Question

A hydraulic jump is formed in a 4m wide outlet just downstream of a control gate, which is located at the upstream end of the outlet. The flow depth upstream of the gate is 20 m. Assume there are no losses in the flow through the gate. If the outlet discharge is 40 m3/s, determine (6 points)a. Flow depth downstream of the jump (y1)b. Energy losses in the jump (between y1 and y2).

Answer 1

Width w = 4m

Glow depth = y1 = 20m

Outlet discharge = 40m

V1= velocity of flow = 40/20*4 = 1/2 = 0.5m/s

Froud number = v1/√gy1

= 0.5/√9.81x20 = 0.0356

1. Y2/20 = 1/2[-1+√1+8*(0.0356)²]

Y2 = 0.05

2. Energy loss in the jump = (20-0.05)²/4x20x0.05

= 1985m