Hydraulic Radius Calculator

The hydraulic radius calculator finds the wetted perimeter and hydraulic radius for five different channel shapes.

Hydraulic radius0.44444 mA ÷ P — a rectangle: b + 2y of wetted perimeter

Flow rate3.2056 m³/s3,205.6 litres a second, 11,540 m³ an hour

Mean velocity2.0035 m/s

Flow area1.6 m²

Wetted perimeter3.6 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 number0.7153subcritical — deep, tranquil flow

No hydraulic jumpflow is subcriticala jump only forms where supercritical flow must return to subcritical

Critical depth0.63985 mfor this discharge in a rectangular section — the depth at which Froude reaches 1

At twice the slope4.5333 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 depth7.9644 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.