Civil Engineering Department
Hydraulics-Discussion / Instructors:
Dr. Said Ghabayen
Dr. Mazen Abu Altayef
T.A. Eng: Motasem abu shaban
Eng: Amal Qarroot
* Solve the following questions:
(1) A 3-m-wide rectangular irrigation channel carries a discharge of 25.3 m3/sec at a uniform depth of 1.2 m. Determine the slope of the channel with Manning’s coefficient, n = 0.022. (S0 = 0.041)
(2) If the discharge in the channel in problem (1) is 50 m3/sec , determine the normal depth of the flow. (yn = 2.0 m)
(3) A trapezoidal open channel has a bottom width of 10 and side slopes with inclination 1:2 . The channel is paved with smooth cement surface (n = 0.011) . If the channel is laid on a slope of 0.0001 and carries a uniform flow at the depth of 2 m, determine the discharge. (Q = 33.03 m3/sec)
(4) If the discharge in the channel in problem (3) is increased to 40 m3/sec , what is the normal depth of the flow. (yn = 1.69 m)
(5) Find the slope of the bed of a rectangular channel of width 5 m when the depth of water is 2 m and the rate of flow is given as 20 m3/sec. Take Chezy’s constant C = 50.(S0 = 1/694.44)
(6) Find the discharge through a trapezoidal channel width 8 m and side slope of 1 horizontal to 3 vertical. The depth of flow of water is 2.4 m and the value of Chezy’s constant C = 50. The slope of the bed of the channel is given 1 in 4000.
(Q = 21.23 m3/sec)
(7) Find the bed slope of a trapezoidal channel of bed width 4 m, depth of water 3 m and side slope of 2 horizontal to 3 vertical, when the discharge through the channel is 20 m3/sec. Take Manning’s coefficient, n = 0.03.(S0 = 1/1692)
(8) Find the diameter of a circular sewer pipe which is laid at a slope of 1 to 8000 and carries a discharge of 800 liters/sec when flowing half full. Take Manning’s coefficient, n = 0.020.(D = 2.296 m)
(9) Find the discharge through a circular pipe of diameter 3.0 m, if the depth of water in the pipe is 1.0 m and the pipe is laid at a slope of 1/1000. Take Chezy’s constant C = 70. (Q = 3.407 m3/sec)
(10) Calculate the quantity of water that will be discharged at a uniform depth of 0.9 m in a 1.2 m diameter pipe which is laid at a slope of 1/1000. Assume Chazy’s C = 58. (Q = 1.007 m3/sec)
(11) An open channel is triangular in cross-section (V-shaped), with side slope 1: 1. If the depth of flow is 25 cm and the discharge is 0.05 m3/sec, calculate the slope. Take Chezy’s , C =50.(S0 = 1/344)
(12) A trapezoidal channel with base width 10 m and side slope 1:1 carries a discharge of 15 m3/sec. Compute the normal depth and the velocity if the slope is 1 in 625 and n = 0.025.(yn = 0.90 m)
Economical sections
(13) Determine the conditions for the most efficient triangular section.
(14) A rectangular channel of width 4 m is having a bed slope 1 in 1500. Find the maximum discharge through the channel. Take value of C = 50. (Q = 10.328 m3/sec)
(15) A rectangular channel caries water at the rate of 400 liters/sec when bed slope is 1/2000. Find the most economical dimensions of the channel if C = 50.
(d = 0.557 m, b = 1.154 m)
(16) A trapezoidal channel has side slopes of 3 horizontal to 2 vertical has to be designed to convey 10 m3/sec at a velocity of 1.5 m/sec, so that the amount of concrete lining for the bed and sides is minimum. Find
(One) the wetted parameter, and
(Two) slope of the bed if Manning’s coefficient, n = 0.014.
( P = 7.48 m, S0 = 1/1729.4)
(17) An open channel has a diameter of 1.68 m. If the channel slope is 1 in 5000, calculate the maximum discharge which the channel can carry. Use Chezy’s formula, C = 70. (Q = 1.49 m3/sec)
(18) A sewer with diameter 0.5 m is laid at a slope 1 in 225. What is maximum velocity of flow that can occur ? What would be the discharge at that velocity ? Take C = 60. (V = 1.56 m/sec, Q = 0.267 m3/sec)
(19) A circular pipe of diameter 1 m has to carry a maximum discharge of 0.80 m3/sec. Calculate the required slope. Use Manning's formula, n = 0.0167.
(S0 = 1/630)
Specific Energy & Critical Flow
(20) Find the specific energy of flowing water through a rectangular channel of width 5 m when the discharge is 10 m3/sec and depth of water is 3 m.(E = 3.0226 m)
(21) Find the critical depth and critical velocity of the water flowing through a rectangular channel of width 5 m, when the discharge is 15 m3/sec.
(yc = 0.972 m, Vc = 3.088 m/sec)
(22) The discharge of water through a rectangular channel of width 8 m, is 15 m3/sec when the depth of flow of water is 1.2 m. Calculate:
(One) specific energy of the flowing water,
(Two) critical depth and critical velocity,
(Three) value of minimum specific energy.
(1.324 m, 0.71 m, 2.639 m/sec, 1.065 m )
(23) A rectangular channel is to carry a discharge of 25 m3/sec at slope of 0.006. Determine the width of the channel for the critical flow. Take n = 0.016.
(B = 3 m)
(24) A discharge of 30 m3/sec flow in a trapezoidal channel with base width 3 m and side slope 2 (horizontal) and 1 (vertical). Calculate the critical depth. Take n = 0.015.
(yc = 1.55 m)
Hydraulic Jump
(25) A 3-m-wide rectangular channel carries 15 m3/sec of water at 0.6 m depth before entering a jump. Compute the downstream water depth and the critical depth.
(y2 = 4.38 m, yc = 1.60 m )
(26) A long, rectangular open channel 3 m wide carries a discharge of 15 m3/sec. The channel slope is 0.004 and the Manning’s coefficient is 0.01. At a certain point in the channel where the flow reaches the normal depth,
(a) determine the state of the flow, is it supercritical or subcritical,
(b) if a hydraulic jump takes place at this length, what is the conjugate depth at the
jump,
(c) estimate the energy head loss through the jump.
(supercritical, y2 = 1.70 m, )
(27) A hydraulic jump occur at an initial depth of 1.5 m in a rectangular channel 4-m wide. If the conjugate depth is 2.2 m, determine the energy loss and the discharge in the channel.( , Q = 30.96 m3/sec)
(28) A sluice gate discharges water into a horizontal rectangular channel with a velocity of 10 m/sec and depth of flow of 1 m. Determine the depth of flow after the jump and the loss in total head. ( y2 = 4.043 m, )
Gradually varied flow & Water profiles
(29) A wide rectangular channel carries a discharge per unit width of 2.5 m3/sec/m on a 0.001 slope and n = 0.025. Compute the backwater curve created by a low dam that has water at a depth 2 m immediately behind the dam. The upstream computation may be carried out to a depth 1% greater than the normal depth. Use the direct step method.
(30) Find the rate of change of depth of water in a rectangular channel of 10 m wide and 1.5 m deep, when the water is flowing with a velocity of 1 m/sec. The flow of water through the channel of bed slope 1/4000, is regulated in such a way that the energy line having a slope of 0.00004.(dy/dx = 0.000217)