Exercise (4): Open Channel Flow - Gradually Varied Flow 1) A wide channel consists of three long reaches and has two gates located midway of the first and last reaches. The bed slopes for the three reaches are S 1 = 0.008, S 2 = 0.00309, and S 3 = 0.0005. The water discharges to the channel from a lake where the water surface is higher than the normal depth at the inlet. If the discharge is 0.675 m 3 /sec/m, and n = 0.015, sketch the possible water surface profiles in the channel for the following cases: a) The last reach terminates in a sudden fall. b) The last reach discharges to a lake of water level higher than the normal depth at the exit. 2) Water flows with constant discharge q=1.0 m 3 /s/m into a wide rectangular channel that consists of two very long reaches where the bed slope changes from S o1 =6.87x10-3 to S o2 =3.24x10-4, Calculate: a) The depth of both uniform and critical flow in both reaches (take n=0.018) b) Draw a neat sketch of the water profile at the transition zone and calculate the water depths and the head losses wherever appropriate. 3) A barrage is constructed across a wide river whose discharge is 6 m 3 /sec/m, and bed slope is 10 cm/km. If the afflux produced at the site of the barrage is 3 m, find the length of the water surface profile produced from the site of the barrage till a point where the water depth is 6.25m. Use the approximate method considering 3 points, Chezy coefficient C = 50. 4) A trapezoidal channel of bed width of 7 m, side slopes 3:2, Manning coefficient n of 0.02 is laid on a slope of 0.001 and carries a discharge of 30m 3 /sec. The channel terminates to a free fall. It is required to compute and plot the water surface profile from downstream to a water depth of 0.9 the normal depth. Use the step by step method (use 3 steps) 5) A steep long channel takes its water from a lake. Prove that the discharge per unit width in the channel is given by: q = 8 27 Two lakes are joined by a wide concrete channel A-B as shown in the figure below, n = 0.02. The water levels in the lakes are constant. g H a) Find the flow rate into the channel for each of the following bed slopes: i. S o = 10 cm/km ii. S o = 0.003924 iii. S o = 0.01 Compare your results and explain how the flow depth at A affects the flowing discharge. b) Sketch the Water surface profile for the above cases and calculate the water depths wherever appropriate. 3 2-1 -
c) Does a hydraulic jump occur? If so, How far upstream point B does it occur? Use the step by step method, considering 5 points. 1.5m A 2.0m n = 0.02, Bed Slope = S o B 6) A 10 m wide, rectangular concrete-lined canal (n = 0.015) has a bottom slope of 0.01 and a constant level lake at the upstream end. The water level in the lake is 6m above the bottom of the canal at the entrance. If the entrance losses are negligible, determine: a) The flow depth 600 m downstream of the channel entrance, b) The distance from the lake where the flow depth is 3.0 m. Use the step by step method. 7) The figure below shows a longitudinal section in a channel of wide cross section. Manning s n = 0.02 and the bed slope is 0.001. q B A S o = 1/1000, n = 0.02 A gate is located at point A. The discharge equation for the gate in case of free outflow is given by: q = C d 2g( H C d) and for a submerged outflow is: q = Cd d 2g( H y) d c - 2 -
Where q is the discharge per unit width (m 2 /sec), C d is the discharge coefficient and is equal to 0.6, d is the height of the gate opening (m), H is the water depth just upstream of the gate (m), y is the water depth downstream the gate (m), and g is the gravitational acceleration (m/sec 2 ). The coefficient of contraction of the gate C c = 0.63. a) If q = 3 m 3 /sec/m, and H = 3m, find the gate opening d, and check if a free hydraulic jump will form downstream of the gate. Assume the channel downstream A is long enough to allow for uniform flow to develop. If a jump will form, how far downstream of A will it be? (Use an appropriate method to calculate the distance) b) Point B is located 600m upstream of the gate. Find the water depth at B. Use the step by step method considering two steps. If the bed level at A = 20.75m, find the water level at B. c) The gate at A is used to maintain a constant water level at B for different values of discharge. What is the required gate opening to keep the water level at B unchanged, for a low flow of 1 m 3 /sec/m? Use the approximate method with only one step. 8) A trapezoidal channel having bottom slope 0.001 is carrying a flow of 30m 3 /s. The bottom width is 10.0m and side slope 2H to 1V. A control structure is built at the downstream end which raises depth at the downstream end to 5.0m. Compute and draw the water surface profile. Manning n for the flow surfaces is 0.013. - 3 -
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