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Civil Engineering April 2023 Review Innovations Hydraulics 13

Alternate Stages of Flow Generally (all sections),

Bc
- In a channel for a given total head or
specific energy E, there are two stages of Q2 A 3c

flow that give the same discharge Q: g Bc
Ac dc
1. The upper stage/ tranquil flow
NF < 1 subcritical

2. The lower stage/ rapid or shooting flow For rectangular sections:


NF > 1 supercritical q2 3. Find the critical depth in the trapezoidal
dc  3 channel shown conveying water at 19 m3/s.
g
NF = Froude number Side slope 1V:3H, n= 0.012.

q = discharge per meter width


Generally (all sections),
1. Water flows in a rectangular channel at a
v
NF  depth of 1.0 m and a velocity of flow of 4
gdm m/s.
a. What is the discharge?
dm = mean/ average depth (m) b. What is the critical depth? 4. A rectangular planed timber flume (n =
A c. What is the Froude number? 0.012) 3 m wide is laid on a slope of 0.0011.
dm 
B d. Is the flow sub or super-critical? For a depth of flow of 0.90 m:
B = width of the l.s. (m) e. What is the alternate depth? a. What is the Manning’s C?
b. What is the uniform flow?
For rectangular sections: 2. A riveted-steel triangular duct, n=0.015,
c. What smallest amount of energy can
flows partly full as shown. If the critical
give the same amount of flow?
depth is 60 cm, compute:
v
NF  a. Critical flow rate.
gd b. Critical velocity.
c. Critical slope.
Critical depth (dc) = depth of flow where the
discharge Q is maximum for a given specific
energy E, or depth of flow where E is minimum
for a given Q.

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Civil Engineering April 2023 Review Innovations Hydraulics 13
5. Water is flowing in a 12 – m wide
rectangular channel at 10.5 m3/s and a
depth of 1.1 m.
a. What is the specific energy?
b. What is the critical depth?

6. The flow rate per unit width in a wide


channel is q = 2.3 m3/s per m width. Is the
flow subcritical or supercritical if the depth
is:
a. 0.2 m
b. 0.8 m
c. 2.5 m

7. A rectangular channel 3 m wide carries 10


m3/s at a depth of 2 m.
a. Is the flow subcritical or supercritical?
b. For the same flow rate, what depth
will give critical flow?

8. Water flows in a 10 – m wide open channel


with a flow rate of 5 m3/s. Determine the
two possible depths if the specific energy of
the flow is E = 0.6 m.

9. A discharge of 4.5 m3/s occurs in a


rectangular channel 1.83 m wide with s = 5) 1.132
0.002 and n = 0.012. 0.427
a. Find the normal depth for uniform 6) supercritical
Supercritical
flow
subcritical
b. Determine the critical depth. 7) subcritical
c. Is the flow subcritical or supercritical? 1.04 m
8) 0.56 m
10. Compute the critical depth for a flow at 0.4 0.173 m
m3/s through a 60° V – notch channel. 9) 1.06 m
0.851 m
Subcritical
10) 0.628

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