Hydraulic Jump: Problem Solving

Water flows through a rectangular channel at 6 meters per second. When a gate at the end of the channel suddenly closes, a wave called a hydraulic jump travels upstream at 2 meters per second. 

In front of the jump, the wave's velocity combines the channel's initial flow, resulting in an effective upstream velocity of 8 meters per second. Behind the jump, the water flows at a speed of 2 meters per second.

Since the flow rate remains constant, the downstream-to-upstream velocity ratio is 1:4, so the downstream depth is four times the upstream depth.

To analyze the hydraulic jump, the Froude number, which relates flow inertia to gravity, is calculated as the upstream velocity divided by the square root of gravitational acceleration times the upstream depth. 

Using this, the upstream depth is determined as 0.652 meters. Multiplying by four yields a downstream depth of 2.61 meters.

As a result, the depth ahead of the jump is 0.65 meters, and behind it, 2.61 meters.