Hydraulic Radius Equation

Published: October 31, 2018 | Last updated: July 5, 2023

What Does Hydraulic Radius Equation Mean?

The hydraulic radius equation is a mathematical formula for calculating the hydraulic radius of a pipe. Hydraulic radius is the cross sectional area of the fluid divided by its wetted perimeter. Most sewer pipes flow as open channels under gravity, and not under pressure. The fluid in a conduit that is only partially full is similar to an open channel that flows at atmospheric pressure. Pipe diameter and depth of flow should be known for calculating hydraulic radius.


Trenchlesspedia Explains Hydraulic Radius Equation

The equations to calculate hydraulic radius are slightly different for pipes flowing more than half full and pipes flowing less than half full. Hydraulic radius is necessary for calculations utilizing Manning's formula.

Hydraulic radius, Rh = A / P

where A – cross sectional area of flow

P – wetted perimeter

For pipe flowing less than half full, the height of flow (h) is equal the depth of flow (y).


For pipe flowing more than half full, the height of flow (h) is (2r – y) where r – radius of the pipe.

h = 2r – y


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