Specific Energy, Critical Depth & the Jump

Worked: below a sluice gate

A 10 ft wide rectangular channel carries 200 cfs, so q = 20 cfs/ft. y_c = (20²/32.2)^(1/3) = 2.32 ft. Just downstream of a gate the flow is 1.0 ft deep at 20 ft/s: Fr₁ = 20/√32.2 = 3.52, supercritical.

y₂ = 0.5 × (−1 + √(1 + 8 × 3.52²)) = 4.51 ft. The jump dissipates (3.51)³/(4 × 1.0 × 4.51) = 2.40 ft of head — a third of the 7.21 ft the flow arrived with.