Question

A rectangular channel 3 m wide carries 4m3/s of water at a depth of 1.5m. if an obstruction 15 cm high is placed across the channel, calculate the elevation of the water surface over the obstruction.

Answer 1

Given B = 3 m y = 1.5 m Q = 4 m^3/sec Area, A = B.y = 3 times 1.5 = 4.5 m^2 velocity, v = Q/A = 4/4.5 = 0.888 m/sec specific Energy E = y + v^2/2g = 4.5 + 0.888^2/2 times 9.81 = 4.540 m Critical depth f = (q^2/g)^1/3 q = Q/B = (4/3) therefore y_c = [(4/3)^2/9.81]^1/3 = 0.565 m specific Energy at critical depth, E_e = 3/2 y_c = 3/2 times 0.565 = 0.847 m As the upstream bed level is raised by 0.15m Specific Energy will decrease new specific Energy = E' = E-0.15 = 4.540-0.15 = 4.39 m As E' > E_c upstream depth of flow will not changed delta Z = E_1-E' = 4.540-4.34 = 0.15 m