Hydraulics II-Ch 1 Tutorial

Hydraulics II (HE-333) TUTORIAL ON CHAPTER ONE
1. A trapezoidal channel having the side slope equal to 60 with he horizontal and
laid on a slope of 1 in 750, carries a discharge of 10m 3/s. find the width at base
and depth of flow for most economical cross-section. Take the value of Chezy’s
resistance coefficient C = 66m1/2/s.
2. A trapezoidal channel is required to carry 6m3/s of water at a velocity of 1.5m/s.
Find the most economical cross-section if the side of the channel is inclined at an
angle of 30 with the horizontal. Use C = 55m1/2/s.
3. Water flows at a steady and uniform depth of 2m in an open channel of
rectangular cross section having base width equal to 5m and laid at a slope of 1 in
1000. It is desired to obtain critical flow in the channel by providing a hump in
the bed. Calculate the height of hump and sketch the profile. Consider the value of
n = 0.02 for the channel surface.
4. A given trapezoidal channel has the following dimensions:
B = 10m, m = 1.5, y = 3m and designed to carry 40m 3/s. Using the same cross-
sectional area and side slopes, how much would the most efficient cross-section
increase the present hydraulic radius and flow capacity? What would be the
corresponding depth and bed width?
5. A sewer with diameter 0.5m is laid at a slope of 1in 225. What is the maximum
velocity of flow that can occur? What would be the discharge at that velocity,
Take C = 60.
6. A rectangular channel which is laid on a bottom slope of 0.0064 is to carry 20m 3/s
of water. Determine the width of the channel when the flow is in critical
condition. Take n = 0.015.
7. In a rectangular channel there occurs a jump corresponding to Froude number (F

= 2.5). Determine the critical depth and head loss in terms of the initial depth y1.
8. A trapezoidal channel having bottom width 10m and side slope 2:1(H:V) carries a
discharge of 100m3/s. Find the depth conjugate to the initial depth of 1m before
the jump. Also determine the loss of energy in the jump.
9. Show that the head loss in a hydraulic jump formed in a rectangular channel may
be expressed as:
(v1  v 2 ) 3
E 
2 g (v1  v 2 )
10. For a trapezoidal channel section of side slope m and B bottom width, show that
the critical depth is expressed as
1/ 3
 Q 2 Z 2 ( Z  2) 
yc  * 
 gB
2
( Z  1) 
i.
 1  Z  1 
ii. EC  YC 1    Where Z = B/my
 2  Z  2 
11. For a hydraulic jump in a horizontal triangular channel show that:
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2 2 r 2  r 3  1
Fr1 
3  r 2  1
Where r = y2/y1
12. In a horizontal triangular channel with sides sloping 1.5 to the horizontal, the
depth before & after jump are observed as 1m and 1.5m respectively. Determine
the discharge flowing through the channel.
13. An over flow spillway has crest length of 7m at elevation of 125.40m and a
horizontal apron at an elevation of 95 .0m on the downstream side. Find the tail
water elevation required to form a hydraulic jump when the elevation of energy
line is 127.0m & also find energy loss in jump. The coefficient of discharge (Cd)
for the flow can be assumed as 0.735. The energy loss for the flow over the
spillway can be ignored. The unit discharge over the spillway is give by:
2
q Cd 2 g H 3 / 2
3
14. Construct a family of specific energy curves for q = 0, 1.5, 3.0, 9.0& 12.0m3/s for
a trapezoidal channel section having bottom width of 6.2m & m = 2.0.
15. Determine the initial & sequent depth of a hydraulic jump in a horizontal
rectangular section 9.25m wide & carrying 8.80m3/s .The loss of energy in the
jump is 1.54m.
16. A triangular channel with side slopes of 450 paved with brick in cement mortar
should deliver 4m3/s. Determine the depth of the flow if the slope is 0.0016.
17. A rectangular chute is designed to transport lumber from a high mountain region
to a lower lake. The channel must remain a uniform depth of 1m with a discharge
of 10m3/s. The channel is to be built of material with n = 0.016. Determine the
slope of the channel if its width is 3m.
18. A triangular highway gutter is designed to carry a discharge of 52m 3/min on a
channel slope of 0.0016. The gutter is 0.8m deep with one side vertical and one
side with slope of 1 in z. The channel surface is clean earth excavation. Determine
the side slope z.
19. A trapezoidal channel with 6.2m wide bottom and side slope z = 2 carries a
discharge of 10m3/s. The channel is built with glazed brick surface on a 0.04
channel slope. Using Chezy’s formula, determine the flow velocity.
20. 100m3/s is flowing in a rectangular channel 12m wide. If the depth of flow is 3m,
what will be the depth when the channel contracts to 8m wide?
21. What would be the minimum excavated volume for a 100m channel cut in rock of
rectangular section? It should deliver 25m3/s in a slope of 0.003.
22. Determine the depth-to-diameter ratio for the most hydraulically efficient circular
section.
23. Determine the side slope of the most hydraulically efficient triangular section.
24. A flow of 100m3/s occurs in trapezoidal canal having a side slope z = 2, and
bottom width of 10m, n = 0.017. Calculate the critical depth and critical slope.
25. A sewer pipe is proposed to be laid on a slope of 1 in 2500 and is required to
carry a discharge of 1.5m3/s. What size of circular pipe should be used if the pipe
is to flow half full and n = 0.015
26. An irrigation canal of trapezoidal section having side slope 2 in 3 is to carry a
flow of 10m3/s on a longitudinal slope of 1 in 5000. The canal is lined for which
the value of frictional coefficient in Manning’s formula is n = 0.012. Find the
dimension of the most economical section.
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27. A flow of 100l/s flows in a rectangular laboratory flume of 0.6m width and
having an adjustable bottom slope. If Chezy’s constant C = 56, determine the
bottom slope necessary for uniform flow with a depth of flow of 0.3m. Also find
the conveyance (K) and state of flow.
28. For a constant specific energy of 1.8Nm/N, calculate the maximum discharge that
may occur in a rectangular channel 5m width.
29. For the purpose of discharge measurement the width of a rectangular channel is
reduced gradually from 3m to 2m and the floor is raised by 0.3m at a given
section. When the approaching depth of flow is 2m, what rate of flow will be
indicated by a drop of 0.15m in the water surface elevation at the contracted
section?( assume no loss).
Typical Values of Manning’s n
Channel Surface n
Smooth steel surface 0.012
Corrugated metal 0.024
Smooth concrete 0.011
Concrete culvert 0.013
Glazed bricks 0.013
Earth excavation, clean 0.022
Natural stream bed, clean, straight 0.030
Smooth rock cuts 0.035
Channel not maintained 0.050-0.10
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Hydraulics II (HE-333) TUTORIAL ON CHAPTER ONE

7. In a rectangular channel there occurs a jump corresponding to Froude number (F

11. For a hydraulic jump in a horizontal triangular channel show that:

Typical Values of Manning’s n

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