Hydraulic Jump Calculator

The hydraulic jump calculator analyzes the jump from a supercritical to a subcritical flow in a rectangular channel.

Depth after a hydraulic jump0.9975 my₁/2 (√(1+8Fr²) − 1) — the conjugate depth

Flow rate3.2469 m³/s3,246.9 litres a second, 11,688.99 m³ an hour

Mean velocity5.4116 m/s

Hydraulic radius0.17647 mA ÷ P — a rectangle: b + 2y of wetted perimeter

Flow area0.6 m²

Wetted perimeter3.4 monly the wetted boundary creates friction, so the best section is the one with least perimeter for its area — for a rectangle that is twice as wide as it is deep, and going deeper than that makes it worse again

Manning's n used0.013Concrete, trowelled — a FITTED coefficient with real scatter, so treat two significant figures as the limit of what this result can support

Froude number3.8641supercritical — shallow, fast flow, and a hydraulic jump is possible downstream

Energy lost in the jump0.6356 mof head — a jump is deliberately used to dissipate energy below a spillway

Depth ratio4.9875×

Critical depth0.49249 mfor this discharge in a rectangular section — the depth at which Froude reaches 1

At twice the slope4.5919 m³/sonly √2 times the flow — Manning has slope to the power one half, so steepening a channel buys less than it seems

At twice the depth9.5717 m³/smore than double, because both the area and the hydraulic radius increase

The formula

v = (1/n)R^⅔S^½; R = A ÷ P; Q = Av

Wetted perimeter, not area

Manning's equation says velocity depends on the hydraulic radius — flow area divided by wetted perimeter — to the power two thirds. Only the wetted boundary generates friction, so of two channels with the same cross-sectional area, the one with less wetted perimeter flows faster. A semicircle is the overall optimum; among rectangles the best is exactly twice as wide as it is deep, and going either wider or deeper than that makes it worse. "Deep and narrow beats wide and shallow" is only true up to that point.

A curious consequence: a circular pipe running half full has exactly the same hydraulic radius as one running full, since both area and perimeter halve. It therefore has the same velocity, and carries half the flow.

The exponents matter for design. Slope enters as a square root, so doubling the gradient increases flow by only 41%. Depth enters through both area and hydraulic radius, so deepening a channel is a much stronger lever than steepening it.

Manning's n is a fitted coefficient, not a measurement. Published ranges for a single surface type often span 30%, and a weedy channel can double against a clean one. Any result here is good to two significant figures at best, and quoting more is false precision.