe flow apply to t h e hydraulice of such s t r u c t u r e s as cu lverta, drop i n l e t s , regular and inverted siphons and various
types of pipelines.
The concept of flow continuity and t h e Bernoulli p r i n c i p l e has been
discuesed i n the preceding section. This section defines laminar and
turbulent flcw, diecueses the comnonly used diecharge equations and outl i n e s the hydraulics of pipelines and culverta.
LAMINAR
AM)
TURBULENT FL(M
Water £1-8
with two different types of motion, laminar and turbulent.
Laminar flow occurs when the individual p a r t i c l e e of water move i n
p a r a l l e l layers. The v e l o c i t i e s of these layers are not necessarily the
same. However, the mean v e l o c i t y of flow v a r i e r d i r e c t l y with the elope
of the hydraulic gradient.
Turbulent flow i e an i r r e g u l a r type of flow i n which the p a r t i c l e s
follow unpredictable paths. In addition t o the main v e l o c i t y i n the direct i o n of flow, there a r e transverse components of velocity. The mean vel o c i t y of flow v a r i e s with the square r o o t of the slope of the hydraulic
gradient
.
Leminar f l o w e e l d m occurs i n pipe flow. . I t is' the type of flow that
water has through s o i l s . For pipe flow the motion i s turbulent.
F r i c t i o n Loss
The l o s s of energy or head r e s u l t i n g from turbulence created a t the
boundary between t h e sides of the conduit and the flowing water i s called
f r i c t i o n loss.
I n a s t r a i g h t length of conduit, flowing f u l l , with constant cross
section and uniform roughness, the r a t e of l o s s of head by f r i c t i o n i s
constant and t h e energy gradient has a slope i n the d i r e c t i o n of flow
equal t o the f r i c t i o n head l o s s per foot of conduit.
Of the many equations that have been developed to expreaa this lose
of head, the following two are the most widely w e d :
Mannin~lrEquation
The general form of Manning'e equation is:
with, the following nomenclature :
a = cros8-eectional area of flow in ft. 2
d = dimeter of pipe in feet
di
diimeter of 'pipe in inchea
g
acceleration of gravity
32.2 ft. per eec. 2
loss
of
head
in
feet
due
to
friction in length, L
Hi
K, head lose c o e f f i c i e n t for any conduit
= head loss coefficient for circular pipe
length of conduit in feet
L
n = Manning's roughneaa coefficient
p = wetted perimeter in feet
hydraulic radius in feet
r
= d for round pipe
--
-
s
v
Q
-
-
P
lone of head in feet per foot of conduit = slope of
energy grade and hydraulic gradelinea in straight
conduits of uniform cross eection
(H1+L)
mean velocity of flow in ft. per eec.
= discharge or capacity in cu.ft. per eec.
-
Starting with Equation 3-6 solve fox e , multiply numerator and denominator of right side of equation by 2g and substitute (Hl+L) for s.
The result i a :
ihe equation can be simplified by substituting
(Eq. 3-7)
then the equation takes the form
(Eq. 3-8)
D
Maption of Equation 3-7 t o c i r c u l a r pipes involver the e u b e t i t u t b n
of (d + 4) for r 4 the change f r m d t o di.
Tables for values of
given i n M i b i t 3 4 .
and I[, f o r the usual ranger of variabler are
iof
EL*'.~lmdbook(l)g t n . a d
r of c-nient
l b n i n g l e formula a d references t o tables that will f a c i l i t a t e theh ume.
Four of these are:
B,
-.
be
Exhibit 3-5, which is baeed an the l a s t of these equations,
used t o determine d i , a, or Q when two of them quantitier a d n are
Values of Manningle n are given in Table 3-1.
&sen-Will itmi Eauat ion
As generally used, t h i a equation is:
Notation i a the 6as given fole Manning's equation with the addit i o n of C, the coefficient of roughneae i n Hazen-Williams formula.
Since Q av, Equation 3-10 may be converted to the f o l l w i n g foemula
for discharge in any conduit:
Q
1
1 . 3 1 8 a C r 0.63
Substitution of a a d r - i n terma of inside diameter of pipe i n incher
i n thia equation gives the follming general formula for discharge i n c i r cular pipee :
Graphical eolutione of Equation 3-11 f o r standard pipe ranging frcm
1 t o 12 inches i n diameter and a wide range i n elope may be made by using
Exhibit 3-6. Exhibit 3-7 gives loaaes f o r aemi-rigid p l a s t i c pipe.
Values f o r C f o r d i f f e r e n t types of pipe a r e given i n Table 3-2.
Rsgardlesa of the designer's preference of equatione, the r e s u l t s
ahould be checked against t h e application of State deeign c r i t e r i a .
Table 3-1
Desar i p t ion of pipe
Values of Mannim'e. n
Values of n
Min I
Desinn
I
Max.
I
Cast-iron, coated
Cast-iron, uncoated
Wrought iron, galvanized
Wrought iron, black
Steel, riveted and a p i r a l
Annular corrugated metal
Helical corrugated metal
Wood stave
,Neat cement surface
Concrete
V i t r i f i e d sewer pipe
Clay, camon drainage t i l e
Corrugated plastic
Table 3-2 Values of Hazen-Williams C
Description of pipe
C
-------------------------- - - - -- -- -- -- -- -- -- -- -- -- - -- -- ---------------------------- -- - -- -- - -- -- -- -- -- -- ---------- -------------- -- -----
Very smooth pipe; s t r a i g h t aligrrmant
Very m o t h pLpe; s l i g h t curvature
new
Cast iron, uncoated
5yearaold
loyearsold
15yearsold
20yearsold
30years0ld
a l l ages
coated
Steel pipe, welded, new
(Same d e t e r i o r a t i o n with age ae c a s t iron, uncoated)
For permanent i n s t a l l a t i o n use
-Wrought i r o n or atandard galvanized steel
dia. 12-in. up
4 t o 12 in. 4in.dcmn-Brassorlead,new
Concrete, very smooth, excellent j o i n t s
smooth, good j o i n t s
r o u & - - - - - - - - - - - - - - - - - - - - Vitrified
Smooth wooden or wood stave
&bestos c e m e n t - - - - - - - - - - - - - - - - - - - - - - Corrugated pipe
Note: Pipes of small diameter, old age, and very rau
inside eurface. mav give value. a. low a8 C
-
-
-
3
-
-
-
-
-
-
-
-
-
I
-- --------------------
..........................
------------------------------ -- ---%
-
140
130
130
120
110
100
90
80
130
130
-
I
100
110
100
80
140
140
120
110
110
120
140
60
-
-
D
Other b e s e e
In a d d i t i o n t o t h e f r i c t i o n head l o e s e s , t h e r e are other l o s s e s of
energy which occur a s t h e r e s u l t of turbulence created by changes i n vel o c i t y and d i r e c t i o n of flow. To f a c i l i t a t e t h e i r inclusion i n . ~ e r n o u l l i ' s
energy equation, such l o s s e s a r e commonly expressed i n terms of t h e mean
v e l o c i t y head a t sane s p e c i f i c c r o s s s e c t i o n of t h e pipe.
--
These loeses are sanetimes c a l l e d minor l o e s e s , which may be a s e r i o u s
misnomer. In long p i p e l i n e s , t h e entrance l o s s , bend losaee, e t c . , may be
only a small p a r t of t h e t o t a l l o s s and i n such cases can be ignored. Such
i s not t h e case i n many s t r u c t u r e s such a a c u l v e r t s , drop i n l e t s , and s i phone which are r e l a t i v e l y s h o r t . Safe design p r a c t i c e r e q u i r e s an estimate of such l o s s e s . I f the estimate i n d i c a t e s t h a t minor l o s s e s amount
t o 5 percent o r more of t h e t o t a l head loss, they should be c a r e f u l l y evaluated and included i n the flow calculations.
As velocities increase, c a r e f u l determination of euch minor loeses
bec-e
more important. With a mean v e l o c i t y of 30 f e e t per second, t h e
neglect of an entrance loam of 0.5 v2& results i n an e r r o r i n head l o s s
of 7 f e e t . Whereas, i f t h e mean v e l o c i t y i s 3 feet per second, neglect of
euch an entrance loea r e s u l t s i n an e r r o r of only 0.07 f o o t .
Data on minor l o s s e s most commonly required a r e contained i n Exhibit
3-8 of t h i s chapter, and Section 5, Hydraulics, (6). and Section 15, Irrigat i o n , of t h e National Engineering Handbook.
HYDRAULICS OP PIPZLINES
The pipe f l o w condition o f t e n found i n SCS work i s t h a t of f r e e f l w
discharge. See Figure 3-6.
The general pipe flow equation is derived through use of the
Bernoulli. and continuity principles.
Equating the energy in Figure 3-6, using Equation 3-5:
where a1
= elevation head at station 1
=2
= elevation head at etation 2
V2
= velocity head at station 2
EKV'J
2g
-
stm of the minor head loemem and pipe friction
Loeses
and fraa the continuity principle
where Q
a
g
H
= discharge-cfs
= pipe area-sq.ft.
.
* acceleration of g r a v i t y 4t/sec 2
Kp
= elevation head diffexential-ft.
= coefficient of minor loasee
= pipe friction coefficient
L
=pipe length-ft.
B
The f o l l w i n g e-lee
are applications of Equation 3-12.
Example 3-12
Determine the discharge of a drop inlet epillway with cantilevered
reinoutlet for a head H of 20 f e e t . The epillway is 24-inch di-ter
i s 1.0
forced concrete pipe with Msnninglrr n of 0.013, Table 3-1.
for bend and entrance lorreem. See refereme, aheet 2 of Exhibit 3-8.
Solution
Ua ing equation ( 3-12)
1.
Area
Reference: Exhibit 3-4
a = 3.14 aq f t
2.
Friction loss coefficient
Reference: E x h i b i t 3-4
= 0.0124
g
3.
Discharge
Q = 62.5 c f a
A corrugated metal pipe with a hooded inlet: and cantilevered outlet
is to discharge 130 cfs when the reservoir water surface is a t elevation
200.0 and the centerline of the outlet i a at elevation 170.0. Determine
the diameter of pipe required. Use Manning's n = 0.024, Table 3-1:
Solution
Select a diameter and determine the diecharge using
Equation 3-12.
Trial 1
1.
Select d = 36 inches
2.
Area
Reference: Exhibit 3-4
a = 7.07 s q . f t .
3.
Friction loee coefficient
Reference : Exhibit 3-4
= 0.0246
5
4.
Minor . l o s s coefficient
Reference: Exhibit 3-8
entrance K,,, = 1.00
5.
Discharge
Q
-
138.0 c f s
(&p&m=&*m&)
B
Trial 2
I.
Select d = 30 inches
2.
Area a = 4.91 eq.ft.
3.
F r i c t i o n 10s. c o e f f i c i e n t
4.
Minor lose c o e f f i c i e n t
5.
Diecharge
Q
Bp
%=
a
0.0314
1.00
90.0 c f e
It can be seen f r a u t h e foregoing two trials that the 36-inch pipe
more nearly e a t i e f i e e the required Q of 130 c f e and i e the one t o be
installed.
An 8-inch diameter concrete side drain i n l e t diechargee belcw the
water surface of a channel. The pipe i s 40 f e e t long and flowing full
with a head of 5 feet. Manning'e n = 0.012, Table 3-1. Determine the
discharge. Aserne
= entrance c o e f f i c i e n t plus bend c o e f f i c i e n t = 1.
The discharge equation for e x i t conditions other than f r e e flow i e
t h e same a e Equation 3-12.
K
X
=
exit c o e f f i c i e n t = 1.0
theref ore
1.
Area
Reference : Exhibit 3-4
a = 0.349 eq.ft.
2.
Friction l o s s coefficient
Reference: Ekhibit 3-4
= 0.0458
5
3.
Discharge
Q
-
3.2 c f e
A pipeline of 250 f e e t of 36-inch and 500 f e e t of 24-inch s t e e l pipe
cwnecte hPo re~ervoiru. Determine the dimcharge i f : the head ie 100 f e e t ,
the entrance coefficient ie 1, the contraction coefficient ie 0.25, and
Manning's n i e 0.011.
To use Equation 3-12 the loam coefficients must be expressed i n terms
of a single-s'ieed pipe.
,
,
In terms of the 24-inch pipe the c o e f f i c i e n t s in the example must be
multiplied by the follcwing r a t i o , C, which i s based on the square of the
ratio of areas.
rea of 24" dia.. v
rea of 36" dia. pipe
of 24" dia. p i p s
of 24" dia.pips
Discharge in terme of 24-inch diameter pipe
-
1.. Areas
Reference : Exhibit 3-4
24-inch dia. a 3.14 e q . f t .
36-inch dia. a
7.07 sq.ft.
2.
Friction lose coefficiente
Reference : Exhibit 3-4
24-inch dia.
0.00889
36-inch d i a . $ 0.00518
5
--
~-
3.
Square of the r a t i o of areas
4.
Sum of the loss c o e f f i c i e n t s
Y
coef f
-
Entrance
36" pipe
0.00518
Contraction
24" pipe
0.00889
Exit
-
5.
Discharge
.
103 cfe
500
250
1.0
1.296
0.25
4.45
1.0
0.196
0.196
0.196
1.0
1.0
0.196
0.254
0.049
4 .45
.
1
.
0
5 .%9
HYDRAULICS OF CULVERTS (2 )
There a r e two major types of c u l v e r t flow: 1) Flow with i n l e t cont r o l , and 2 ) f l w with o u t l e t c o n t r o l . For each type, d i f f e r e n t factors
and formulaa a r e used t o compute t h e hydraulic capacity of t h e c u l v e r t .
Under inlet c o n t r o l , t h e slope, roughness and diameter of the c u l v e r t barrel, t h e i n l e t shape and t h e amount of headwater o r ponding a t t h e entrance
must be considered. Outlet c o n t r o l involves the additional consideration
of the e l e v a t i o n of t h e t a i l w a t e r i n t h e o u t l e t channel and the length of
the culvert.
The need f o r making involved computations t o d e t e m b e t h e probable
type of flow under which a c u l v e r t w i l l operate may be avoided by computing headwater depths fran & h i b i t s 3-9 through 3-12 f o r both i n l e t c o n t r o l
and o u t l e t c o n t r o l and then using the higher value f o r design.
Both i n l e t c o n t r o l and o u t l e t c o n t r o l types of flow are diecussed
briefly i n t h e following paragraphs.
Culverta Flawinp,With Inlet Control
Inlet c o n t r o l mean8 t h a t t h e discharge capacity of a c u l v e r t l a cont r o l l e d a t t h e c u l v e r t entrance by the depth of headwater. (IW) and the
shape of t h e entrance. Figure 3-7 shows i n l e t c o n t r o l flw for three
types of c u l v e r t entrance@.
In i n l e t c o n t r o l t h e length of t h e c u l v e r t b a r r e l and o u t l e t condit i o n s a r e not f a c t o r s i n determining c u l v e r t capacity.
In all c u l v e r t design, headwater o r depth of ponding a t t h e entrance
t o a c u l v e r t i s an important factor i n c u l v e r t capacity. Thq headwater
depth i s t h e v e r t i c a l d i s t a n c e from t h e c u l v e r t i n v e r t at t h e entrance t o
t h e energy l i n e of t h e headwater pool (depth + v e l o c i t y head). Because
of the low v e l o c i t i e s i n most entrance pools, t h e water surface and t h e
energy l i n e a t t h e entrance a r e assumed t o coincide.
Headwater-discharge r e l a t i o n s h i p s f o r various types of c i r c u l a r c u l v e r t s flawing with i n l e t c o n t r o l a r e baaed on l a b o r a t o r y research with
models and v e r i f i e d i n some instances by f u l l - s c a l e t e a t s . Exhibite 3-9
and 3-10 give headwater-discharge r e l a t i o n e h i p a for round concrete and
CM pipe c u l v e r t s flowing with i n l e t c o n t r o l .
Example 3-16
It i s desired t o determine t h e maximum discharge of an e x i s t i n g
42-inch concrete c u l v e r t . The allowable headwater depth (HW) upstream i s
8.0 f e e t and the slope of t h e c u l v e r r i s 0.02 f t / E t . The c u l v e r t haa a
p r o j e c t i n g entrance condition and t h e r e w i l l be no backwater from d m etream flow. Assume i n l e t control.
Figure 3-7
Culverts w i t h i n l e t control
Uei*
Exhibit 3-9, compute
At 2.29
on
D
ecale 3, projecting entrance, draw a horizontal l i n e t o
ecale 1. From t h i s point on scale 1 draw a connecting line between it a d
42-'inch diameter w s c a l e 4.
C ~ Iecale 5 read Q = 128 cfs.
Check for i n l e t control
where
>
= symbol for "is greater than"
So
= installed rlope of culvert
-
en = neutral elope t h a t elope of which the lose
of head dua t o f r i c t i o n i a equal t o the gain
in head due t o elevation.
f r & Table 3-1, n(desiga) for concrete pipe = 0.012
f o r Q = 128 cfr and D = 42 inchee
therefore, the culvert is i n i n l e t control,
0.02 >0.013
lkamle 3-17
Determine the required d i m e t e r of a corrugated metal culvert pipe t o
be i n s t a l l e d i n an exieting channel. Q = 100 cfe, EW max. = 7.0 f e e t and
eo = 0.03. There w i l l be no b a c b a t e r fran downstream flow.
Entrance t o
be mitered t o confonn t o the slope of the embankment.
The solution of t h i s problem must be made by t r i a l pipe dimnetere
and eolution o f . HW by uae of Earhibit 3-10.
draw a l i n e thrwgh 36 inch on scale 4 and
100 cfe on ecale 5 t o an intereection with
ecale 1, then a horizontal l i n e fran wale I
to scale 2, mitered i n l e t . On scale 2 read
then W
-
3.8(3) = 11.4 feet
too haLgh
Try D = 48"
D
read from s c a l e 2 , tw = 1 - 4 5
HW = 1.45 (4) = 5.80 f e e t
HW
D
read from r c a l e 2 , --=
I34 = 2.23(3.5)
-
law
2.23
7.8 f e e t
high
From t h e foregoing t r i a l s , it w i l l be neceseary t o i n e t a l l t h e 48-inch
diameter pipe if t h e HW i s t o be 7 . 0 f e e t maximum.
Check f o r i n l e t c o n t r o l
from F x h i b i t 3-5, eheet 6 of 6
0.03 > 0.017
therefore, i n l e t control
Culverts Flowing With O u t l e t Control
Culverte flowing w i t h o u t l e t c o n t r o l can flow with t h e culvert b a r r e l
f u l l fox a l l o r p a r t of t h e b a r r e l length. See Figure 3-8. I f t h e e n t i r e
c r o s s s e c t i o n of t h e b a r r e l is f i l l e d with water f o r the t o t a l l e n g t h of
t h e b a r r e l , t h e c u l v e r t i s s a i d t o be i n f u l l flaw, Figure 3-8(a) and (b).
One o t h e r type of o u t l e t c o n t r o l is shown i n Figure 3-8(c).
For this condit i o n , t h e e l e v a t i o n of t h e energy g r a d e l i n e a t t h e exit of t h e c u l v e r t i s
assumed a t 3/4D. This is n o t an e x a c t f i g u r e b u t it w i l l give reasonable
results.
The head, H, Figure 3-8(a), o r energy r e q u i r e d t o pass a given quant i t y of water through a c u l v e r t with o u t l e t c o n t r o l i s made up of t h r e e
p a r t s . The p a r t s are expressed i n f e e t of water and include a v e l o c i t y
head, &, an entrance l o s s , He, and a f r i c t i o n l o s s , Hf. This energy i s
obtained from ponding of water a t t h e e n t r a n c e and i s expressed by t h e
equation
H=&+H,fHf
(Eq. 3-13)
This equation i n similar £ o m has been derived i n t h e s e c t i o n on
Hydraulics of p i p e l i n e s .
The entrance l o s s , I&, depend8 upon t h e shape of t h e i n l e t edge. This
loss i s expressed as a c o e f f i c i e n t , K,, times the b a r r e l velocity head.
That i s , I& = Ke
Entrance l o s 8 c o e f f i c i e n t s , &, f o r v a r i o u s types of
v.
*
2g
e n t r a n c e s when flow i s i n o u t l e t c o n t r o l are given i n Table 3-3.
Figure 3-8
Culverts with outlet control
I
Type of Structure and Design of Entrance
I
I
Table 3-3 Entrance Loaa Coefficients
l~oefficientKe
I
Pipe. Concrete
--- ------ - -------- ---------- --- --- --- ------
Projecting from fill, socket end (groove-end)
0.2
Projecting fran fill, sq. cut end - - 0.5
Headwall or headwall and wingwalls
0.2
Socket end of pipe (groove-end)
S q u a r e d e n d - - - - - - - - - - - - - - - - - - - - - - - 0.5
-'Rounded (radiue 1112~)
0.2
Mitered to cbnform to fill slope 0.7
0.5
*End-section conforming to fill slope
-----------
I
I
Pipe, or Pipe-Arch. Corrugated Metal
---------------------------- ------------------
Projecting frm fill (no headwall)Headwall or headwall and wingwalla
square-edge- -Mitered to conform to fill slope
*End-section conforming to fill slope
- ---
Note:
- ' -
0.9
0.5
0.7
0.5
*"End-section conforming to fill slope," made of either metal or
concrete, are the sections commonly available frcm manufacturers
From limited hydraulic teats they are equivalent in operation to
a headwall in both inlet and outlet control.
.
The friction loss, Hf, is the energy required to overcane. the roughness of the culvert barrel and is expressed by the equation
I$ valuee
can be taken £run Exhibit 3-4.
Headwater depth can be expressed as an equation for all outlet control
conditions, including all depths of tailwater, '1W. This is done by designating the vertical distance from the culvert invert: at the outlet to the
elevation from which H is measured as ho.
where B
e,
H
-
length of culvert
elope of culvert in feet per foot
= head lorr in feet as determined from the
appropriate exhibit
=
When the elevation of the water rurface in the outlet channel is
equal to or above the top o f the culvert opening at the outlet,
Figure 3-9 (a), ho i r eq&l
to the tailrater depth. If the tailwater
elevation is b e l w the tap of the culvert opening at the outlet,
Figure 3-9 (b), ho, is then by definition 3/4D.
3 0 = h o -I
sol
Figure 3-9
Culvmrt a t e r depth ra,latloaahipo
Headwater-discharge relationships for varioue types of circular culverts flowing with outlet control may be eolved by the use of Exhibits 3-11
and 3-12. For a different roughnear coefficient nl than that of the
exhibit,n, use the length m a l e s shown vith an adjusted length,, J l , calculated by the formula
-
Example 3-18
It i s desired t o i n s t a l l 50 f e e t of concrete c u l v e r t p i p e , ' n
0.012,
i n a drainage channel f o r a road croseing. Design Q i e 80 c f r with a
t a i l w a t e r depth of 3.0 f e e t . Slope of t h e c u l v e r t w i l l be 0.002 f o o t per
foot. Maximum headwater depth (HW) is 5 f e e t
.,
from Equation 3-14
HW = H + h , - eoa o r , H = HW
3.0 + .002(50)
H = 5.0
H = 2.1 f e e t
-
- ho + sol
and from Table 3-3
f o r a concrete pipe projecting from t h e f i l l with
socket end upstream
K,
= 0.2
entering Exhibit 3-11
draw a l i n e between H = 2.1 f e e t on t h e head ecal'e and
Q = 80 c f s on t h e discharge scale. Then on t h e length
s c a l e f o r K, = 0.2, draw a second l i n e from t h e 50-feet
mark through the i n t e r s e c t i o n of t h e f i r s t l i n e with t h e
"turning l i n e " and on t o t h e pipe diameter scale. The
diameter s c a l e i n t e r s e c t i o n i s a t approximately 39 inches,
therefore, use a 42-inch pipe.
Erosive Culvert Exit Velocitiee
A c u l v e r t , becauee of i t s hydraulic c h a r a c t e r i s t i c s , increases t h e
v e l o c i t y of flow over t h a t i n t h e adjacent channel. High v e l o c i t i e s may
be damaging j u s t downstream from t h e c u l v e r t o u t l e t and t h e erosion potent i a l a t t h i s point should be considered i n c u l v e r t design. I n many cases
i t is necessary t o r i p r a p t h e channel f o r a s h o r t distance dournettem of
the c u l v e r t e x i t .
6.
OPEN CHANNEL FLW
The flaw of water i n an open channel d i f f e r s from pipe flow in one
important respect. See Figure 3-5. Open channel f l m must have a f r e e
water surface, whereas pipe flow has none since water must f i l l the whole
conduit.
Flow calculatione f o r open channels are complicated by t h e f a c t t h a t
the p o s i t i o n of t h e water surface i e likely t o change with respect t o t i n e
and t h e cross-sectional area. Also t h e depth of flaw, discharge, and slopea
of the channel bottom and water surface a r e - interdependent. Channel c r o s s
sections can vary from semicircular t o the i r r e g u l a r forms of n a t u r a l
streams. The channel surface may vary from t h a t of polished metal used i n
t e s t i n g flumes t o t h a t of rough, i r r e g u l a r riverbed$+ Wreover, the roughness i n an open channel v a r i e s with t h e p o s i t i o n of t h e f r e e v a t e r surface.
Therefore, the proper s e l e c t i o n of f r i c t i o n c o e f f i c i e n t s i e more uncertain
f o r open channels than f o r pipes. I n geqeral, t h e treatment of open channel flow is somewhat more empirical than t h a t of pipe f l w , but the empirical
method i s t h e b e s t available. I f cautiously applied, it r e s u l t s i n p r a c t i c a l
values.
TYPES OF CHANNEL FLOW
Open channel flar can be c l a s s i f i e d according t o t h e change i n flow
depth w i t h r e s p e c t t o t h e time i n t e r v a l being considered and t h e channel
c r o a a - e e c t i o n a l a r e a occupied by t h e flow.
1.
Steady flcw
a.
b
.
Uniform flow
Nonunif o m f l o w
(1) Gradually v a r i e d flow
(2)
2.
Rapidly v a r i e d flaw
Unsteady flow
a.
Unsteady uniform flaw (rare)
b.
Unsteady v a r i e d . flow
(1)
Gradually varied uneteady f l o w
(2)
Rapidly varied uneteady flow
Steady Flow and Unsteady Flow:
Based on Time I n t e r v a l
Flaw i n an open channel i s steady i f t h e depth of flaw a t a given
c r o s s s e c t i o n does n o t change, o r if i t can be aeeumed t o be c o n s t a n t ,
during t h e time i n t e r v a l being coneidered. The flaw i s unsteady i f t h e
depth of flow a t a given croaa s e c t i o n changer with time.
I n moat open-channel pxoblems i t i s necessary t o study flow behavior
only under steady c o n d i t i o n s . I f , however, t h e change i n flow c o n d i t i o n
w i t h r e s p e c t t o time is of majot ccmcern, t h e f l o w should be t r e a t e d ae
unsteady. In floode and surges, f a r i n s t a n c e , which are t y p i c a l examplea
of uneteady flow, t h e s t a g e of flow changes instantaneously a8 t h e waves
p a s s by, and the t i m e element become8 important i n t h e design of c o n t r o l
structures.
Uniform Flow and Nonuniform Flow:
Based on Channel Space Used
Open-channel flou ie uniform if t h e depth of flow i s the same at
every s e c t i o n of the channel. A uniform flow may be steady o r uneteady,
depending on whether o r not t h e depth c h a n g e s d u r i n g t h e t i m e period being
considered.
Steady uniform flaw is t h e b a s i c type of f l o w t r e a t e d i n open-channel
h y d r a u l i c s . The depth of t h e flow does n o t change during t h e time i n t e r v a l under consideration. Unsteady uniform flow means t h a t the water
D
eurface f l u c t u a t e 8 from t i m e t o time while remaining p a r a l l e l t o t h e chann e l bottom, which i s p r a c t i c a l l y impossible.
Flow i e nonuniform i f t h e depth of flow change6 along t h e l e n g t h of
t h e channel. Nonuniform flow may be e i t h e r steady o r uneteady.
Nonuniform flow may be c l a s s e d as e i t h e r r a p i d l y o r g r a d u a l l y v a r i e d .
The flow i e r a p i d l y v a r i e d i f t h e depth changes a b r u p t l y over a comparat i v e l y a h o r t d i s t a n c e ; o t h e m i e e , i t i s gradually v a r i e d . Examples of
r a p i d l y v a r i e d flow a r e t h e hydraulic jump and t h e hydraulic drop.
Various types of flow a r e shown i n Figure 3-10.
CHANNEL CROSS- SECTION ELEMENTS
The elemente of c r o e s aections of an open channel r e q u i t e d f o r
hydraulic camputatione a r e :
a , t h e c r o s s - s e c t i o n a l a r e a of flow;
p, t h e wetted perimeter, t h a t i s , t h e l e n g t h of t h e
boundary of t h e c r o s s s e c t i o n i n c o n t a c t with t h e
water ;
r
9, t h e h y d r a u l i c r a d i u e , which i a t h e c r o e e - e e c t i o n a l
P
a r e a of t h e stream divided by t h e wetted perimeter.
General formulae f o r determining a r e a , wetted perimeter, h y d r a u l i c
r a d i u s , and top widthe of t r a p e z o i d a l , r e c t a n g u l a r , t r i a n g u l a r , c i r c u l a r ,
and p a r a b o l i c eectione a r e given i n Exhibit 3-13. Many t a b l e e a r e a v a i l a b l e showing hydraulic elements f o r v a r i o u s e i e e s and ehapee of channels,
The U S D I Bureau of Reclamat i o n "Rydraul i c and Excavation ~ a b l e s " ( 3) and
Corps of Engineere "Excavation ~ a b l e s " ( 4 ) a r e good booka i f t h e r e i e much
of t h i s work t o be done.
MANNING' S EQUATION
The most widely used open channel formulas exprees mean v e l o c i t y of
flow a8 a f u n c t i o n of t h e roughness of t h e channel, t h e h y d r a u l i c r a d i u s ,
and t h e slope of t h e energy g r a d i e n t . They a r e equations i n which t h e
v a l u e s of c o n s t a n t s and exponents have been derived f r o m experimental
data. Manningt@equation i s one of t h e most widely accepted and commonly
used of t h e open channel formulas:
(Eq. 3-15)
= mean v e l o c i t y of flow i n f e e t per second
r
= hydraulic r a d i u s i n f e e t
s
= elope of t h e energy g r a d i e n t
so 3 s l o p e of channel bottom
n
= c o e f f i c i e n t of roughness
v
Constant depth
%
-
Chonge of
-
depth from
to ti-
,
pt
Unsteady unlform
m
m flow-fWh0
loborotory channel
flow - Rare
-I--.?----------
GVF- Flood wove
Figure 3:10
RYF- Rare
Unsteady f b w
Various types o f open-channel f l o w . G.'.!.Y.
gradually yarieti Iluu; I
. = rapi J i y v a r i e d
flow.
Manning's equation has t h e advantage of s i m p l i c i t y and gives values
of v e l o c i t y consistent with experimental data. Exhibit 3-14, s h e e t s 1
through 4, may be used t o solve fox v , r , 8 , and n when any t h r e e are
known.
Since Q = av, Manning's equation may aleo be w r i t t e n :
(Eq. 3-16)
where a = croea-sectional area i n equare f e e t .
There are many other forme of Manning'e equation which are developed
by algebraic changee(l) t o eolve f o r varioue elements when the other e l e ments a r e known. Thene forms ehould be studied c a r e f u l l y . Having mastered
the use of the formula, the t a b l e s , . rvlplographe Bad charts can be ueed w i t h
confidence.
Coefficient of Roughness, n
The
reliable
estimate
requires
computed discharge f o r any given channel o r pipe w i l l be only as
a8 the estimated value of n ueed i n making t h e computatian.
This
a f f e c t s the deeign discharge capacity and t h e c o e t , and therefore,
c a r e f u l consideration.
In the cane of pipes and l i n e d channele, t h i r a r t h a t e i a e a s i e r t o
make but i t should be made with care. A given situation w i l l afford
s p e c i f i c information on euch fastorm as r i s e armd ahape of cross section,
alignment of t h e pipe 02: channel, end t h e type ard condition of the mater i a l forming the wetted perimeter.
Knowledge of these f a c t o r e , along with the r e s u l t s of experimental
i n v e s t i g a t i o n s and experience, makes possible eelectione of n values
within reasonably well-defined l i m i t s .
Natural channels and excavated channels, eubject t o varioue type8
and degrees of change, present a . m r e d i f f i c u l t problem. The s e l e c t i o n
of appropriate valuee f o r deeign of drainage, i r r i g a t i o n , and other excavated channels i s covered by manual data r e l a t i n g t o those subjects.
The value of n i a influenced by several factors; those having the
greateet in£luence axe :
Physical Rou~hnesa
The types of n a t u r a l m a t e r i a l forming the bottom and s i d e s and the
degree of surface i r r e g u l a r i t y are the guides t o evaluation. S o i l s made
up of f i n e p a r t i c l e e on smooth, uniform surfacee r e s u l t i n r e l a t i v e l y low
values of n. Coarse m a t e r i a l s , euch as gravel or boulders, and pronounced
surface i r r e g u l a r i t y cause higher values of n.
Vegetation
The value of n ehould be an expreseion of t h e r e t a r d a n c e t o flow a s
i t w i l l be a f f e c t e d by h e i g h t , d e n s i t y , and type of vegetation. Conside r a t i o n should be given t o d e n s i t y and d i s t r i b u t i o n of t h e v e g e t a t i o n along
t h e reach and t h e wetted perimeter; t h e degree t o which t h e v e g e t a t i o n occup i e s o r blocks t h e c r o s s - s e c t i o n a l a r e a of flow a t d i f f e r e n t depths; and t h e
degree t o which t h e v e g e t a t i o n may be bent o r t h e channel "shingled" by
flows of d i f f e r e n t depths.
Cross Section
Gradual and uniform i n c r e a s e s o r decreases i n c r o s s - s e c t i o n size w i l l
not s i g n i f i c a n t l y a f f e c t n, but abrupt change8 i n e i e e o r the a l t e r n a t i n g
of mall and l a r g e s e c t i o n s call f o r the use of a emewhat l a r g e r n. Uniformity of c r o s s - s e c t i o n a l shape w i l l cauee r e l a t i v e l y l i t t l e resistance
t o flow; whereas v a r i a t i o n , p a r t i c u l a r l y i f i t causee meandering of t h e
major p a r t of t h e flow from s i d e t o s i d e of t h e channel, w i l l i n c r e a s e n.
Channel A1 ignment
Curvee w i t h a r e l a t i v e l y l a r g e r a d i u s and without frequent changes
i n d i r e c t i o n of c u r v a t u r e w i l l offer comparatively low r e s i s t a n c e t o flow.
Severe meandering w i t h t h e curves having r e l a t i v e l y small r a d i i w i l l aign i f i c a n t l y i n c r e a s e n.
S i l t i n g o r Scourinq
Whether e i t h e r o r both of t h e s e processes a r e a c t i v e , and whether
they are l i k e l y t o continue o r develop i n t h e f u t u r e , i e important.
Active silting o r scouring, s i n c e they r e s u l t i n channel v a r i a t i o n of one
form o r another, w i l l tend to i n c r e a s e n.
Obstruct ion8
Lag jams and d e p o s i t s of any type of d e b r i s w i l l i n c r e a s e the value
of n; t h e degree of e f f e c t i s dependent on the number, type, and size of
obstructions.
T h e v a l u e of n, i n a n a t u r a l o r constructed channel i n e a r t h , v a r i e s
w i t h t h e eeason and f r m year t o y e a r ; i t i s not a f i x e d value. Each year
n i n c r e a s e e i n t h e s p r i n g and summer as v e g e t a t i o n grows and f o l i a g e develops, and diminishes i n t h e f a l l a s t h e dormant season develops. The annual
growth of v e g e t a t i o n , uneven accumulation of sediment i n t h e channel, lodgment of d e b r i s , e r o s i o n and sloughing of banks, and o t h e r f a c t o r s a l l tend
t o i n c r e a s e t h e value of n from year t o year u n t i l t h e hydraulic e f f i c i e n c y
of t h e channel i s improved by c l e a r i n g o r clean-out.
A l l of t h e s e f a c t o r s should be s t u d i e d and evaluated with r e s p e c t t o
kind of channel, degree of maintenance, seasonal requirements, season of
the y e a r when t h e design storm normally occurs, and o t h e r c o n s i d e r a t i o n s
as a b a s i s f o r s e l e c t i n g t h e v a l u e of n. A s a general guide t o judgment,
i t can be accepted t h a t c o n d i t i o n s tending t o induce turbulence w i l l i n c r e a s e retardance. Refer t o Chapters 7 and 14 of t h i s manual f o r guidance
i n s e l e c t i n g r e t a r d a n c e and n values.
SPeCfFIC ENERGY IN CHANNELS
The s p e c i f i c energy equation i a used t o solve many open channel
problems such as water surface profiles upstream of c u l v e r t s and channel
junctions and the water surface p r o f i l e i n a chute epillway.
Figure 3-11 shows s s e c t i o n s f channel i n unifonn flow. Here, f o r
a given slope, roughness, croes s e c t i o n and rate of flow, t h e depth may
be calculated from the Manning equation.
Figure 3- 11 Channe 1 energy re lationshipa
Assuming a uniform v e l o c i t y d i s t r i b u t i o n , the Bernoulli equation may
be w r i t t e n f o r a t y p i c a l reach of channel a s :
which shows that energy i s l o s t as flow occurs. However, t h e distance
from channel bottom t o energy l i n e remains constant and i s given by
(Eq. 3-17)
i n which H, i s known as t h e s p e c i f i c energy. Obviously the s p e c i f i c
energy i n an open channel i s t h e sum of the water depth and t h e v e l o c i t y
head.
The following s e c t i o n on c r i t i c a l flow i l l u s t r a t e s another a p p l i c a t i o n
of t h e s p e c i f i c energy equation t o solve channel flow problems.
CRITICAL FLOW CONDITIONS
C r i t i c a l flow i s t h e term used i n open channel f l o w t o d e f i n e a d i v i d ing p o i n t between s u b c r i t i c a l ( t r a n q u i l ) and s u p e r c r i t i c a l ( r a p i d ) f l o w .
A t t h f e p o i n t t h e r e exists c e r t a i n r e l a t i o n s h i p s between s p e c i f i c energy
and d i s c h a r g e and epecif i c energy and depth of f l o w . Ae shown p r e v i o u s l y ,
s p e c i f i c energy i s t h e t o t a l energy head a t a cross s e c t i o n measured from
t h e bottom of t h e channel. There a r e two c o n d i t i o n s which d e s c r i b e c r i t ical flow:
1.
The d i s c h a r g e i s maximum f o r a given specific energy head.
2.
The s p e c i f i c energy head i s minimum f o r a given discharge.
S t a t e d simply, t h e foregoing Bays t h a t f o r a given channel s e c t i o n
t h e r e i s one and only one c r i t i c a l d i s c h a r g e f o r a given e p e c i f i c energy
head. Any discharge greater or less than t h a t requires the a d d i t i o n of
spec i f i c energy.
General Equation f o r C r i t i c a l Flow
The general equation f o r c r i t i c a l f l o w i n any channel i s
From Equation 3-18,
and s i n c e
$ ,v2 and
a = d,,,T,the s p e c i f i c energy equation when flow i a c r i t i c a l i s
(Eq. 3-19)
where:
Q
a
d
-
t o t a l discharge
= cross-sectional area
= depth of flow t o t h e bottom of t h e s e c t i o n
-=
mean'depth of flow
a/T
a c c e l e r a t i o n of g r a v i t y
H, specific energy head, i.e., t h e energy head
r e f e r r e d t o t h e bottom of channel
T = t o p width of t h e stream
v = mean v e l o c i t y of f l o w
d,
g
B
0
A study of the specific energy diagram, Figure 3-12, w i l l give a more
thorough understanding of the relationrhipr. between discharge, energy, and
depth when flow i s c r i t i c a l .
Figure 3-12
The S p e c i f i c Cnergy Diagram
While studying t h i s d i a g r m , consider the f o l l m i n g c r i t i c a l flow
terms and t h e i r d e f i n i t i o n s :
C r i t i c a l Dischaxne
The maximum discharge f o r a given specific energy, or a discharge
which occurs with minimum specific energy.
C r i t i c a l Depth
The depth of flaw a t which the discharge is meximwn f o r a given
epecific e&rgy, or the depth a t which a given diecharge occurs with minb u m epec i f i c energy.
C r i t i c a l Velocity
The mean velocity when the discharge
16
critical.
C r i t i c a l Slope
That d o p e which will sustain a given diecharge a t uniform, c r i t i c a l
depth i n a given channel.
Subcritical F l m
Those conditions of flcw for which the depth i m greater than c r i t i c a l
and the velocity i s l e e s than c r i t i c a l .
S u ~ e r c r i t i c a lFlm
Thoae conditions of flow for which the depth is leas than c r i t i c a l
and the velocity i s greater than c r i t i c a l .
The curve shave t h e v a r i a t i o n of s p e c i f i c energy w i t h depth of flaw
f o r a c o n s t a n t Q i n a channel of a given c r o a s s e c t i o n . Similar curves for
any d i s c h a r g e a t a s e c t i o n of any form may be obtained from Equation 3-17.
C e r t a i n p o i n t s , aa i l l u s t r a t e d by t h i s curve, should be noted:
I n a e p e c i f i c energy diagram t h e p r e s s u r e head and v e l o c i t y
head are shown gxaphically. The p r e s s u r e head, depth i n
open channel flow, i e r e p r e s e n t e d by t h e h o r i z o n t a l s c a l e
a s t h e d i s t a n c e from t h e v e r t i c a l a x i s t o t h e l i n e along
which H, = d , t o t h e curve of c o n s t a n t Q.
For any d i s c h a r g e t h e r e i s a minimum a p e c i f i c energy, and
t h e depth of flow corresponding t o t h i s minimum s p e c i f i c
energy i r r t h e c r i t i c a l depth. For any e p e c i f i c energy
g r e a t e r than t h i s minimum t h e r e are two d e p t h s , sometime8
c a l l e d a l t e r n a t e s t a g e s , of equal energy a t which t h e d i a charge may occur. One of t h e s e depths i s i n t h e s u b c r i t i c a l range and t h e o t h e r i e i n t h e e u p e r c r i t i c a l range.
A t depthe of f l o w near t h e c r i t i c a l f o r any d i s c h a r g e , a
minor change i n s p e c i f i c energy w i l l cauee amuch g r e a t e r
change i n depthe.
Through t h e major p o r t i o n of t h e e u b c r i t i c a l range t h e
v e l o c i t y head f o r any d i s c h a r g e ia r e l a t i v e l y small when
compared t o s p e c i f i c energy, and changes i n depth are approximately equal t o changes i n s p e c i f i c energy.
Through t h e s u p e r c r i t i c a l range t h e v e l o c i t y head f o r any
d i s c h a r g e i n c r e a s e s r a p i d l y a s depth d e c r e a s e s , and changes
i n depth a r e a s s o c i a t e d w i t h much g r e a t e r changes i n s p e c i f i c
energy,
I n s t a b i l i t y of C r i t i c a l Flow
The i n s t a b i l i t y of uniform flow a t o r near c r i t i c a l depth i s u s u a l l y
defined i n terms of c r i t i c a l s l o p e , sc.
-
sc = c r i t i c a l alope
t h a t alope which w i l l s u s t a i n a given
d i s c h a r g e i n a given channel a t uniform, c r i t i c a l depth.
The c r i t i c a l s l o p e , sc, i s :
(Eq. 3-20)
Uniform flow a t ox near c r i t i c a l depth i s u n s t a b l e . This r e s u l t s
from t h e f a c t t h a t t h e unique r e l a t i o n s h i p between energy head and depth
of £loot which must exist i n c r i t i c a l flow is r e a d i l y d i s t u r b e d by minor
changes i n energy. Those who have seen uniform flow a t o r near c r i t i c a l
D
depth have observed t h e u n s t a b l e wavy s u r f a c e t h a t i s caused by apprec i a b l e changes i n depth r e s u l t i n g from minor changes i n energy. This
u n s t a b l e range i s defined as follows:
Unstable zone i n t h e range 0.7sc< s o < 1 . 3 s ,
where
<= t h e
symbol £or "is l e s s than"
Because of t h e u n s t a b l e flow, channels c a r r y i n g uniform flaw a t o r
near c r i t i c a l depth should not be used u n l e s s t h e s i t u a t i o n allows no
a l t e r n a t i v e . I n this c a s e allowance must be made i n design for t h e height
of t h e wave generated. Often when topography r e s t r i c t s the channel s l o p e
t h e flow can be f m c e d i n t o s u b c r i t i c a l s t a b l e o r s u p e r c r i t i c a l s t a b l e by
varying the width of the channel.
Open Channel Problems
Example 3-19
Given : Trapezoidal sect'ion
n = 0.02
To determine:
Solution:
Q i n c f s , and v i n f p s
from E x h i b i t 3-13
e n t e r Exhibit 3-14 with r = 1.695, s = 0.006, n = 0.02,
and read v = 8 . 1 9 f p s
then Q = av = 32.5(8.19)
= 266 c f s
Example 3-20
Given: Triangular s e c t i o n
n = 0.025
s = 0.006
To determine:
Q i n c f s and v i n f p s
Solution:
from Exhibit 3-13
enter Exhibit 3-14 with r = 1.455, s = 0.006, n = 0.025
and read v = 5 . 9 1 f p s
then Q = av = 36(5.91)
= 213 f p s
Example 3-21
Given:
Trapezoidal s e c t i o n
Q = 300 cfs
n = 0.02
s = 0.0009
To determine : d i n f t
Solution:
15f t.
. and v i n f
t/sec.
This can be solved by trial. First, assume a value for
d and compute the values of a, p , r;.then from E x h i b i t 3-14
f i n d v and compute Q.
Plot d against Q for trial 2 and 3 and read d = 3.39 ft.,
for Q = 300 c f s
D
For t h o s e having much of t h i s work t o do, t h e use of t a b l e s i n
King's Handbook, based on t h e e q u a t i o n K ' =
Qn
, w i l l provide
rapid d i r e c t solutions, i.e.,
b 8 / 3 ,112
then K' =
(300)(.02) = 0.146
(1370)(.03)
From t h e t a b l e of K ' v a l u e s f o r 2:l sides and K 1 = 0.146
D = (15)(0.226)
= 3.39 f e e t
The same p r o c e d u r e s c a n b e followed i n s o l v i n g f o r t r i a n g u l a r
sect i o n s .
7.
D
WEIR FLOW
A w e i r i s a notch of r e g u l a r form through which water flows. The
s t r u c t u r e c o n t a i n i n g t h e n o t c h i s a l s o c a l l e d a w e i r . The edge o v e r which
the w a t e r flows i s t h e c r e s t of t h e w e i r . Two types of w e i r c r e s t s are
common i n s o i l c o n s e r v a t i o n work, s h a r p - c r e s t e d weirs and b r o a d - c r e s t e d
weirs.
The s h a r p - c r e s t e d weir i s used only t o measure t h e discharge o f a
channel o r stream. The s h a r p edge c a u s e s t h e w a t e r t o s p r i n g c l e a r of the
crest.
Most h y d r a u l i c s t r u c t u r e s i n s o i l c o n s e r v a t i o n work have b r o a d - c r e s t e d
w e i r s . The c r e s t i s h o r i z o n t a l and l o n g i n t h e d i r e c t i o n of flow s o t h a t
t h e w a t e r l a y s on t h e c r e s t r a t h e r t h a n s p r i n g i n g c l e a r . The primary u s e
of t h e b r o a d - c r e s t e d w e i r i s f o r t h e c o n t r o l of f l o o d f l o w s , a l t h o u g h water
measurement c a n be i n c o r p o r a t e d as a secondary f u n c t i o n . Chapter 6 ,
S t r u c t u r e s , of t h i s manual d e s c r i b e s i n d e t a i l i t s many a p p l i c a t i o n s .
Examples o f t h e two t y p e s of w e i r c r e s t a r e shown i n F i g u r e 3-13 and
3-14.
channel
_ _ _- --
Figure 3-13
Sharp-crested weir
Figure 3 - 1 4
Broad-crested weir
If the overflowing sheet of water (nappe) discharges into the a i r ,
as above, the weir has free discharge. If the discharge i s p a r t i a l l y
under water, as shown i n Figure 3-15, the weir i s submerged or drowned.
Figure 3-15
Submerged weir
BASIC EQUATION
The basic equation for a l l weirs i s :
(Eq. 3-21)
where :
Q
H
L
C
discharge
measured head
length of weir
= weir c o e f f i c i e n t
=
=
=
Corrections are required to include e f f e c t s of end contractions,
v e l o c i t y of approach and submergence.
CONTRACTIONS
The weir i s c o n t r a c t e d when t h e r e s p e c t i v e d i s t a n c e s from t h e s i d e s
and t h e bottom of t h e channel of approach t o t h e s i d e s and c r e s t of t h e
w e i r are g r e a t enough t o allow t h e water f r e e l a t e r a l approach t o t h e
c r e s t . I f t h e weir conforms t o t h e s i d e s of t h e approach channel above
t h e c r e s t and t h e channel s i d e s extend downstream beyond t h e c r e s t , t h e r e b y
p r e v e n t i n g l a t e r a l expansion of t h e nappe, t h e w e i r h a s end c o n t r a c t i o n s
suppressed.
End c o n t r a c t i o n s reduce the e f f e c t i v e l e n g t h of a w e i r . To allow f o r
end c o n t r a c t i o n s , t h e l e n g t h 05 w e i r i n t h e b a s i c e q u a t i o n i s a d j u s t e d a s
follows :
where :
L =
L' =
N =
e f f e c t i v e l e n g t h of w e i r
measured l e n g t h of w e i r
number of c o n t r a c t i o n s
The above e q u a t i o n i s g e n e r a l l y a p p l i e d o n l y f o r s h a r p - c r e s t e d w e i r s
i n s o i l c o n s e r v a t i o n work. For most b r o a d - c r e s t e d weirs t h e end c o n t r a c t i o n s w i l l be e i t h e r f u l l y o r p a r t i a l l y suppressed. For drop s p i l l w a y s
t h e b a s i c formula can be used w i t h o u t modifying f o r c o n t r a c t i o n e f f e c t .
The v e l o c i t y of approach i s t h e average v e l o c i t y i n t h e approach
channel.
It i s measured a t a d i s t a n c e of about 3 H upstream from t h e w e i r .
The v e l o c i t y head i s added t o t h e measured head t o determine the d i s c h a r g e .
Theref o r e :
(Eq. 3-23)
WE=
COEFFICIENTS
Values of t h e weir c o e f f i c i e n t , C , v a r i e s w i t h t h e type of c r e s t
used. Weir c o e f f i c i e n t s f o r s h a r p - c r e s t e d w e i r s normally used i n s o i l
c o n s e r v a t i o n work a r e given under t h e f o l l o w i n g s e c t i o n on water measurement. The weir c o e f f i c i e n t f o r b r o a d - c r e s t e d w e i r s c m o n l y used i n s o i l
c o n s e r v a t i o n work i s C = 3.1.
SUBMERGED FLOW
D
When a weir i s submerged, Figure 3-15, t h e d i s c h a r g e w i l l be l e s s
t h a n f o r t h e head i n f r e e flow. The r e d u c t i o n i n flow can be expressed
i n terms of t h e r a t i o of t h e upstream head, H i , t o t h e downstream head, H2.
When t h e r a t i o of H2/Hi f o r s h a r p - c r e s t e d w e i r s r e a c h e s 0.3 t o 0.4,
t h e d i s c h a r g e may be reduced by 5 t o 1 0 p e r c e n t . For H 2 / H l r a t i o s of
0.6 t o 0.7, r e d u c t i o n s of 20 t o 40 p e r c e n t may b e e x p e c t e d .
There i s no g r e a t r e d u c t i o n i n d i s c h a r g e f o r b r o a d - c r e s t e d weirs
u n t i l t h e r a t i o of ~ 2 1 r~e a1c h e s 0.67.
Then t h e d i s c h a r g e r e d u c e s r a p i d l y
~
0.75 t o 0.85, r e as t h e submergence i n c r e a s e s . For v a l u e s of H ~ / Hfrom
d u c t i o n s from 10 t o 30 p e r c e n t o c c u r .
When a p p r e c i a b l e submergence i s t o b e e n c o u n t e r e d , a c c u r a t e d i s c h a r g e
c a n be computed o n l y through t h e u s e of r e f i n e d p r o c e d u r e s .
8.
WATER MEASURING
The purpose of t h i s s e c t i o n i s t o o u t l i n e t h e most commonly used
The h y d r a u l i c p r i n c i p l e and e q u a t i o n of f l o w i s
given f o r most methods. For convenience, t h e s u b j e c t i s d i v i d e d i n t o open
water measuring methods.
c h a n n e l f l o w and p i p e flow.
OPEN CJ3ANNELS
The f o l l o w i n g methods of measurement a p p l y t o flows i n open c h a n n e l s .
O ri f i c e s
An o r i f i c e i s a h o l e of r e g u l a r form through which w a t e r flows.
Figure 3 - 1 6
Flnw through an o r i f i c e
The o r i f i c e
Flow through an o r i f i c e i s i l l u s t r a t e d i n F i g u r e 3-16.
shown i s sharp-edged; i.e., i t h a s a s h a r p upstream edge s o t h a t t h e w a t e r
i n p a s s i n g touches o n l y a l i n e . If t h e o r i f i c e d i s c h a r g e s i n t o t h e a i r ,
i t i s s a i d t o have f r e e d i s c h a r g e ; and i f i t d i s c h a r g e s under w a t e r , i t i s
s a i d t o be submerged. O r i f i c e s may b e c i r c u l a r , s q u a r e , r e c t a n g u l a r , or of
m y o t h e r r e g u l a r form.
The Bernoulli equation w r i t t e n from p o i n t 1 t o p o i n t 2 , Figure 3-16,
is
Point 2 , located where t h e j e t has ceased t o c o n t r a c t i s known a s t h e
vena c o n t r a c t a . I t s pressure i s t h a t of the surrounding f l u i d . For d i s charge i n t o t h e atmosphere P2 i s t h e r e f o r e zero on the gage s c a l e . For
l a r g e tanks, v l i s so small t h a t i t may be neglected. Replacing Pl/w with
h and dropping the s u b s c r i p t of v2, t h e equation may now be written
Neglecting energy l o s s e s , t h e equation f o r t h e t h e o r e t i c a l v e l o c i t y ,
vt, becomes
The energy l o s s may be taken care of by applying a c o e f f i c i e n t of
v e l o c i t y Cv t o t h e t h e o r e t i c a l v e l o c i t y as follows :
The discharge through an o r i f i c e i s obtained from t h e product of t h e
v e l o c i t y and t h e a r e a a t t h e vena c o n t r a c t a . The a r e a a t t h e vena contracts, a 2 , i s l e s s than t h e a r e a of t h e o r i f i c e , a . The r a t i o between
t h e two a r e a s i s c a l l e d t h e coefEicient of c o n t r a c t i o n Cc, Therefore,
and
The product of C, and ,C i s c a l l e d t h e c o e f f i c i e n t of discharge C.
Equation f o r discharge may t h e r e f o r e be w r i t t e n
(Eq. 3 - 2 5 )
The submerged o r i f i c e i n F i g u r e 3-17 i s t h e type most o f t e n used i n
s o i l c o n s e r v a t i o n work.
Figure 3-17
Submerged o r i f i c e
A s i n t h e f r e e d i s c h a r g e o r i f i c e , Equations 3-24 and 3-25 a l s o apply
t o t h e submerged o r i f i c e .
The c o e f f i c i e n t of d i s c h a r g e f o r submerged o r i f i c e s i s approximately
t h e same a s t h a t f o r f r e e d i s c h a r g e o r i f i c e s . The wide range i n types of
o r i f i c e s and g a t e s , a s p e c i a l form of o r i f i c e , makes i t i m p r a c t i c a l t o
i n c l u d e t a b l e s of c o e f f i c i e n t s c o v e r i n g an adequate range of c o n d i t i o n s .
Manufacturers' p u b l i c a t i o n s a r e normally the b e s t source of r e l i a b l e coe f f i c i e n t s f o r v a r i o u s t y p e s of g a t e s and o t h e r appurtenances involving
o r i f i c e flow.
Weirs
Sharp-crested w e i r s are used e x t e n s i v e l y f o r measuring t h e flow of
water. The most common t y p e s - - r e c t a n g u l a r , C i p o l l e t t i , and 90' V-notch
w e i r s - - a r e shown i n F i g u r e 3-18.
Sides slope l horizontal
to 4 vertical
Rectangular Weir
Cipolletti Weir
90° Notch Weir
Figure 3-18
Types of weirs
As given i n t h e preceding s e c t i o n , Weir Flow, t h e b a s i c equation
is
Measurements made by means of a w e i r a r e a c c u r a t e only when t h e
w e i r i s p r o p e r l y set and t h e head r e a d a t a p o i n t same d i s t a n c e above t h e
c r e s t so t h a t t h e reading w i l l not be a f f e c t e d by t h e downward curve of
t h e water. See Figure 3-19. The weir should be a t r i g h t angles t o t h e
stream a t a p o i n t where t h e channel i s s t r a i g h t , f r e e from eddies and of
s u f f i c i e n t width t o produce f u l l end c o n t r a c t i o n s . The c r e s t of t h e weir
must b e e x a c t l y l e v e l f o r t h e r e c t a n g u l a r and C i p o l l e t t i types. The b o t tom of t h e notch must be set above t h e bottom of t h e channel a h e i g h t
equal t o a t least twice t h e maximm head, p r e f e r a b l y more. I f a weir i s
t o continue t o give, r e l i a b l e r e s u l t s , it must be maintained i n such a way
as - t o p r e s e r v e t h e above-mentioned c o n d i t i o n s .
r
Point to Measure
De~th(H1
Elevntion- of
Wait Crest
1
Water Surfoce
Sharp- Crested Weir
-
Figure 3-19
--
Profile of a sharp-crested weir
Rectangular Contracted Weir
A r e c t a n g u l a r c o n t r a c t e d w e i r h a s i t s c r e s t and s i d e s s o far removed,
r e s p e c t i v e l y , from t h e bottom and s i d e s of t h e w e i r box o r channel i n which
it i s s e t , t h a t full c o n t r a c t i o n , o r reduced a r e a of flow, i s developed.
See F i g u r e 3-20.
I
Figure 3-20
Point to Measure Depth (HI
Rectangular contracted w e i r
For t h e r e c t a n g u l a r w e i r t h e c o e f f i c i e n t , C , i s 3.33.
t h e c o n t r a c t ions
Allowing f o r
where :
Q
L
H
d i s c h a r g e i n c u b i c f e e t p e r second n e g l e c t i
city
of approach
= t h e i i n g t h of weir, i n f e e t
= head on-the w e i r in f e e t measured a t a p o i n t no l e s s
than 4 H upstream from t h e w e i r .
=
Discharges may be taken from E x h i b i t 3-15.
Rectangular Suppressed Weir
A r e c t a n g u l a r suppressed w e i r h a s i t s c r e s t s o far removed from t h e
bottom of t h e approach c h a n n e l t h a t f u l l c r e s t c o n t r a c t i o n i s developed.
The s i d e s of t h e weir c o i n c i d e w i t h t h e s i d e s of t h e approach channel which
extend downstream beyond t h e c r e s t and p r e v e n t l a t e r a l expansion of t h e
nappe. A suppressed weir i n a flume drop i s illustrated i n F i g u r e 3-21.
Special care should be taken with this type of weir to provide aeration beneath the overflowing sheet at the crest. T h i s i s usually done by
venting the underside of the nappe to the atmosphere at both sides of the
weir box.
Figure 3-21
Suppressed weir in a flume. drop
The discharge equation for the rectangular suppressed weir i s
Q = 3.33 L H3 12
and including the velocity of approach
2
where h, = (velocity of approach)
2g
Discharge tables are available in the Bureau of Reclamation Water
Measurement Manual, Table 8, pages 177 to 179.
C i p o l l e t t i Weir
A C i p o l l e t t i weir, Figure 3 - 2 2 , i s t r a p e z o i d a l i n shape. I t s c r e s t
and s i d e s , which are of t h i n p l a t e , a r e s o f a r removed from t h e bottom
and s i d e s of t h e approach c h a n n e l as t o develop f u l l c o n t r a c t i o n of flow
a t t h e nappe. The s i d e s i n c l i n e outwardly a t a s l o p e of 1 t o 4.
Since t h e C i p o l l e t t i w e i r i s a c o n t r a c t e d weir, i t should be i n s t a l l e d
a c c o r d i n g l y . However, i t s d i s c h a r g e is essentially as though its end cont r a c t i o n s were suppressed. The e f f e c t of end c o n t r a c t i o n s i n r e d u c i n g d i s c h a r g e h a s been overcome by s l o p i n g t h e s i d e s of the w e i r .
Figure 3-22
Cipol1,etti weir
The e q u a t i o n g e n e r a l l y a c c e p t e d f o r computing t h e d i s c h a r g e through
C i p o l l e t t i weirs w i t h complete c o n t r a c t i o n s i s :
The s e l e c t e d l e n g t h of n o t c h (L) should be a t l e a s t 3 H and p r e f e r a b l y
4 H or longer.
Discharges may b e t a k e n from E x h i b i t 3-16.
90'
V-Notch Weir
The c r e s t of t h e 90° V-notch w e i r c o n s i s t s of a t h i n p l a t e , t h e s i d e s
of t h e n o t c h b e i n g i n c l i n e d 45' from t h e v e r t i c a l . T h i s w e i r h a s a cont r a c t e d n o t c h and all c o n d i t i o n s f o r a c c u r a c y s t a t e d f o r t h e s t a n d a r d cont r a c t e d r e c t a n g u l a r w e i r apply. The minimum d i s t a n c e from t h e s i d e of t h e
w e i r t o t h e channel bank should b e measured h o r i z o n t a l l y from t h e p o i n t
where t h e maximum w a t e r s u r f a c e i n t e r s e c t s t h e edge of t h e w e i r . The minimum bottom d i s t a n c e should be measured between t h e p o i n t of t h e n o t c h and
t h e channel f l o o r .
Figure 3 - 2 3
90° V-notch weir
The V-notch weir, F i g u r e 3-23, i s e s p e c i a l l y u s e f u l f o r measuring
s m a l l d i s c h a r g e s . The d i s c h a r g e equatiofi used i s
where
H = v e r t i c a l d i s t a n c e in f e e t between t h e e l e v a t i o n of t h e
v o r t e x o r l o w e s t part of t h e n o t c h and t h e e l e v a t i o n
of t h e w e i r pond.
E x h i b i t 3-17 may be used f o r d e t e r m i n i n g the discharge.
Parshall Flume
With a Parshall flume, Figure 3-24, the discharge i s obtained by
measuring the lose i n head caused by forcing a stream of water through
the throat section of the flume, which has a depressed bottom.
1
i
!
I
Diverging
Section
: ~ h r o aYsectim
tf
Converging
Section
I
I
I
I
/A
I
L
I
II
I
I
I
I
i
t4:
Plan
k'igure 3 - 2 4
Parshsll flume
There i s no need of a pond above t h e P a r s h a l l flume a s t h e v e l o c i t y
of approach has l i t t l e e f f e c t on t h e ' a c c u r a c y of t h e measurement. It uses
a small amount of head and can have a high degree of submergence without
having t o make c o r r e c t i o n s i n t h e free-flow formula. It does not c l o g
r e a d i l y w i t h f l o a t i n g t r a s h and keeps i t s e l f clean of sand and s i l t . It
r e q u i r e s but one reading of head (Ha) f o r determining t h e discharge except
i n c a s e s of extreme submergence when both Ha and Hb should be read.
Table 9-14, Chapter 9 , Section 1 5 , of the National Engineering Manual
g i v e s free-flow discharge v a l u e s f o r t h e P a r s h a l l flume.
Trapezoidal Flme
The t r a p e z o i d a l flume, Figure 3-25, o b t a i n s t h e discharge by measuri n g t h e l o s s i n head caused by f o r c i n g a stream of water through t h e t h r o a t
of a flume w i t h a l e v e l bottom. See Figure 3-25.
An advantage of t h e t r a p e z o i d a l flume i s t h a t t h e c r o s s , s e c t i o n c o r r e sponds t o t h e shape 05 t h e common i r r i g a t i o n channel. It i s p a r t i c u l a r l y
s u i t e d f o r use i n c o n c r e t e l i n e d i r r i g a t i o n channels.
The equation f o r discharge derived by Robinson and Chamberlain
(Transactions of t h e ASAE, 1960) i s
where :
= discharge, cfs
a 1 = a r e a a t t h e flume e n t r a n c e , s q . f t .
h l = head a t t h e entrance, f t .
h2 = head a t t h e t h r o a t , f t .
C ' = discharge c o e f f i c i e n t t h a t includes t h e geometry
of t h e s t r u c t u r e
Q
Further information on t h e t r a p e z o i d a l flume can be found i n USDA
A g r i c u l t u r a l Research Service B u l l e t i n 41-140, dated March 1968.
Current Meter
B a s i c a l l y , t h e c u r r e n t meter i s a wheel having s e v e r a l cups o r vanes.
This wheel i s r o t a t e d by t h e a c t i o n of t h e c u r r e n t and t h e speed of t h e
r o t a t i n g wheel i n d i c a t e s t h e v e l o c i t y of t h e c u r r e n t , based on a r a t i n g
t a b l e furnished by t h e manufacturer.
A zero s t a t i o n o r r e f e r e n c e p o i n t i s e s t a b l i s h e d on one bank of t h e
stream, and a t a p e i s s t r e t c h e d a c r o s s t h e stream f o r measuring h o r i z o n t a l
d i s t a n c e s . Soundings and current-meter readings a r e taken a t v e r t i c a l s
spaced a t r e g u l a r i n t e r v a l s , u s u a l l y from 2 t o 10 f e e t , depending on t h e
width of t h e stream. Readings a l s o should be made where t h e r e a r e abrupt
changes i n v e l o c i t y o r i n t h e depth of flow.
Plan View
Flow
Profile View
I
I
1.00
45
(c)
End View
Figure 3-25
(d 1
Throat Section
Trapezoidal flume
A cannnon method used t o determine mean v e l o c i t y r e q u i r e s t h a t readi n g s be taken a t only two p o i n t s i n each v e r t i c a l ; namely, 0.2 and 0.8 of
t h e sounded depth measured from t h e water s u r f a c e . The average of t h e s e
two readings i s t h e mean v e l o c i t y i n t h e v e r t i c a l . Where t h e depth i s too
shallow t o o b t a i n two r e a d i n g s , one reading taken a t 0.6 depth w i l l r e p r e s e n t t h e mean v e l o c i t y .
The discharge of each segment of stream between a d j a c e n t v e r t i c a l s
i s t h e product of t h e area OF t h e segment and t h e mean v e l o c i t y i n t h e
segment. If d l and d2 r e p r e s e n t t h e depths of flow a t two a d j a c e n t v e r t i c a l s , v l and v2 t h e r e s p e c t i v e mean v e l o c i t i e s i n t h e s e v e r t i c a l s , and W
t h e d i s t a n c e between t h e v e r t i c a l s , t h e n t h e discharge i n t h a t p a r t of t h e
c r o s s section i s computed as followe:
The t o t a l discharge of t h e stream i s t h e sum of such computations f o r
the e n t i r e cross section.
See Reference (1) f o r more d e t a i l e d information.
Water-Stage Recorder
0
A water-stage r e c o r d e r combines a c l o c k and an instrument t h a t draws
a graph r e p r e s e n t i n g t h e rise and f a l l of a water s u r f a c e w i t h r e s p e c t t o
time. Water-stage r e c o r d e r s are i n comnon u s e a t permanent gaging s t a t i o n s .
Water-stage r e c o r d e r s are d e s i r a b l e under t h e following c o n d i t i o n s :
1.
The flow i n t h e stream o r channel f l u c t u a t e s r a p i d l y , and
o c c a s i o n a l staff-gage r e a d i n g s would not give a satisfactory
e s t i m a t e of discharge.
2.
The gaging s t a t i o n i s hard t o g e t t o , o r t h e a v a i l a b l e
observers are n o t r e l i a b l e .
3.
There i s a need f o r continuous r e c o r d s of flow f o r l e g a l
o r t e c h n i c a l purposes.
By t h e combined use of t h e stage-discharge curve (Figure 3-26) and
t h e water-stage r e c o r d e r , a hydrograph of t h e f l o w i n a stream o r channel
may b e ' p l o t t e d . A hydrograph i s a curve developed by p l o t t i n g discharge
on a v e r t i c a l s c a l e a g a i n s t time p l o t t e d on a h o r i z o n t a l s c a l e . The a r e a
beneath t h e curve r e p r e s e n t s t h e volume of water p a s s i n g t h e gaging s t a t i o n
during any s e l e c t e d time period.
Discharge (cubic feet per second)
Figure 3-26
Stage-discharge curve f o r
unlined i r r i g a t i o n c a n a l s
Measurements by F l o a t s
The v e l o c i t y of a c a n a l or stream,and hence i t s discharge, nay be
determined approximately by t h e use of s u r f a c e f l o a t s and channel c r o s s
s e c t ions.
A s t r e t c h of t h e c a n a l , s t r a i g h t and uniform i n c r o s s s e c t i o n and
grade, w i t h a minimum of s u r f a c e waves, should be chosen f o r t h i s method,
Surface v e l o c i t y measurements should be made on a windless day, f o r even
under t h e b e s t c o n d i t i o n s t h e f l o a t s o f t e n are d i v e r t e d from a d i r e c t
course between measuring s t a t i o n s .
The width of t h e c a n a l should be divided i n t o segments, and t h e averThe segments should be narrower i n
the o u t e r t h i r d s of t h e c a n a l than i n t h e c e n t r a l t h i r d . F l o a t courses,
age depth determined f o r each segment.
should be l a i d o u t i n t h e middle of the s t r i p s defined by t h e segments.
For regular-shaped channels flowing i n a s t r a i g h t course under favorable
c o n d i t i o n s , t h e mean v e l o c i t y of a s t r i p i n t h e channel i s approximately
0.85 times i t s surface v e l o c i t y . This v a l u e i s an average of many observat i o n s . For any p a r t i c u l a r channel i t may be as low a s 0.80 o r a s high a s 0 .
The v e l o c i t y of t h e f l o a t i n each s t r i p , a f t e r being a d j u s t e d t o mean
v e l o c i t y , m u l t i p l i e d by t h e c r o s s - s e c t i o n a l a r e a of t h e s t r i p , w i l l g i v e
t h e discharge. The sum of t h e discharges of t h e s t r i p s i s t h e t o t a l d i s charge. On small streams, r a t h e r than d i v i d i n g t h e stream i n t o segments
a number of f l o a t runs can be made and an average of t h e s e used f o r t h e
s u r f a c e v e l o c i t y of t h e stream. The f l o a t method i s an approximate method
and should be used only w i t h i t s l i m i t a t i o n s i n mind.
Slope-Area Method
The slope-area method c o n s i s t s of using t h e s l o p e of t h e water s u r f a c e
i n a uniform r e a c h of channel, and t h e average c r o s s - s e c t i o n a l a r e a of t h a t
reach, t o give a r a t e of discharge. The d i s c h a r g e may be computed from
Manning's Equation 3-16:
A s t r a i g h t course of t h e channel should be chosen, a t l e a s t 200 f e e t
and p r e f e r a b l y 1,000 f e e t i n l e n g t h . The course should be f r e e of r a p i d s ,
abrupt f a l l s , sudden c o n t r a c t i o n s , o r expansions.
The s l o p e of t h e water s u r f a c e may be c a l c u l a t e d by d i v i d i n g t h e d i f f e r e n c e i n t h e water s u r f a c e e l e v a t i o n s a t t h e two ends of t h e course by
t h e l e n g t h of t h e course. I f it i s d e s i r e d t o develop a stage-discharge
curve f o r t h e channel, gage p o i n t s , c a r e f u l l y referenced t o a common datum
l e v e l , should be placed one on each bank of t h e channel and one i n t h e
c e n t e r of t h e stream, i n s t i l l i n g - w e l l s i f p o s s i b l e .
I n i r r e g u l a r channels, t h e a r e a and t h e wetted perimeter a t s e v e r a l
c r o s s s e c t i o n s i s r e q u i r e d and a mean value should be used i n computing
hydraulic r a d i u s .
Inasmuch a s t h e proper s e l e c t i o n of t h e roughness f a c t o r n f o r many
streams i s d i f f i c u l t , t h e discharge determined by t h e slope-area method i s
only approximate. Care must be taken t o determine t h e s l o p e and a r e a s
simultaneously when t h e water l e v e l s a r e changing. Various h y d r a u l i c t e x t books and handbooks provide t a b l e s t o assist i n t h e computation of d i s charges from t h e above f i e l d d a t a .
Velocity-Head Rod
The velocity-head rod i s a simple inexpensive rod t h a t can be used
t o measure t h e approximate v e l o c i t y i n open channels, i f depths and veloci t i e s a r e not too g r e a t . This infrequently-used method i s discussed i n
d e t a i l i n Chapter 9, Section 15, SCS National Engineering Handbook.
PIPE FLOW
The f o l l o w i n g methods may b e used i n d e t e r m i n i n g p i p e flow:
O r i f i c e Flow
Pipe o r i f i c e s , F i g u r e 3 - 2 7 , u s u a l l y a r e c i r c u l a r o r i f i c e s p l a c e d i n
o r a t the end of a h o r i z o n t a l p i p e . The head on t h e o r i f i c e i s measured
w i t h a manometer.
Where t h e orifice i s p l a c e d i n t h e p i p e , t h e d i s c h a r g e w i l l n o t be
f r e e and t h e head must b e measured a t p o i n t s b o t h upstream and downstream
from t h e o r i f i c e . For a f u r t h e r d i s c u s s i o n of t h i s t y p e of o r i f i c e , r e f e r
t o King's Handbook of H y d r a u l i c s ,
The p i p e o r i f i c e commonly used i n measuring i r r i g a t i o n w a t e r and t h e
d i s c h a r g e from w e l l s w i t h i n a r a n g e of 50 t o 2,000 gal-lons p e r minute h a s
t h e c i r c u l a r o r i f i c e l o c a t e d a t t h e end of t h e p i p e .
The p i p e must be l e v e l . A g l a s s . - t u b e manometer i s p l a c e d about
24 i n c h e s upstream from t h e o r i f i c e . N o e l b o w s , v a l v e s , o r o t h e r f i t t i n g s
should be c l o s e r t h a n 4 f e e t upstream from t h e manometer. The r a t i o of
t h e o r i f i c e diameter t o t h e p i p e d i a m e t e r should be no l e s s t h a n 0.50 nor
greater t h a n 0.83.
The r a t i o t o b e s e l e c t e d , however, must c a u s e t h e p i p e
t o flow f u l l . The head i n t h e manometer i s measured w i t h an o r d i n a r y
carpenter's rule.
as the orifice p
1"
Orifice plate
thick
with hole of exact size
F i g u r e 3-27
Pipe o r i f i c e
Discharge through the o r i f i c e is computed by Equation 3-25, or i t can
be read d i r e c t l y from Exhibit 3-18.
rwhere :
Q = orifice discharge i n gallons per minute
C = c o e f f i c i e n t which v a r i e s with the r a t i o of the o r i f i c e
diameter t o tHe p i p e diameter a s well a s with a l l the
other f a c t o r s a f f e c t i n g flaw i n o r i f ices. The value
of the c o e f f i c i e n t (C) may be taken £ran Figure 3-28
a = cross-sectional area of the o r i f i c e i n square inches
g = acceleration due t o gravity
32.2 feet per eecond
per second
h = head on the o r i f i c e i n inches meaaured above it8 center
-
Figure 3-28
Orifice coef f i c i e n t a
C a l i f o r n i a Pipe Method
B. R. Vanleer developed a method f o r measuring the discharge from t h e
open end of a p a r t i a l l y - f i l l e d h o r i z o n t a l pipe discharging f r e e l y i n t o t h e
a i r . This method can a l s o be adapted t o t h e measurement of discharge i n
small open channels where such flow can be d i v e r t e d through a h o r i z o n t a l
pipe flowing p a r t i a l l y f u l l and discharging f r e e l y i n t o t h e a i r .
The method has four requirements f o r accurate r e s u l t s : 1 ) The d i s charge pipe m u s t be l e v e l ; 2 ) it must discharge p a r t i a l l y f u l l ; 3 ) it must
discharge f r e e l y i n t o a i r ; and 4 ) t h e v e l o c i t y of approach must be a minimum. Figure 3-29 i l l u e t r a t e e one method of meeting theee requirements.
Other designs may be possible. With euch an arrangement, t h e only measurements necessary a r e t h e i n s i d e diameter of t h e pipe and t h e v e r t i c a l d i e t a m e from t h e upper i n s i d e surface of t h e pipe t o t h e surface of t h e flowing water a t t h e o u t l e t end of the pipe. The discharge may then be computed
by the equation:
(Eq. 3-30)
where
Q
discharge i n cubic f e e t per second
a = d i s t a n c e , i n f e e t , measured a t t h e end of t h e pipe,
from t h e top of t h e i n s i d e s u r f a c e of t h e pipe t o
t h e water ~ l u r f g c e
d = i n t e r n a l dimneter of the pipe i n f e e t .
This equation was developed fram experimental d a t a f o r pipes 3 t o
10 inches i n d i m e t e r . I n t e a t s made by t h e S o i l Conservation Service i t
was discovered t h a t f o r depths g r e a t e r than one-half t h e diameter of t h e
pipe, o r a/d l e s s than 0.5, t h e discharges d i d not follow t h e equation.
Extreme c a r e ehould t h e r e f o r e be taken i n using t h e equation and t a b l e s f o r
conditions where a/d i s less than 0.5.
Flow
Figure 3-29
Measuring flaw by the California pipe method
0
Tables 48 and 49 i n t h e Water Measurement Manual, Bureau of Reclamat i o n , provide a s s i s t a n c e f o r so1ving)the equation f o r discharge.
Coordinate Method
In t h i s method, coordinate8 of the j e t issuing from the end of a pipe
a r e measured. The f l w from pipes may be meaeured whether t h e pipe i s d i s charging v e r t i c a l l y upward, horizontally, o r a t sane angle with t h e h o t i aontal. Since the discharge pipe can be s e t i n a horizontal p o s i t i o n f o r
measurement purposes, t h e r e is no need here f o r a discussion of flow from
pipe i n an angular position.
Coordinate methode a r e used t o measure t h e f l o w from flowing wells
(discharging v e r t i c a l l y ) and from small pmping p l a n t s (discharging horieontally). These methods have limited accuracy owing t o the d i f f i c u l t y i n
making accurate meaeurementa of t h e coordinates of the jet. They should be
used only where f a c i l i t i e s f o r making more accurate maaeurementr by other
methods a r e not a v a i l a b l e and where an e r r o r of up t o 10 percent i s penniasible.
Figure 3-30
Required meaeuremento t o obtain
flow from v e r t i c a l pipes
To measure the flow from pipes discharging v e r t i c a l l y upward, i t i s
necessary t o measure only t h e i n s i d e diameter of t h e pipe and the height
of t h e j e t above t h e pipe o u t l e t (H), Figure 3-30. Exhibit 3-19 gives d i s charge values f o r pipe diameters up t o 12 inches and jet heights up t o
40 inches.
To measure the flow fran pipee discharging horizontally, it ie necesrary to'measure both a horieontal and a v e r t i c a l distance from the top of
t h e inaide of the pipe t o a point on the top of the jet. See Figure 3-31.
Theee horizontal and v e r t i c a l distances axe called X and Y ordinates,
reepec t i v e l y
.
Figure 3-31 Required measurements t o obtain
flow frm hoxitontal pipes
For reasonably accurate r e e u l t e , the diecharge pipe must be level and
long enough t o permit the water t o flaw smoothly aa it isaues from the pipe.
Exhibit 3-20 gives diecharge valuee f o r pipe diameters up t o 6 inches where
t h e ordinate X ie eelected t o be 0, 6, 12, o r 18 inchee. For pipes flawing
l e a e than 0.8 f u l l a t the end, the v e r t i c a l distance Y can be measured a t
the end of the pipe where X = 0. Exhibit 3-20 i e ueed t o obtain the diecharge. Exhibit 3-20 i s a l e o applicable e i t h e r t o conditione of f u l l f l m
o r p a r t i a l flow.
T I N S THIS
TnIS
CIVeS YOU THIS
VOLW
1 gallon (gal)
I
231
1
cubic inchsm (cu in.)
I
I
.I337
1
cubic f e e t (cu f t l
I
1 m i l l i o n g a l l o n (mg)
acre feet (acre-ft)
3.0689
c u b i c inchor
1,728
1 cubic f o o t
7.48
gallone
1
cubic f e e t
43,560
1 a c r e f o o t (amount of wacer
required t o cover one a c r e
one foot drop)
325,850
I
ga 1l o n r
1
1
12
I
L gallon
8.33
pounds ( l b )
1 cubic f o o t
62.4
Pod*
1 g a l l o n par minuto ( g p )
c u b i c foat per roeond ( c f s )
0.00223
gallon* plr day (24 hour.)
1,440
r
I
I
I
1 million
r all on par 24
hour.
1.M7
(wd)
I
a c r e inchma
I
cubic f e e t p s r second
1
69 5
1 cubic foot
p r rmcond
I
1
I
7.48
gallon.
I
per recond (gps)
gallonm p.r minute
448.8
'666,272
I
,992
gallon8 psr minute
1
1.983
g a l l o n # pmr day (24 hours)
acre inch p r hour
a c r e f o o t por day (211 hour*)
I
GO
I
I
II
I
1 rniner'm inch
50
38.4
3
5
11.25
f
I
-2/1 /
-
9
I
1
I
I
minor*' incher ( l e g a l value
2')
miner's inches (lmgal value
2
'
)
minor's
incher ( i n Colorado)
miner's inchem ( i n B r i t i s h
Columbia)
I
gpm when e q u i v a l e n t co 1/40
recond foot
i
gpa h e n e q u i v a l e n t t o 1/50
oecond foot
In Arizona, C a l i f o r n i a , Montana, Nevada and Oregon
I n Idaho, Kanaas, Nebrarka, New Hexlco, North Dakota, South Dakota, and Utah
Exhibit 3 - 1
1
Water volume, weight and Flow equivalents
Exhibit 3-2 Preraure d i a g r a s and methods of computing
hydrostatic loads (Ref. NEH Section 5 , ES-31)
(Sheet 1 of 2 )
Exhibit 3-2
Pressure diagrams and methods o f cmputinn
hydrostatic loads (Ref. NEH Section 5 , ES-31)
(Sheet 2 of 2 )
2ao
2 0.0
15.0
IQO
9.0
F
w ao
7.0
o,
3
W
x
5.0
4.0
I . .
.
.
10
I
L.0
1.5
1
.o
2.0
1.1
5.0
THICKNESS OF BOARD IN INCHES
ao
I .o
1.5
CORRECTION
Exhibit 3-3
2.0
FACTOR
Required thickness of flashboards ( r e f .
Western S t a r e s Engineering Handbook Section 6)
Exhibit 3-4 Head loss coefficients for circular and square
conduite floving full ( R e f . NEH Section 5 , E S - 4 2 )
DiscIkrgB (01-,Cubic feel pw M
Discharge (01-Cubic Feet per Sacmd
~-
-
Solution of HazenWilliams formula for
round pipes (Ref. NEH
Section 5, ES-40)
Q
1-inch
Gallons
per min.
1.189 ID
1%-inch
1.502 ID
1%-inch
For IPS Pipe
2-inch
2%-inch
1.720 ID 2.149 ID 2.601 ID
3-inch
3%-inch
Q
Gallons
3.166 ID 3.620 ID per min.
Friction Head Loss in Feet per Hundred Feet
2
4
6
8
10
.15
.54
1.15
1.97
2.98
.04
.17
.37
.63
.95
.02
.09
.19
.32
.49
.03
.06
.ll
.16
.01
.02
.04
.06
.O1
.02
.01
4
6
8
10
15
20
25
30
35
40
45
50
6.32
10.79
16.30
22.86
2.03
3.46
5.22
7.32
9.75
12.46
15.51
18.87
1.04
1.78
2.70
3.78
5.03
6.46
8.02
9.75
.35
.60
.91
1.27
1.70
2.18
2.71
3.30
.14
.23
.36
.50
.67
.86
1.07
1.30
.05
.09
.13
.19
.25
.32
.40
.49
.02
.04
.07
.10
.13
.17
.21
.25
15
20
25
30
35
40
45
50
11.64
13.64
15.85
18.19
20.65
23.28
3.94
4.62
5.36
6.14
6.99
7.86
8.81
9.79
10.82
11.89
1.54
1.81
2.10
2.42
2.75
3.10
3.47
3.85
4.25
4.69
.59
.69
.80
.92
1.06
1.19
1.33
1.48
1.64
1.80
.30
.36
.41
.47
.55
.62
.69
.77
.85
.93
55
60
65
70
75
80
85
90
95
100
14.21
16.69
19.35
22.21
5.59
6.56
7.63
8.73
9.94
11.20
12.51
13.90
15.39
16.91
2.14
2.52
2.92
3.36
3.82
4.29
4.80
5.35
5.92
6.50
1.11
1.31
1.53
1.75
1.99
2.24
2.50
2.79
3.08
3.38
110
120
130
140
150
160
170
180
190
200
20.19
23.73
7.77
9.12
10.57
12.11
13.78
15.52
17.37
19.27
21.33
23.45
4.04
4.76
5.51
6.32
7.18
8.10
9.07
10.08
11.13
12.22
220
240
260
280
300
320
340
360
380
400
13.40
14.59
15.86
17.15
18.50
420
440
460
480
500
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
22.48
.
2
Table based on Hazen-Williams
equation - C1 = 150
220
240
260
280
300
320
340
360
380
400
420
440
460
480
500
E x h i b i t 3-7
To find friction head loss in PVC
or ABS pipe having a standard dimension
ratio other than 21, the values in the
table should be multiplied by the appropriate conversion factor shown
below:
SDR No.
13.5
17
21
26
32.5
41
51
Conversion
Factor
1.35
1.13
1.00
.91
.84
.785
.75
F r i c t i o n head l o s s i n semirigid p l a s t i c i r r i g a t i o n
p i p e l i n e s manufactured of PVC or ABS compounds.
Standard dimension r a t i o
SDR = 21. (Ref. SCS Fort Worth, Texas, 1967)
-
Sheet 1 of 5
Q
Gallons
per min.
9.728
!et per Hu
ID
I u.sw, m
Q
Gallon8
per min.
red Feet
15
20
25
30
35
40
45
50
55
60
.01
65
70
.01
.O1
01
01
.01
.02
75
80
85
90
95
100
.
.
.02
.02
.03
.03
-07
.08
110
120
130
140
150
160
170
180
190
200
.09
220
10
240
260
280
300
320
340
360
380
400
.04
.05
.05
olZ
.
-07
.12
.14
.17
.19
.21
.24
.26
-28
.31
.34
.37
.41
.43
-52
420
440
460
480
500
550
600
.61
Exhibit 3-7
Fr l e t ion head loss i n ammfr igid plart i e irrigation
pipelinen manufactured of PVC or ABS compound8
Standard dimenaion r a t i o
SDR = 21. (Ref. SCS
Fort Worth, Texar, 1967)
-
.-
Sheet 2 of 5
Q
2'
Gallons
Gallons
per min.
per min.
Hundred Feef
.21
.24
.28
-32
.36
.40
.44
.49
.54
-59
.65
.70
.76
.82
.88
.95
1.01
1.08
1.15
1.30
1.45
1.62
1.79
1.97
2.15
2.34
2.55
'2.76
2.97
3.20
3.43
3.67
3.92
4.17
4.43
4.71
4.97
5.27
5.56
5.85
6.17
6.47
6.79
7.11
Exhibit 3-7
FrLction h a d lor8 Ln ammirigid plastic irrigation
piprlimr unufacturrd of PWZ or ABS compoundm.
Standard dlwnrion ratio SDR
21. (Rmf. SCS
Fort Worth, Taxar, 1967)
-
-
-
sheet 3 of 5
3-87
For PIP Pipe
Q
:allone
per d m .
Table baaed on Buea-Villi-
equation
- C1
-
150.
fa find f r i c t i o n h e 4 lor. i n
or N M pipe having
atandard
dirsPrioa r a t i o other than 21, the
valuer i n the table 8bDuld be r u l t i p l i e d by the appropriate cowera i m Euctor mholm b e l w :
Exhibit 3-7
F r i c t i o n haad lor8 in remlrigid p l a a t i c irrigation
p i p l i m e manufactured of PVC or ABS coapoundr.
Standard d b n a i o n ratio 5061 21. (Uf. SCS
Fort Worth, Taxm, 1967)
-
-
-
3-88
For PIP Pipe
Q
10-inch
Gallons
Gallons
per win.
9.228 ID
11.074 ID
per Hundrec
.31
.36
-41
.46
-52
.58
.u
.70
.77
.83
.91
.98
1.Q
1.14
1.22
1.30
1.39
1.48
1.67
1.87
2.00
2.29
2.52
2.76
3.01
3.27
3.54
3.82
4.10
4.40
4.71
5.02
5.35
5.68
6.03
6.38
6.74
7.11
7.50
7.89
8.28
8.69
9.11
Exhibit 3-7 miction & ~ dlo88 in remirigid plmrtlc Irrigation
p i p l i n m r unufmctured of P W or rllBS compoundr.
Standard d b n r i o n ratio 8DR
21. (Ref. SCS
Port Worth, Tmxar , 1967)
-
-
-
per rrin.
I
PIPE ENTRANCES
SHARP -CORNERED'
INWARD PROJECTING PIPE
'
HOODED INLET
-
BELL MOUTH
SLIGHTLY ROUNDED
I
PIPE BEN1
STANDARD -TEE
STANDARD 909- ELBOW
Exhibit 3-8
LONG RADIUS ELBOW
-
Head loas coefficients for p i p e entrances and bends
(Sheet 1 of 2 )
I
PIPE BENDS
4s0 ELBOW
I
ENLARGEMENTS AND CONTRACTIONS
-
7
SUDEN ENLARGEMENT
v
KaE
T
SUDDEN CONTRMTION
GRAWAL ENLARGEMENT
K FACTORS FOR A 8 8
SEE:
REFERENCEt
HANOBOOK OF HYDRAULICS
B'Y H.W. KING
PAGES 6
- 18
(FOURTH EDITION)
WIDE OPEN
FOOT VALVE
VAI IES
RPRTIALLY
K
CLOSED
FOR K FACTORS
REFERENCE 1
SEE:
GLOBE VALVE
BY H.W. KING
ANGLE VALVE
PAGES 6 18
GATE VALVE
Exhibit 3-8
-
(FOURTH EDITION)
Head lora eoefficientm for pipe entrances and bends
(Sheet 2 of 2 )
(5)
10,000
EXAMPLE
-
- 1-,
-800
-
-600
- 500
/
-400
m
-
/'
300
/
/
4
3
"
-
100
-60
O-40
,PO
----1I0
-6
-I
-4
:
SO
-
3
0 SGALE
ENTRANGE
TYPE
(11
wmmrr
dth
healroll
a
ern 111m i t ~
131
o r w e end
preJeetlag
hwdwmll
To w r meelm 121 or (3) p e W t
horlzmtelly tm maah ( ~ ) , t h r o
n r rtrmlght locllnrl 1100 t h t y h
D and 0 armlam, w t a w m a am
Illrmtretel.
e
- 1.0
Exhibit 3-9 Headwater depth for concrete pipe culverts with
inlet control (Ref. Hyd. Eng. Cir. No. 5, USBPR,
1965)
Exhibit 3-10
Headwater depth fox CM p i p e culverts with i n l e t
control (Ref. Hyd. Eng. Cir. No. 5, USBPR, 1965)
Exhibit 3-11 Head for concrete p i p e culverts £loving f u l l with
outlet control n = 0.012 (Ref. Hyd. Eng. Cir.
No. 5 , USBPR, 1965)
Slop.
so--.
W H M D OUTLET CULVERT F M l N G FULL
Exhibit 3-12
-
Head for CM pipe culverts flowing full with
outlet control n
0.024 ( R e f . Hyd. Eng. Cir.
No. 5, USBPR, 1965)
Section
Exhibit 3 - 1 4
Solution o f ?tanning'm formula for uniform
flow (Ref. NEH Section 5 , E S - 5 4 )
Sheer 1 o f 4
Exhibit 3-14 Solution of thnning'a formula for uniform
Sheet 2 of 4
flow (Ref. NEH Section 5 , ES-54)
Exhibit 3-14 Solution of Manning's formula for uniform
flow (Ref. NEH Section 5, ES-54)
m
0.1.
RH
a,r
a*
err
0.I4
a11
RIt g
/'
0.11
Exhibit 3-14 Solution of Manning's formula for uniform
f l o w ( R e f . NEH Section 5 , ES-54)
S k e t 4 of 4
3-100
disc ha^, Q,for oreat length,
Fed
0.10
. 11
. 12
.. 14
la
.. 1s
I6
17
... 18
19
I font
1.5
feet.
2 feet
1feet
4 feet
8Wond-jtd
Smcomti- mi
3nond-/sc
0. 11
. 12
. 14
. 16
. 17
. 19
.., a123
25
.27
.a0
.21
.29
.
a1
.a4
.a6
.24
.as
. 26
.27
..28
. a8
.40
.4a
.46
.48
. 29
-60
.80
. 68
. 33
.5R
darond-Jrd
0. ItJ
. 1R
.!lo
..2I
22
.28
.81
.81
.87
h o d - &
a d
. 86
0. 88
. a7
.4a
.47
.M
.w
.w
.26
. 28
. az
;48
.on
.47
.61
.bs
.M
.70
.7a
.88
.. 4427
.a
.sQ
.89
.w
..M
17
.8I
.w
.68
.72
.7a
.m
.84
.a
-6u
.?2
. 77
.a
1. 18
.86
.91
.MI
1. 03
1. 28
I. a1
1. 88
1. 48
1. 58
1. 61
1. 69
1. 77
1. 88
.M
.. a1aa
.w
-8s
.a6
.MI
1. 00
1. 81
1. 08
1. it
1. 17
1. 41
1. 61
1. 67
2 a7
1. 21
1. 28
1. 8
a 413
.a8
.m
.40
.41
.42
.48
.44
.4b
.46
.65
m
...7?1
4
.77
.m
.a
.I
.(18
.91
.M
.47
.99
1. M
.49
1. 08
.48
.M)
.61
.52
.5a
.M
.sb
1. w
1. 1 1
1. 15
1. 18
1. 21
1. 25
1.
as
.66
1. 81
.59
1. 85
1. 88
1. 42
.57
.MI
.Bo
'.61
.62
.u
.64
8 feet
10 feet
Strond- uut
8econd-ftet
1, 05
I. 45
1. 49
1. 52
1. be
I. 80
Exhibit 3-15
.92
1. 01
1. XI
1. 86
1. 40
1. u
1. 49
1. 64
1. 19
1. 64
1. ai3
1. 78
1. 78
1. &
1. 88
1. m
1. 98
a04
2. 08
a 1s
2. 20
2 35
2 81
286
24a
1. ro
1. 69
1. 7&
1.p1
1M
2 11
9. Po
s.!m
1. 81
9.16
26s
a 74
1. 04
9.00
3.08
ao8
1. gs
am
a. 18
220
+w
2.88
*a
a 12
an
a a1
x 41
8. C1
1. 46
1. a
a 61
s. 78
ass
2Bo
a 09
alro
a 6'1
2 74
2. 81
9. 88
296
am
a. 10
8. 17
am
d
Sarond-fttt
0. 62
.64
71
. 93
1. 04
1. LO
1. 24
1, 39
1. 21
1. 88
1. 56
1. 74
.w
1. 15
1. 27
1. 89
1. 51
1. 70
1. 86
a ia
a. a3
1. 64
2. 20
2. 7K
1. 78
1. 91
2, 55
a a7
2. 97
a 19
a
.bo
. h7
.
..8079
1. 08
1. 11
1. 1Q
.
I 1. 28
1. M
1. a7
1. 00
1. 46
1. 07
1. 12
1. 18
1. 18
1. I
.87
6 feet
~
.n
. aa
.81
. a2
L,of-
4. 01
4. 16
4. M
!
4.
w
4. 47
4. 69
4. 6Q
4. 81
4. m
1, 56
1. 6s
1. 76
1. 85
1. 9s
2 06
1. 18
2, 26
a. a7
0. 48
2. 60
2. 71
9. 82
294
am
a. 18
aso
a. 42
a s4
.7a
.8a
1..52
a 06
a. 19
2 BS
2. 48
2. 68
2 78
2. 93
ao8
a. 2s
a 41
8. 58
3. 76
8. 92
4. 08
4. w
e 44
4. 62
4. 80
4. w
a 67
A 17
6. 86
6. 66
8. 76
4. 06
4. 18
a 34
4. 45
8.74
4. I 8
a 95
a 80
a. ea
4. 82
4. 72
4. 88
4. 88
6.19
an
6. 49
5. 58
6. 70
5.8s
6. 00
6. 14
6. 29
B. 44
6.58
6. 94
6. 14
6. 64
7. 15
*
0 . J
.97
a. oa
2. 78
2. M
a. I t
a 81
a 51
a 71
a a2
4 13
4. 34
4. 66
4. 78
5. 01
6.'24
6. 47
5. 70
5. 94
6. 18
8. 48
6.67
6. 9a
7. 18
7. 48
7. 68
7. 95
a 22
a 48
a 75
9.oa
9. ao
7. 57
7. 79
9. 58
9. $4
10. 1
10. 4
8.M)
10.7
7. 86
a 22
8. 4a
a 65
8.88
9. 10
9. 33
8. 66
9. 78
ia o
1. 98
2. 58
a 4a
am
am
4. 14
4. 88
4 65
4. 91
5. 17
5. 44
6. 71
6. 99
6. 27
8.511
6.86
7. 14
7. 44
7. 74
a OK
US6
8. 87
8.88
9. a1
9.89
9. OB
10. 8
10. 6
11. 0
11. a
11. 7
12. 0
12. 4
12. 7
13. 1
11. 8
11. 8
11. 9
la. 4
19. 8
14. D
14. 6
14. 9
la. 2
12.6
12. 8
16.a
15. 7
18. 1
11.
0
13. 1
la. 4
Discharge for contracted rectangular weirs
( R e f . Parshall, R.L., Measuring Water in
Irrigation Channels, U.S. D e p t . Agr. Cir.
843, 1950)
(Sheet
16. 4.
16. 4
r
Discharge, Q, for crest length,
Head, HI
1 foot
--
Fed
0. 66
.a
. 07
.86
.69
..7071
. 74
.76
.76
. 77
.78
.79
1.5 feet
1
I
2 feet
1
3 feet
1
4 feat
L,of-
I
6 feet
8 feet
10
feet
--
Inchea
Wio
7'Ho
8Ka
8%a
8%
8%
9
9%
9%
9%
9%
E x h i b i t 3-15
Discharge for contracted rectangular weirs
( R e f . Parshall, R.L., Xeasuring Water in
Irrigation Channels, U.S. Dept. Agr. Cir.
8 4 3 , 1950)
(Sheet 2 of 3 )
Discharge. Q, for crest length, L, of-
Head, Hi
1 foot
4 fe<!t
.?ecnncl-fee~
.......
Second- eel
8. 1 6
8. 26
8. 35
8. 46
8. 56
.-....
......
......
..----
......
I
6 fcct
Second-Jeel
10. R
16. 8
17. 0
17. 2
Sccorrd-Jccl
42. 7
8. 66
.......
--
........
..----
---".......
......
-
......
......
......
--.-"......
......
.
......
.......
......
..----
........
........
........
-
.,
-"
........
........
..- - .-
--
.........
........
........
........
.........
........
........
---
-----
........
IValues of discharge for heads u t o 0.20 foot (crest lengths 1, 1.5, 2, 3, and 4 fcct) do not follow thc formula, but are taken directly
from the calibration ourve. The Jsoharge for heads 0.10 t o 1.5 feet for the 6-, 8-, and 10-foot wcirs aro as cornpntd by the formula
9=3.33 (L-0.211) nu¶.
Exhibit 3-15
Discharge for contracted rectangular weirs
(Ref. Parshall, R.L. , Measuring Water, in
Irrigation Channels, U.S. Dept. Agr.
Cir.
(Sheet 3 of 3 )
Dieoharge, Q. for m e t 1engt.h. L,ot-
Bed,HI
1 foot
1.6 feet
2 fect
Serond-,feel Serond-fed
0. 23
0. 16
. 26
. 18
.21
-29
. 32
. 24
.36
. 26
-29
. az
. 36
. 39
. 42
.45
. 48
. 52
.55
. 59
. 39
.43
.47
. 51
. 56
. 60
. 64
. 69
. 74
3 feet
.43
.48
.64
... 59
85
71
. 77
. 83
.90
. 97
1. 04
1. 1 1
1. 18
. 63
. 87
. 70
. 74
. 79
. 84
.89
. 94
. 99
1. 04
1. 25
1. 33
1. 40
1. 48
1. 56
. 83
. 87
. 91
. 95
1. 10
1. 15
1. 21
1. 27
1. 64
1. 73
1. 32
1. 80
1. 89
1. 98
1. 04
1. 09
1. 13
1. 18
1. 23
2. 07
2. 16
2. 25
2. 34
2. 43
1. 28
1. 32
1. 37
1. 42
1. 47
2.53
2.62
2. 72
2. 81
2. 91
1. 53
1. 68
1. 74
3.01
3. 11
3. 21
3.32
3. 42
1. 79
1. 85
1. 90
1. 96
2. 02
3. 53
3. 64
3. 74
% 85
3. 96
2. 07
4.07
4. I8
4. 30
4. 41
4. 53
1. 58
1. 63
2. 13
2. 19
2. 25
2.31
2. 37
2. 43
2. 49
2. 55
2.62
10 feet
8econd-feel
0. 33
. 38
.79
1. 00
8 feet
4. 64
4. 76
4. 88
5.00
5. 12
Exhibit 3-16 Discharge for Cipolletti weirs ( R e f . Parshall,
R.L., Measuring Water in Irrigation Channels,
U . S . Dept. Agr. Cir. 843, 1950)
(Sheet 1 of 3 )
3-104
niscliarge,
Head,
Q. for
1.5 feet,
2 lcct
3 fcet
4 feet
. 66
. 67
.68
.69
. 70
.71
. 72
. 73
.74
.75
. 76
.77
. 78
. 70
. 80
. 81
.82
. 83
- 84
.85
.86
.87
. 88
. a9
.w
.91
.92
. ga
. 94
.95
.96
.97
. 98
.99
1. 00
1. 01
I. oa
1. 03
1. 04
1. 05
1. 06
1. 07
1. 0s
1. 09
ti feet
...
I
Fcct
L,of-
-1 foot
0.65
crcst Icnyth,
HI
Seconrl-feel
1. 84
1. 89
1. 93
1. 98
2. 02
Serond-feet
2. 68
2. 75
2. 81
2. 87,
2. 94
Serond-fed
3. s3
3. 61
3. 70
3. 79
3. 87
Serond-feel
5. 24
5 36
5. 48
5. 61
5. 73
2. 07
2. 12
2. 16
2. 21
2. 26
3. 01
3. 07
3. 14
3. 21
3. 28
3. 05
4. 04
4. I3
4. 22
4. 31
5. 80
5. 99
6. 12
6. 24
6. 38
2. 31
3. 35
4. 40
4. 49
4. 58
4. 67
4. 76
6. 51
6. 61
6. 77
6. 90
7. 04
2.-36
2. 41
2. 46
2. 51
3. 42
3. 49
3. 56
3. 63
a. 70
Second-Jeel
6. 95
7. 11
7. 28
7. 44
7. 61
7. 77
7. 04
8 feet
--.
Seroidfcet,
10. 6
10. 8
11. 1
11. 3
11. 6
11. 8
12. 1
12. 3
12. 6
12. 9
10 fcet
....
SurodJwl
14. 1
14. 4
14. 8
15. 1
15. 4
Serond-fcct
17. 6
18. I
la 5
18. 9
19. 3
15. 8
16. 1
18. 5
17. 1
19. 7
20. 1
20. 0
21. 0
21. 1
8. 80
8.97
9. 15
9. 33
13, 1
13. 4
13. 6
13. 0
14. 2
17. 5
17. 8
18. 2
18. 6
18. 0
21. 0
22. a
22. I
23. 2
23. 6
I!). 3
8. I 1
8. 28
8. 45
8.62
16. 8
2. 56
2. 61
2. 66
2. 71
2. 77
3. 77
3. 84
3.92
3. 99
4. 85
4. 95
5. 04
5. 14
5. 23
7. 18
7. 31
7. 45
7.59
7. 73
9. 51
9. R!)
9. 87
10. 0
10. 2
14. 5
14. 7
15. 0
15. 3
15. 6
20. 0
20. 4
20. 7
24. I
24. 5
25. 0
25. 5
25. 0
2. 82
2. 87
2. 93
2. 98
3. 04
4. 07
4. 14
4. 22
4. 29
1. 37
5. 33
5. 4a
5. 52
5. 62
5. 72
8. 15
7. 87
8. 01
10. 4
10. 6
10. 8
11. 0
11.2
15. 8
10. 1
18. 4
16. 7
17. 0
21. I
21. 5
21. 9
22. 2
22. n
20. 4
20. 9
27. 3
27. 8
28. 3
3. 09
3. 15
3. 20
3. 26
3. 32
4. 45
4. 53
4. 60
4. 68
4. 76
5. 82
5. 92
R, 02
6. 13
6. 23
11. 4
11. 6
17. 2
17. 5
17. 8
18. 1.
18. 4
23. 0
23. 4
23. 8
24. 2
24. 5
28. 7
29. 2
29. 7
30. 2
30. 7
3. 37
3. 43
3. 49
3. 55
3. 61
4. 84
4. 02
5. 00
5. 09
5. 17
6. 33
6. 44
6. 55
0. 04
6. 75
24. 9
25. 3
25. 7
26.1
26. 5
31. 2
31. 7
32. 2
32. 7
33. 2
3. 67
5. 25
6. 86
6. 96
20. 2
26. 9
27. 3
27. 7
28. 2
28. 6
33. 7
34. 2
34. 7
35. 2
35. 7
36. 2
36. 7
37. 3
57. R
38. 3
......
......
......
......
......
-
-.
......
......
-
5. a3
5. 42
5. 50
5. 59
a 30
8. 44
a 59
a 73
9. 32
la. 3
12. 5
12. 7
12. 9
13. 1
YO. 1
10. 2
10. 4
10. 6
7. 20
7. 40
7. 51
7. 62
7. 73
11. 7
11. 0
12. 1
9. 48
9. 02
g. 78
9. 93
7. 07
7. 18
5. 67
5. 76
5. 84
5. 93
6. 02
8. 88
9. 03
9. 17
13. 3
13. 5
13. 7
13. 9
14. 2
10. 7
18. 7
19. 0
19. 3
19. 6
19. 9
20. 5
20. 8
21. 1
21. 4
14. 4
14. 6
14. 8
15. 0
15. 2
21. 7
22. 0
21. 4
22. 7
23. 0
29. 0
20. 4
29.8
7. 84
lo. 9
If. 0
11. 2
11. 4
11. 5
31. 1
31. 5
31. 9
32. 4
32. 8
38. 8
39. 4
39. 9
40. 4
33. 2
33. 6
34. 1
34. 5
41. 5
42. 1
42. 6
43. 2
43. 7
1. 1u
1. 11
1. 12
1. 13
1. 14
.."_
......
6. 11
6. 20
6. 29
6, 38
7. 96
8. 07
8. 18
8. 20
8.41
11. 711. 8
12. 0
12. 2
12. 3
15. 4
15. 6
15. 8
16. 0
16. 3
23.
23.
23.
24.
24.
1. 15
1. 16
1. 17
1. 18
1. I 9
0. 56
......
6. 85
~ - - . " . 0. 74
a 53
12. 5
12. 7
12. 8
13. 0
16. 5
16. 7
16. 9
17. 2
17. 4
24. 9
25. 2
25. 6
25. 9
26. 2
......
......
......
6. 47
......
......
___-_-
6. 83
6. 93
19. e
8.65
8. 76
8. 88
am
13. 2
3
0
9
3
6
30. 2
30. 6
3.5,n
Exhibit 3-16 Discharge f o r Cipolletti weirs (Ref. Parshall,
R.L. , bleasuring Water in Irrigation Channels,
U.S. Dep t Agr C'ir 8 4 3 , 1950
.
.
.
41. 0
Discharge, Q, for creat length, L, of-
Head, HI
Feet
1. 20
1. 21
1. 22
1. 23
1. 24
Inches
1 foot
1.bfeet
Second-fsd
Second- cat
7.
7. 11
7. ao
7. 80
7. 40
---.-.
---.--
14
14p
14h
-----------
------
,a
I
2frt
Srmd-fed
9.
la
9. 24
9. 86
9. 48
9. BO
I
6 feet
8 t h
d
Second- ect
la.
18.5
13. 7
13. 9
14. o
Stcod-feel
17. 6
17. 8
la o
la a
la 5
8feet
1
10 feet
a
%~(lnd-feet
as. 4
35. 8
Second- cut
41
44 8
45. 4
45. 9
46. 5
So. 5
as, a
as. 7
a7. a
30.8
30.6
aas
40. 4
40. 8
21. 1
?I. 8
21. s
21. s
22. o
31. 7
82.0
32. 4
32. 7
aa. 1
42. 2
42. 7
48. a
540
44 1
6.5. a
a0. i
1. 81
1. 32
I
61. 1
1. 34
1. a6
1. 88
1. 89
-------- -...-----.-16.0
.
1. a7
l6Sa
lSLKo
-
-
--------
16.6
16.8
-._"--------
.
4a
7
62. 8
68. 4
54 6
23.5
as. s
24.0
a4 a
14 5
a4 8
I
I
1 Valuea of discharge for head8 up to 0.20 foot (omt length 1, 1.5, 2,a and 4 feet) do not follow the formula but are hken directly
from t,he calibration curve. The dlsoham for ha& 0.10 to 1.6 feet for the &, '8,- and 10-foot weir. are as oomputed by the formula
Q- ~ ~ L W I = .
~ x h i b i t3-16
Discharge f o r C i p o l l e t t i weirs (Ref. P a r s h a l l ,
R.L., Measuring Water i n I r r i g a t i o n Channels,
U.S. Dept. Agr. Cir. 843, 1950)
(Sheet 3 o f 3)
Exhibit 3-17
Discharge for 90° v-notch weirs (Ref. Parshall,
R.L., Measuring Water in Irrigation Channels,
U.S. Dept. Agr. Cir. 843, 1950)
3-in.
Head
(inches1
orlfice
6-in.
Pipe
;.p.m.
82
94
104
114
123
132
140
148
156
164
171
177
183
189
195
200
205
210
214
219
224
229
234
238
243
248
252
257
262
266
271
275
280
4-in.
orif ice
%in.
orifice
6411.
orif ice
7-in.
mif ice
8411.
orif i c e
10-in.
pipe
10-in.
Pipe
G.p.m.
935
loco
1120
1194
1266
1336
1404
1471
1529
1585
1641
1697
1753
1809
1865
Exhibit 3-18 Discharge from circular p i p e orifices w i t h free
discharge (Ref. Layne Well Water Systems, Layne
and B o w l e r , Inc. , M e m p h i s , Tenn. , 1951)
Diameter of pipe (inches)
Jet
height
(inches)
2
Std
.
3
Std
:.p.m.
57
69
78
86
92
98
10.4
115
125
134
143
152
167
182
195
208
220
248
275
300
320
. 0.D.34 Std . O.D. 5Std .
G.p.m.
G.p.m.
75 86 103 115
95 108 132 150
112 128 160 183
124 145 163 210
135 160 205 235
144 173 225 257
154 184 240 275
169 205 266 306
186 223 293 336
202 239 315 360
215 254 335 383
227 268 356 405
255 295 390 450
275 320 420 485
295 345 455 520
315 367 480 555
333 386 510 590
377 440 580 665
420 Ce5 640 740
455 525 595 800
490 565 745 865
6
3.D.
Std
.
O.D.
8
S.td .
10
12
Std . O.D. Std .
O.D.
G.p.m.
137 150
182 205
225 250
262 293
295 330
320 365
345 395
385 445
420 485
450 520
480 550
510 585
565 650
610 705
655 755
700 800
740 850
830 960
925 1050
LOO0 1150
LO75 1230
Standard pipe .
' Outside diameter of well casing .
.
Exhibit 3-19 Flow of water from v e r t i c a l p i p e s (Ref Discharge
Curves in Utah Eng . Expt . St.a. Bulletin 5 .
"kleasurement of Irrigation Water, June 1955)
Y
Size of pipe (naminal d i a m e t e r )
( inches )
Exhibit 3-20
Flow of water from horizontal p i p e s (Ref. Purdue
Eng. Expt. B u l l e t i n 32, "Measurement of pipe flow
by the coordinate method," ~ u g u s t1928)
(Sheet I of 3 )
WHEN X = 6 INCHES
Size of pipe (naminal diameter)
Y
(inches )
-
0.24
.36
.48
.60
.72
.84
-96
1.08
1.20
1.80
2.40
3.00
3.60
4.20
4.80
5.40
6.00
6.60
7.20
7.80
8.40
WHEN X = 12 INCHES
.96
1.08
1.20
1.80
2.40
3.00
3.60
4.20
4.80
5.40
6.00
6.60
7.20
7.80
Exhibit 3-20
Flow of water from horizontal p i p e s (Ref, Purdue
En&. Expt. Bulletin 32, ''Measurement af p i p e flow
by the coordinate method," August 1928)
(Sheet 2 of 3 )
3-111
WHEN X = 18 INCHES
Y
Size of pipe ( n d n a l diameter)
(inches)
1.80
2.40
3.00
3.60
4.20
4.80
5.40
6.00
1 6.60
7.20
7.80
8.40
Exhibit 3-20
Flow of water from horizontal pipes (Ref. Purdue
Eng. Expt. Bulletin 32, "Measurement of p i p e flow
by the coordinate method," August 1928)
(Sheet 3 of 3 )
Chapter 3
References
1.
Handbook of Hydraulics, King & Brater, Fifth Edition
2.
Hydraulic Charts for the Selection of Highway Culverts,
Hydraulic Engineering Circular No. 5, Bureau of Public Roads,
Department of Transportation
3.
Hydraulic and Excavation Tables, U. S. Department of Interior,
Bureau of Reclamation
4. Hydraulic Tables, U. S. Department of Defense, Corps of Engineers
5. Chow, VenTe; Open-Channel Hydraulics, McGraw-Hill Book Co., Inc.,
1959
6. National Engineering Handbook, Section 5, Hydraulics
In addition to the above references, liberal use was made of
material from the following references:
a.
Hydraulics Correspondence Course by George A. Lawrence,
State Conservation Engineer, State of Utah
b.
Utah State Engineering Handbook, Section 5 , Hydraulics
c. Vinnard, J. K.; Elementary Fluid Mechanics, John Wiley
and Sons, Inc , 1948
.