Date post: | 14-Apr-2018 |
Category: |
Documents |
Upload: | fatima-chelihi |
View: | 219 times |
Download: | 4 times |
of 38
7/30/2019 Hydraulics of Structures(2)
1/38
Hydraulics of Structures
7/30/2019 Hydraulics of Structures(2)
2/38
Structures in this context are simply something
placed in the channel to either measure or controlflow.
Example: A principle spillway is used as part ofa 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 freesurface or
Pipe flow in which the flow is in a closed conduitunder pressure.
7/30/2019 Hydraulics of Structures(2)
3/38
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 thehead-discharge relationships for several flow
control structures.
7/30/2019 Hydraulics of Structures(2)
4/38
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
7/30/2019 Hydraulics of Structures(2)
5/38
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.
7/30/2019 Hydraulics of Structures(2)
6/38
Sharp Crested Weir
Hnappe
7/30/2019 Hydraulics of Structures(2)
7/38
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 flowconditions.
Rectangular weirs have larger capacity but are less
sensitive for flow measurement.
7/30/2019 Hydraulics of Structures(2)
8/38
Sharp Crested Weir
Using Bernoullis equation
)hzH(g2
v)zH(
g2
v 222
1
H h dh
z
V12/2g
V22/2g
7/30/2019 Hydraulics of Structures(2)
9/38
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 v12/2g is negligible and:
gh2v2
H
Crest
dh
L
LdhvdQ2
or
Ldhgh2dQh
7/30/2019 Hydraulics of Structures(2)
10/38
Integrating this from h = 0 to h = H gives
23Hh
0h
21
Hg2L3
2hg2LQ
Adding a loss term to compensate for thedeviation from ideal flow we get:
23
d Hg2L
3
2CQ
When H1/3 L, an approximate value for Cd is 0.6 to 0.62
leaving:
23
LH33.3Q
7/30/2019 Hydraulics of Structures(2)
11/38
Rectangular Weirs
A rectangular weir that spans the full width of the channel is
known as a suppressed weir.
23
CLHQ
H
L
H
Coefficient of Discharge
7/30/2019 Hydraulics of Structures(2)
12/38
Hydraulic head (H) for weirs is simply the heightof 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 theheight of the weir) C= 3.33 can be used.
For 0.4 < H/h < 10, C = 3.27 + 0.4 H/h
7/30/2019 Hydraulics of Structures(2)
13/38
A rectangular weir that does not span the whole channelis 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
NH1.0'LL
Where N is the number of
contractions and L is the
measured length of the
crest.
7/30/2019 Hydraulics of Structures(2)
14/38
Triangular (v-notch ) weirs Used to measure flow in low flow
conditions.
Q H
5.2H
2
tanKQ
7/30/2019 Hydraulics of Structures(2)
15/38
ForQ = 90, K = 2.5 (typically),tan (Q/2) = 1 therefore,
25
H5.2Q
For other angles
g2158CK d
Where Cd is based on the angle, Q, and head, H.
7/30/2019 Hydraulics of Structures(2)
16/38
Note: Your handout with Figure 12.28presents the equation for a v-notch weir as:
25
KHQ
with
2tang2
158CK d
7/30/2019 Hydraulics of Structures(2)
17/38
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.
7/30/2019 Hydraulics of Structures(2)
18/38
The discharge equation for orifice flow is:
21
)gH2(A'CQ 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
7/30/2019 Hydraulics of Structures(2)
19/38
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.
7/30/2019 Hydraulics of Structures(2)
20/38
Example
A 36-in, circular, vertical riser constructed from corrugated
metal pipe (CMP) serves as the inlet for the principal spillwayof a detention structure. Estimate the discharge if the head on
the riser is 1ft. Estimate the discharge if the head is 3 ft.
7/30/2019 Hydraulics of Structures(2)
21/38
Pipes as Flow Control Devices
0.6D
D
H
g2
vKH
2
ee
g2
vKH
2
bb
g2
vLKH
2
cc
g2
v2
H
Energy GradeLine
Elbow and TransitionL
cbe
2
HHHg2
v
'H
7/30/2019 Hydraulics of Structures(2)
22/38
LKKK1g2v
'H cbe
2
21
cbe
21
)LKKK1(
)'gH2(v
21
cbe
2
1
)LKKK1(
)'gH2(aQ
7/30/2019 Hydraulics of Structures(2)
23/38
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 typicallygiven a value of 0.5 for circular risers connected toround conduits.
For risers with rectangular inlets, the bend head lossesand entrance head losses are typically combined to a
term Ke where values of Ke can be found in Table 5.3and :
21
ce
21
)LK'K1(
)'gH2(aQ
7/30/2019 Hydraulics of Structures(2)
24/38
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.
7/30/2019 Hydraulics of Structures(2)
25/38
Frequently, when the drop inlet is the samesize 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.
7/30/2019 Hydraulics of Structures(2)
26/38
Example
A 36-in diameter corrugated metal pipe is attached to a
36-in vertical riser. It is being used as the principal
spillway for a detention structure. The pipe is 40 feetlong and has one 90 bend. The top of the inlet riser is
10 ft above the bottom of the outlet. Assume a free
outfall and estimate the discharge under pipe flow if
the water elevation 30 ft from the inlet is 2 ft higherthan the top of the riser.
7/30/2019 Hydraulics of Structures(2)
27/38
ExampleA 48-in coated cast iron riser is connected
to a 24-in coated cast iron barrel by one 90
bend. The spillway is 65 ft long. The topof the riser is 15 ft above the outlet.
Assume a free outfall and estimate the
discharge if the water elevation 25 ftupstream of the inlet is 1.8 ft. above the top
of the riser.
7/30/2019 Hydraulics of Structures(2)
28/38
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 fromall sides of the inlet interferes so that the inlet begins toact 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 fora given head is the actual discharge used.
7/30/2019 Hydraulics of Structures(2)
29/38
Example 2
Given the previous example, develop a stage-discharge
curve.
7/30/2019 Hydraulics of Structures(2)
30/38
Broad Crested Weirs
W
H
5.1LH087.3Q
Where L is the width of the weir.
7/30/2019 Hydraulics of Structures(2)
31/38
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.
7/30/2019 Hydraulics of Structures(2)
32/38
have
h1
dh
h2
dl
ROCKFILL
HYDRAULIC PROFILE
7/30/2019 Hydraulics of Structures(2)
33/38
Modified Darcy-Weisbach
Equation
g
V
d
f
dl
dhk
2
21
7/30/2019 Hydraulics of Structures(2)
34/38
Rockfill as Control Structure
Model
VdRe
Reynolds Number Equation
Friction factor
dl
dh
V
gdfk 2
2
7/30/2019 Hydraulics of Structures(2)
35/38
Friction Factor-Reynolds
Number Relationship
83.31600
e
k
R
f
7/30/2019 Hydraulics of Structures(2)
36/38
h2have Relationships
dhhh
21
221 hhhave
7/30/2019 Hydraulics of Structures(2)
37/38
Example 1 A rockfill dam is composed of rock having
an average diameter of 0.04 m, porosity
equal to 0.46, standard deviation of 0.002m, and length dl equal to 2.0 m. Water
with a kinematic viscosity of 1 X 10-6
m/sec is flowing through the rock at a rateq of 5.0 cms/m width. Down stream
conditions control the exit depth of the
water h2 at 1.0 m. Find the upstream height
7/30/2019 Hydraulics of Structures(2)
38/38
Example 2 If the rock fill in Example 1 is 3 m wide
and as used as spillway from a sediment
detention pond, determine the stagedischarge relationship up to an upstream
depth of 2 m using depths of 0.5, 1.0, 1.5
and 2.0 m. Assume that the downstreamslope is such that the downstream depth is
negligible.