Fig 3

1. A rectangular, concrete channel 50 ft wide is to carry water at a flow rate of 800 cfs.
The channel slope is 0.00025. Find the depth of flow.

2. A corrugated metal pipe of 500 mm diameter flows half-full at a slope of 0.0050 (see
Fig. 4). What is the flow rate for this condition?

Fig 4

3. A 24-in-diameter cast iron pipe on a 1/400 slope carries water at a depth of 5.6 in, as
shown in Fig. 5. What is the flow rate?
 Fig 5

4. A 500-mm-diameter concrete pipe on a 1/500 slope is to carry water at a flow rate of

0.040 m3/s. Find the depth of flow. See Fig. 6.

Fig 6

5. A concrete pipe must carry water at a slope of 0.0075, at a velocity of 0.76 m/s, and
at a depth of flow equal to one-tenth its diameter. What is the required pipe
diameter?
Banha University 2nd Year Civil
Shubra Faculty of Engineering Hydraulics (2)
Civil Engineering Dpt. 2012/2013
Sheet 2

1. Differentiate formulas for shear stress and velocity in open channel.

2. Water is to flow in a rectangular flume at a rate of 1.42m 3/s and at a slope of
0.0028. Determine the dimensions of the channel cross section if width must be
equal to twice the depth. Use n = 0.017.
3. Rework Prob. 2, assuming width must be equal to the depth. Note which solution
gives the smaller (and therefore more efficient) cross section
4. A rectangular channel (n = 0.011) 18 m wide is to carry water at a flow rate of 35
cfs. The slope of the channel is 0.00078. Determine the depth of flow.
5. The trapezoidal channel shown in Fig. 14-13 is laid on a slope of 0.00191. The
channel must carry 60 cfs. Determine the depth of flow. Use n = 0.015.

6. An open channel is to be designed to carry 1.0 m3/s at a slope of 0.0065. The

channel material has an n value of 0.011. Find the most efficient cross section for
a semicircular section
7. Find the most efficient cross section for Rob. 1 for a rectangular section.
8. Find the most efficient cross section for Rob. 1 for a triangular section
9. Find the most efficient cross section for Prob. 1 for a trapezoidal section.
10.Calculate the discharge in steady flow through the channel and floodway of Fig.
take s = 0.0010 and y = 2.438 m.
11.For 25000 cfs through the section of previous prob., find the depth of flow in the
floodway (i.e., evaluate y) in feet when the slope of the energy grade line is
0.0004.
Banha University 2nd Year Civil
Shubra Faculty of Engineering Hydraulics (2)
Civil Engineering Dpt. 2012/2013
Sheet 3
The energy principle in open channel
1-a) Define and prove the energy principle in open channel.
1-b) A discharge of 15 m3/sec flows in a wide channel of 20 m width of a uniform water
depth of 1.5 m. Find Froude number, Channel bed slope, and critical depth.
(n=0.022)
2-a) Define and draw a sketch for the specific energy showing critical, sub critical and
supercritical flow range.
2-b) A discharge of 400 m3/sec flows in a wide channel of 40 m width of uniform water
depth of 1.5 m. find specific energy and flow state

3-a) Define the critical state of flow.

3-b) Differentiate formula for the critical state of flow for non-rectangular section.
3-c) For a trapezoidal channel with bottom width of 7 m and side slope of 3:2.
Calculate the critical depth of flow and Frude number if the flow rate is 20 m3/sec.
3-d) A trapezoidal Channel 5 m wide conveys a discharge of 8 m 3/sec at a uniform flow
depth of 1.25 m and side slope of 1:1. Determine:
1. The critical depth
2. The critical velocity
3. The minimum energy.
4. The flow condition.
5. Frude number at depth 1.25 m.

4-a) Differentiate formulas for critical depth, critical discharge per unit width, critical
velocity, critical specific energy, and critical slope for rectangular section.
4-b) A rectangular channel 6 m wide conveys a discharge of 10 m 3/s at a uniform flow
depth of 1.25 m, n=0.015. Determine the following:
1. The critical depth
2. The minimum energy.
 3. The critical velocity.
4. The flow condition.
5. Frude number at critical depth and at depth of 1.25 m.
6. The critical slope.

5-a) Prove that the maximum flow rate occurs at critical state and draw a sketch for
specific discharge diagram showing the point of max discharge.
5-b) For a constant specific energy of 3 m, what is the maximum flow rate that may
occur in a rectangular channel of 7 m width?. Draw the (Q-Y) curve for this
section.
6) For the same conditions given in Prob. 1 determine the status of flow (i.e., is it
critical, subcritical, or supercritical?).
7) The triangular channel (n = 0.012) shown in fig. is to carry water at a flow rate of 10
m3/s. Find the critical depth, critical velocity, and critical slope of the channel.

8) Find the critical depth for flow at 1.6m3/s per meter of width.
Banha University 3rd Year Civil
Shubra Faculty of Engineering Hydraulics (2)
Civil Engineering Dpt. 2012/2013
Sheet (4)
Applications of the specific energy
1-Flow over raised channel floor

1) Sketch the water surface profile, the T.E.L. , and the critical depth line for the flow in case of
subcritical flow and supercritical flow when:
a. A hump occurs at the channel bed.
b. A depression occurs at the channel bed.

2) Water flows at a velocity of 1.5 m/sec and 2.5 m depth in a rectangular channel of width 4 m.
a hump of 0.5 m high is constructed on the channel bed. Find the following:
a. The flow depth on the hump.
b. The hump height to provide critical flow on the hump without the effect of the upstream
conditions.
c. The heading up if the hump is raised by 0.25m on top of height in part b.

3) The critical depth is maintained at a point in a rectangular channel 6 ft wide by building a

gentle hump 12 inch high in the bottom of the channel. When the depth over the hump is 26
inch, what are the possible water depths just upstream the hump.

4) A 11.3 m3/s flow in a rectangular channel with 3.6 m wide which ends in a free outfall. The
slope is 0.0009 and n=0.017. A frictionless broad crested weir is to be installed near the end of
the channel to produce uniform flow. What is the maximum required weir height?

5) A uniform flow in a rectangular channel occurs at a depth of 10 ft and velocity of 5 ft/s.

When a smooth frictionless hump of 2 ft high is built in the floor of the channel, solve and
discuss the following:
a- What is the expected water depth on the hump?
b- What would be the required hump height to produce critical depth hump?
c- What would happen if a higher hump was installed?

6) A uniform flow at a depth of 3.1 m occurs in a long rectangular channel of width 6 m having
a manning coefficient of 0.015 and longitudinal slope of 0.001 find the following:
a. The type of flow
b. The minimum hump height which can be built on the channel floor to produce critical
depth.
c. If the hump height is 0.3 m , what is the water depth above the hump?.

Good Luck …
Banha University 3rd Year Civil
Shubra Faculty of Engineering Hydraulics (2)
Civil Engineering Dpt. 2012/2013
Sheet (5)

Applications of the specific energy

2-Contraction in open channels

1) Sketch the water surface profile, the T.E.L., and the critical depth line for the flow in case of
subcritical flow and supercritical flow when:
a. A contraction occurs at the channel bed.
b. An enlargement occurs at the channel bed.

2) Water flows at a velocity of 1.5 m/sec and 2.5 m depth in a rectangular channel. The width
contracts smoothly from 2.0 m to 1.5 m. Determine:
a. the depth of water within the contraction.
b. the required width to provide critical flow at the contraction without effecting the U.S.
condition.
c. the heading up in the channel if the width at the contraction is 0.15 m less than the width
found in part b.

3) A rectangular channel of width 12 ft is narrowed to a width of 6 ft to cause critical flow in the

contracted section. If the depth in this section is 3 ft, calculate the flow rate and depth in the
12 ft section, neglecting head losses in the transition zone. Sketch the energy line and water
surface showing all vertical dimensions.

4) In a trapezoidal channel of 5m bed width and 1:1 side slopes, a discharge of 37.5 m 3/sec flows
uniformly at a depth of 4 m. the cross section is then changed to a rectangular section of the
same bed width. Neglecting the local head losses, what is the minimum height of hump which
may be installed in the construction to produce critical depth there?

5) A rectangular channel is 4 m wide and 2 m deep. If the slope is 1 cm/Km and Manning’s
coefficient is 0.015, determine the following without changing the water level at the
upstream:
a. The width of the throat to produce critical depth.
b. The height of the hump to produce critical depth.
c. If the hump height in (b) is increased by 0.25m, what is the effect on the upstream water
level?. Sketch your answer showing the specific energy curve.

Good Luck …
Banha University 3rd Year Civil
Shubra Faculty of Engineering Hydraulics (2)
Civil Engineering Dpt. 2012/2013
Sheet (6)

The specific force

1-Rapidly varied flow

1-a) Define the following:

a. Specific force. (Draw a sketch for its diagram)
b. Rapidly varied flow.
c. Hydraulic jump.
d. Sequent (conjugate) depths.
e. Alternate depths.

1-b) A long rectangular channel of 6 m width carries a discharge of 25 m 3/s, bed slope of 0.05,
and n=0.025 .At a certain section , the channel bed slope is changed to 0.003. Determine:
a. the length of the channel through which the flow is non-uniform.
b. the power loss through the jump, if any.

2-a) Considering the formation of a hydraulic jump over a horizontal frictionless rectangular
channel derive a relationship between the sequent depths as a function of critical depth and
Frude number.

2-b) A rectangular channel is 5 m wide, has an initial water depth of 0.5 m and velocity of 5 m/s.
can a hydraulic jump take place? If so, find the following:
a. the sequent depth.
b. the energy loss.
c. the length of the jump.

3-a) Prove that the critical flow state occurs at minimum specific force.

3-b) A discharge of 50 m3/s flows in a rectangular channel having a width of 4 m. if the sequent
depth of the jump is 4 m, determine the following:
a. The initial depth.
b. The initial Froude number.
c. The height of the jump.
d. The energy before and after the jump.
e. The horsepower lost in the jump.

Good Luck …
Banha University 3rd Year Civil
Shubra Faculty of Engineering Hydraulics (2)
Civil Engineering Dpt. 2012/2013
Sheet (7)

The specific force

2-Gradually varied flow

1-a) Define the Gradually Varied Flow.

1-b) Classify the channel bed slopes.

2-a) A very wide channel 35 m wide carries 250 m3/sec. it has a bed slope if 2 in 10000 and
n=0.012 . if an over flow weir is installed across the channel which raises the water level at
the weir to a depth of 3.5 m .
1) Classify the water surface profile.
2) Compute the distance U.S. the weir to where the water depth 3.3 m using two steps
only.
3) find the water depth at a distance of 1 Km U.S. the weir using two steps only.

2-b) A river supply is 600 million m3/day, with bed slope 6 Cm/Km is terminated by a fall at
which the water depth is equal to 1.15 of the critical depth. If the river width is 600 m and
Manning’s coefficient of roughness is 0.025.
1) Classify the water surface profile.
2) Compute the distance U.S. the fall to where the water depth 3.05 m using two steps
only.
3) Find the water depth at a distance of 0.7 Km U.S. the fall using two steps only.

3-a) What is the difference between Gradually Varied Flow & Rapidly Varied Flow?

3-b) At the toe of a spillway, whose crest length is 50 m, the velocity of flow is 14 m/s and the
discharge is 250 m3/s. the normal flow depth on the reinforced concrete apron is 3 m, n=
0.016.
1) Classify the water surface profile.
2) How long should the apron be built?

Good Luck …