Exercise (1): Open Channel Flow – Uniform Flow - UniMasr · Exercise (1): Open Channel Flow – Uniform ... decided to decrease the side slopes of the channel to be 2:1 due to slope

CAIRO UNIVERSITY HYDRAULICS Faculty of Engineering 3rd year Civil Eng. Irrigation & Hydraulics Department 2010 – 2011

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Exercise (1): Open Channel Flow – Uniform Flow

1) Derive expressions for the flow area A, wetted perimeter P, hydraulic radius R,

top water surface width B, and hydraulic depth D for the following channel cross sections:

a. Rectangular (bottom width = b ) b. Trapezoidal (bottom width = b, side slope = t :1) c. Triangular (side slope =t :1) d. Partially full circular (diameter = D)

2) At a point in a rectangular channel 15.2 m wide, 2.1 m deep, and 15 cm/km bed

slope, the discharge is 20 m3 /sec and C = 62 (metric) in Chezy's formula. a. Show whether the flow is uniform or non-uniform. b. Show whether the flow is shooting or streaming.

3) A rectangular canal has a bed slope of 8 cm/km, and a bed width of 100 m. If at

a depth of 6 m the canal carries a discharge of 860 m3/sec at uniform flow. Find the roughness n, Chezy's coefficient C, and the coefficient of friction f. Also find the average shear stress on the bed.

4) Figure (1) shows the section of a channel with flood way. Manning coefficient is

taken 0.025 for the main channel and 0.035 for the flood way. Knowing that the bed slope is 10 cm/km, calculate the discharge.

5) The following table shows values of average Manning coefficient (n) and the corresponding water depth (y) for a laboratory flume laid at a slope of 1:100. The flume has a rectangular cross section of width b = 30 cm, the sides are made of glass while the bed is made of stainless steel.

y (m) 0.1 0.2 0.3 0.4 0.5 0.6 n (metric) 0.02 0.016 0.013 0.011 0.01 0.01

a. Draw the relation between y and n then explain why the average roughness

coefficient decreases while increasing the water depth. Do you expect the same behavior in natural open channels? Why?

b. Find the water flow depth that corresponds to a discharge of 100 lit/sec if the slope is kept the same.

6.0 2.0 3.0 0.753.0

2.0

Figure (1)


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6) Design a channel to irrigate 54000 feddans at a water duty of 60 m3/fed/day. The

soil allows side slope of 1:1, n = 0.025 (metric), and the bed slope is 12 cm/km. Find the channel dimensions for each of the following cases:

a. The maximum allowable velocity being 0.7 m/s. b. The maximum allowable boundary shear stress being 0.27 kg/m2. c. y = 0.1(b)(0.5S0 + 4) where S0 is in cm/Km. d. The channel is of best hydraulic cross section.

7) Two channels designed to be most economic sections, the first one is trapezoidal

with side slope of 1:1, and the second one is of semi-circular section. Both have the same area, discharge, and Manning coefficient (n = 0.02). If the trapezoidal channel is 3m in bed width and is laid at a slope of 15 cm/km, what will be the diameter and the slope of the semi-circular channel?

8) A trapezoidal channel of side slopes 1:1, bed width b = 5.0m and roughness

coefficient n = 0.02 was used to convey water at a depth of 1.5m until it's decided to decrease the side slopes of the channel to be 2:1 due to slope stability problems. What is the new bed width if the discharge, water depth and the bed slope are to be kept the same?

9) A wide rectangular navigation channel consists of three reaches with an average

Manning coefficient of 0.025. The bed slopes for the three reaches are 8, 7, and 10 cm/km. The monthly flows are as follows:

Month 1 2 3 4 5 6 7 8 9 10 11 12 Q (m3/sec) 16 11 14 13 15 18 17 19 10 10 13 11

It is required to design the channel such that the water depths through the channel are always greater than 1.5 m and less than 3 m. Find the suitable range of the bed width.

10) In a river of bed width 600 m, and bed slope 10 cm/km, it is found that the bed

material just begins to move when the discharge is 150 million m3/day. Supposing the mean velocity to vary with the depth and the slope according to the relation:

V = 120 S(2/3) y (in m/s)

Find the slope at which the same tractive stress on the bed would be produced with a discharge of 600 million m3/day.

11) A canal of bed slope 8 cm/km and side slope of 1:1 has a bed width of 10 m and depth of 2.5 m. The area irrigated by this canal is drained by a drain of 1:1 side slope and 10 cm/km longitudinal slope. Half of the water for irrigation is escaped to the drain, the Manning coefficient of the drain is 4/3 that of the canal. Design the drain if the relation between depth and width is :

345.1 by =


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12) Design a canal for non-silting, non-scouring condition given the following data:

Discharge = 50 m3/sec, bed slope = 9 cm/km, n = 0.025, the constant in Kennedy's formula = 0.28 and side slope =1:1, where Kennedy's formula may be written as:

V = C y(2/3)

13) An irrigation canal 16 m bed width, 1:1 side slope, and of 10 cm/km bed slope

runs at a normal depth of 4 m. The canal is to be widened to serve 25% more area. Find the necessary bed width; all other data are the same. Use Manning's formula.

14) A circular conduit 2 m in diameter carries different discharges under uniform

flow conditions with a free surface and 10 cm/km bed slope. If n = 0.01, Draw the curves showing the variations of mean velocity Vm and discharge Q with the water depth. Find the depths of maximum Q and maximum V.

15) A circular sewer 1.2 m in diameter, laid at a slope of 1:100 is to run at maximum velocity. What would be the discharge passing? Take C = 60 (metric).

16) A transmission cast iron pipeline (n = 0.01) is proposed to convey a maximum discharge Qmax of 1.45 m3/sec of treated water from the waste water treatment plant (WWTP) of a city to a main drain: The transmission pipeline will be laid at a. slope of 1/1000.

a. Select the minimum pipeline diameter D such that the flow depth does not

exceed half the pipe diameter. The available pipe sizes are: 1.0, 1.25, 1.5, 1.75, 2.0,... m.

b. Calculate the mean flow velocity. c. Calculate the flow depth and mean flow velocity for a low flow of Qmax/4.


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Problems to be solved by computer:

a) Create an Excel spread sheet that can calculate the flow area A, wetted perimeter P, hydraulic radius R, top water surface width B, and hydraulic depth D for the following channel cross sections:

a. Rectangular (bottom width = b ) b. Trapezoidal (bottom width = b, side slope = t:1) c. Triangular (side slope = t:1) d. Partially full circular (diameter = D) Make your spread sheet dynamic as much as you can. You can follow the instructions in the tutorial files to get familiar with the Microsoft Excel interface.

b) For the channel section with flood way shown in figure 1 (problem 4), calculate using Microsoft Excel the discharge flowing into the channel for water depths 0.1, 0.2, 0.3… 8.0m. Plot the variation of Q with water depth (in the specified range). Make your spread sheet as dynamic as possible so it can be used for different cross section geometries and manning coefficients. (Hint: The formulae used in calculating the discharge will vary when water depth is more than 3m. You can follow the example in the tutorial files for a simpler problem).

c) A circular conduit 2m in diameter carries different discharges under uniform

flow conditions with a free surface, lies at a slope of 10 cm/km with manning coefficient of 0.01 (metric). Using Microsoft Excel,

a. Calculate the velocity and discharge under uniform flow conditions for the

following depths: 0.05, 0.10, 0.15, … ,1.95 m b. Plot two curves showing the variations of mean velocity Vm and discharge

Q with the water depth. c. Find the depths of maximum Q and maximum V.

d) Make an Excel spread sheet to calculate the depth of uniform flow for the

following channel cross sections (use Manning equation):

a. Rectangular b. Triangular c. Trapezoidal d. Semi-Circular The spread sheet should be able to calculate the normal depth for the above cross section shapes for different values of discharge and channel geometry (side slope (t), bed width (b), bed slope (So), diameter (d), and manning coefficient (n).

CAIRO UNIVERSITY HYDRAULICS Faculty of Engineering 3rd year Civil Eng.

Irrigation & Hydraulics Department 2010 – 2011

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Model Answer



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When the water depth increases, the wetted perimeter (contact length causing friction to the flow) of the sides made of glass increases. On the other hand, the contact length with the bed (stainless steel) remains the same. This implies that the overall average manning coefficient of the cross section will approach that of glass (will decrease) with increasing the water depth.

We don’t expect to have the same behavior in natural open channels. In natural open channels, roughness increases with increasing the water depth due to the growth of weeds on the berms.



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Exercise (1): Open Channel Flow – Uniform Flow - UniMasr · Exercise (1): Open Channel Flow – Uniform ... decided to decrease the side slopes of the channel to be 2:1 due to slope