Hydraulic Radius Calculator

Hydraulic radius is a geometric measure of how efficiently a channel cross section conveys fluid. It is defined as the flow area divided by the wetted perimeter. The wetted perimeter includes only boundary surfaces touching the fluid; it does not include a free water surface. A larger hydraulic radius generally means less boundary contact for a given flow area and therefore lower resistance. Despite its name, hydraulic radius is not usually the same as a physical radius. For a rectangular open channel, flow area is bottom width multiplied by water depth, while wetted perimeter is the bottom width plus twice the depth. For a trapezoidal channel with side slope expressed as horizontal distance per unit vertical rise, area equals depth multiplied by bottom width plus side slope times depth. Its wetted perimeter includes the bottom and both sloping sides. For a completely full circular pipe, area is pi times diameter squared divided by four and wetted perimeter is pi times diameter, so hydraulic radius simplifies to one quarter of the pipe diameter. Hydraulic radius appears in the Manning and Chezy equations for uniform open-channel flow and in relations involving hydraulic diameter. Hydraulic diameter equals four times hydraulic radius. For a full circular pipe, hydraulic diameter therefore equals its physical diameter. In partially full circular pipes and noncircular ducts, the wetted geometry must be evaluated for the actual fluid depth. This calculator's circular option represents a completely full pipe, not a partly filled circular channel. Accurate dimensions are important because depth changes both area and perimeter and can strongly affect predicted discharge. Use dimensions normal to the flow direction and keep all inputs in the same length unit. The numerical radius will be in that same unit, even though the labels here use metres. Natural streams and irregular channels can be divided into subsections or evaluated from surveyed coordinates, but simple idealized shapes may not capture benches, vegetation, compound floodplains, sediment, or local obstructions. This calculator supplies the geometric values needed for subsequent flow analysis; it does not calculate velocity or discharge by itself. To estimate those quantities, combine hydraulic radius and flow area with channel slope and a suitable roughness coefficient. Verify whether the selected equation and roughness value apply to the actual flow regime and lining. For design work, also check freeboard, erosion velocity, transitions, nonuniform flow, and uncertainty in the surveyed water level.