How this calculator works
Flow resistance depends on the amount of wetted boundary relative to the area carrying water. Hydraulic radius combines these two quantities. The top surface is open to air and is not wetted wall. Trapezoidal and triangular modes use identical side slopes on both banks. Hydraulic diameter, often used in Reynolds-number calculations, equals four hydraulic radii and should not be confused with the radius of a circular pipe.
Formula
R = A/P. Full circle: A = pi r^2, P = 2 pi r, R = r/2. Rectangle: A = by, P = b + 2y. Symmetric trapezoid: A = y(b + zy), P = b + 2y sqrt(1 + z^2); triangle has b = 0.
Worked example
A rectangular channel 4 m wide and 1 m deep has area 4 m2, wetted perimeter 6 m and hydraulic radius 2/3 m. A full pipe of radius 0.5 m has hydraulic radius 0.25 m.
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Frequently asked questions
Is hydraulic radius the water depth?
Only approximately for a very wide rectangular channel. In general, calculate area divided by wetted perimeter.
What is the side slope convention?
A value z = 2 means two metres horizontal for each metre vertical, on each bank.
Is a half-full pipe hydraulic radius half the full value?
No. Both area and wetted perimeter halve at half depth, leaving the same hydraulic radius.