Hydraulics of structures

1. Hydraulics of Structures

2. What are structures?
 Structures in this context are simply something
placed in the channel to either measure or control
flow.
 Example: A principle spillway is used as part of a
dam design to control the rate at which water is
discharged from a reservoir.
 Include both inlet and outlet control devices.
 Control devices can operate as :
 Open channel flow in which the flow has a
free surface or
 Pipe flow in which the flow is in a closed
conduit under pressure.

3. Most basic principle of hydraulics
of structures:
As head on a structure increases, the flow that
is discharged through the structure increases.
 Figure 5.1 (Haan et al., 1994) shows the
head-discharge relationships for several flow
control structures.

4. Weirs
 At its most basic, just an obstruction placed in a
channel that constricts flow as it goes over a
crest.
 The crest is the edge of the weir over which the
water flows.
 As the water level (head) over the crest increases,
the flow rate increases dramatically.
 Two basic types of weirs
 sharp crested
 broad crested

5. Sharp Crested Weirs
 A sharp crested weir is defined by a thin
crest over which the water springs free as it
leaves the upstream face of the weir.
 Flow over a weir is also called the nappe.
 Sharp crested weirs are generally
constructed of sheet metal or similar thin
material.

6. Sharp Crested Weir
H
nappe

7. Sharp Crested Weirs
 Can have several shapes
 Triangular (or v-notch)
 Rectangular
 Trapezoidal
 Classified by the shape of its notch.
 V-notch weirs have greater control under low flow
conditions.
 Rectangular weirs have larger capacity but are less
sensitive for flow measurement.

8. Sharp Crested Weirs-General
v
2
2
1
g
H h dh
Using Bernoulli’s equation
v
2
2
2
2
1 + + = + + -
(H z h)
v 22
(H z) v
2g
2g
z
g

9.  Making the assumption that the velocity head at
the upstream point will be much smaller than the
velocity head as the flow goes over the weir we
assume v2/2g is negligible and:
1
v 2gh 2 =
H
Crest
dh
L
dQ v Ldh 2 =
or
dQ = 2ghLdh h

10. Integrating this from h = 0 to h = H gives
2
3
=
Q L 2g h 2 L gH
= ò =
0
1 2
2
3
h H
h
=
Multiplying by a loss term to compensate for
the deviation from ideal flow we get:
2
3
Q = C 2
d L 2gH
3

11. Rectangular Weirs
A rectangular weir that spans the full width of the channel
is known as a suppressed weir.
2
Q = CLH3
H
L
H
Coefficient of Discharge

12.  Hydraulic head (H) for weirs is simply the height
of the water surface above the weir crest,
measured at a point upstream so that the influence
of the velocity head can be ignored.
 L is the length of the weir.
 The coefficient of discharge (C) is dependent
upon units and of the weir shape.
 For a suppressed weir with H/h < 0.4 (where h is the
height of the weir) C= 3.33 can be used.
 For 0.4 < H/h < 10, C = 3.27 + 0.4 H/h

13. A rectangular weir that does not span the whole channel
is called a weir with end contractions . The effective
length of the weir will be less than the actual weir length
due to contraction of the flow jet caused by the sidewalls.
L’
L = L'-0.1NH
Where N is the number of
contractions and L’ is the
measured length of the
crest.

14. Triangular (v-notch ) weirs
 Used to measure flow in low flow
conditions.
Q H
Q = K tan q
H2.5
2

15.  For Q = 90°, K = 2.5 (typically),
tan (Q/2) = 1 therefore,
2
Q = 2.5H5
For other angles
2g
K C 8 d =
15
Where Cd is based on the angle, Q, and head, H.

16.  Note: Your handout with Figure 12.28
presents the equation for a v-notch weir as:
2
Q = KH5
with
= q
2
2g tan
K C 8 d
15

17. Broad Crested Weirs
H
W
Q = 3.09LH1.5
Where L is the width of the weir.

18. Broad Crested Weirs
 Broad crested weirs support the flow in the
longitudinal direction (direction of flow).
 They are used where sharp-crested weirs
may have maintenance problems.
 The nappe of a broad crested weir does not
spring free.

19. Roadway Overtopping
( ) 3
2
o d r Q = C L HW
Where
Qo – overtopping flowrate
Cd - overtopping discharge coefficient
L – length of roadway crest
HWr – upstream depth
Cd = ktCr
Cr – discharge
coefficient
kt – submergence
factor
Figure 5.7

20. Orifices
 An orifice is simply an opening through
which flow occurs.
 They can be used to:
 Control flow as in a drop inlet
 Measure the flow through a pipe.

21.  The discharge equation for orifice flow is:
2
Q = C'A(2gH) 1
Where:
C’ is the orifice coefficient (0.6 for sharp edges, 0.98 for
rounded edges).
A is the cross-sectional area of the orifice in ft2
g is the gravitational constant
H is the head on the orifice

22.  At low heads, orifices can act as weirs.
 Calculate the discharge using the suppressed
weir equation where L is equal to the
circumference of the pipe.
 Calculate the discharge using the orifice
equation.
 The lower discharge will be the actual
discharge.

23. Pipes as Flow Control Devices
0.6D
D
H’
H K v
2
2g
e e =
H K v
2
2g
b b =
H K L v
2
2g
c c =
v2
2g
H
Energy Grade
Line
Elbow and Transition L
H'= v + + +
e b c
2
H H H
2g

24. 2
H' v e b c
(1 K K K L)
2g
= + + +
2
1
2
1
v (2gH')
+ + +
(1 K K K L)
e b c
=
2
1
2
1
Q a(2gH')
+ + +
(1 K K K L)
e b c
=

25. Head Loss Coefficients
 Ke is the entrance head loss coefficient and is typically
given a value of 1.0 for circular inlets.
 Kb is the bend head loss coefficient and is typically
given a value of 0.5 for circular risers connected to
round conduits.
 For risers with rectangular inlets, the bend head losses
and entrance head losses are typically combined to a
term Ke’ where values of Ke’ can be found in Table 5.3
and :
2
1
Q a(2gH')
+ +
e c
2
1
(1 K ' K L)
=

26. Head Loss Coefficients
 Kc is the head loss coefficient due to
friction.
 Values for Kc are given in Tables 5.1 and
5.2 for circular and square pipes.
 Kc is multiplied by L, the entire length of
the pipe, including the riser.

27.  Frequently, when the drop inlet is the same
size as the remainder of the pipe, orifice
flow will control and the pipe will never
flow full.
 If it is desirable to have the pipe flowing
full, it may be necessary to increase the
size of the drop inlet.

28. Using Flow Control Structures as
Spillways
 A given drop inlet spillway can have a variety of
discharge relationships, given the head.
 At the lowest stages the riser acts as a weir.
 As the level of the reservoir rises, water flowing in from
all sides of the inlet interferes so that the inlet begins to
act as an orifice.
 As the level continues to rise, the outlet eventually begins
to flow full and pipe flow prevails.
 A stage-discharge curve is developed by plotting Q vs. H
for each of the three relationships. The minimum flow for
a given head is the actual discharge used.

29. Rockfill Outlets as Controls
ROCKFILL
have
h1
dh
h2
dl
HYDRAULIC PROFILE

30. Rockfill Outlets
 Advantages
 Abundant
 Generally available
 Usually inexpensive
 Relative permanence

31. Rockfill Outlets
 Major expenses
 Grading
 Transporting
 Placing stone

32. Rockfill Outlets
 Used for
 Protective channel linings and breakwaters
 Add stability to dams
 Provide energy dissipation zones for reservoir
outlets
 Flow control structure

33. Modified Darcy-Weisbach
Equation
V
g
1
x
d
f
dh
dl
k
2
2
=

34. Rockfill as Control Structure
Model
Reynolds Number Equation
( )
nx
R = d -
s V e
Friction factor
dh
dl
x 2 =
f gd k 2
V

35. Friction Factor-Reynolds
Number Relationship
= 1600 +3.83
k R
e
f

36. h2 – have Relationships
h1 = h2 + dh
h h1 h2 ave
= +
2