Downstream Depth of a Hydraulic Jump
Mediumopen channelhydraulic jump
A rectangular channel 4 m wide carries 12 m3/s. Just upstream of a hydraulic jump the flow is supercritical at a depth of 0.5 m. The depth immediately downstream of the jump is most nearly:
- A0.15 m
- B0.97 m
- C1.7 m
- D3.4 m
Show solutionHide solution
Answer: C. 1.7 m
Unit discharge q = Q/b = 12/4 = 3.0 m²/s, so V₁ = q/y₁ = 3.0/0.5 = 6.0 m/s and Fr₁ = V₁/√(gy₁) = 6.0/√(9.81×0.5) = 2.71. The sequent-depth relation gives y₂ = ½y₁(√(1+8Fr₁²) − 1) = ½(0.5)(√(1+8×2.71²) − 1) ≈ 1.7 m. The value 0.97 m is the critical depth (q²/g)^(1/3), which is where the jump passes through, not where it ends. Dropping the factor of ½ gives 3.4 m.
Practice this deckUntimed, one problem at a time, with your progress saved.
Related problems
- Flow over a Contracted Rectangular Weir · Hydrology & Stormwater
- Density from Mass and Volume · Fluids & Hydraulics
- Gauge Pressure at Depth in Water · Fluids & Hydraulics