A trapezoidal channel having a bottom width of 6.1 m and side slopes of 1.5H : 1 V is carrying a flow of 126 m3/s at a flow depth of 5.79 m. The bottom slope is 0.00008, Manning n = 0.013 and the channel length is 5 km. There is constant-level reservoir at the upstream end of the channel. A sluice gate at the downstream end is suddenly closed at time t = 0 s. (a) Compute the transient conditions until t = 2000 s by using the method of characteristics. (b) Plot the computed flow depth in the channel at t = 0, 500, 1000, 1500 and 2000 s. (c) Plot the variation of the flow depth with time at 1.5, 2.5, 3.0 and 5.0 km from the reservoir. (d) By using different values of Δt/Δx, investigate the effect of interpolation error on the computed wave height and wave shape. (e) Show that the method of characteristic fails when a shock or bore is formed when the gate is closed in 10 s and the wave propagates in the channel.
A trapezoidal channel having a bottom width of 6.1 m and side slopes of 1.5H : 1 V is carrying a flow of 126 m3/s at a flow depth of 5.79 m. The bottom slope is 0.00008, Manning n = 0.013 and the channel length is 5 km. There is constant-level reservoir at the upstream end of the channel. A sluice gate at the downstream end is suddenly closed at time t = 0 s.
(a) Compute the transient conditions until t = 2000 s by using the method of characteristics.
(b) Plot the computed flow depth in the channel at t = 0, 500, 1000, 1500 and 2000 s.
(c) Plot the variation of the flow depth with time at 1.5, 2.5, 3.0 and 5.0 km from the reservoir.
(d) By using different values of Δt/Δx, investigate the effect of interpolation error on the computed wave height and wave shape.
(e) Show that the method of characteristic fails when a shock or bore is formed when the gate is closed in 10 s and the wave propagates in the channel.
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