# Hydraulic Radius

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Hydraulic radius, abbreviated as $$r_h$$, is the area cross-section of water in a pipe or channel divided by the wetting perimeter.

## Hydraulic Radius formulas

 $$\large{ r_h = \frac { A_c } { P_w } }$$ $$\large{ r_h = \left( C \; n \right)^6 }$$ (roughness coefficient) $$\large{ r_h = \frac{1}{m} \; \left( \frac{v}{C} \right)^2 }$$ (Chezy formula) $$\large{ r_h = \left( \frac{v\; n}{1.49 \; S^{0.5} } \right)^{\frac{1}{0.66}} }$$ (Manning equation)

### Where:

$$\large{ r_h }$$ = hydraulic radius

$$\large{ A_c }$$ = area cross-section of flow

$$\large{ C }$$ = Chezy coefficient

$$\large{ n }$$ = Manning's roughness coefficient

$$\large{ n }$$ = roughness coefficient

$$\large{ m }$$ = slope

$$\large{ S }$$ = channel slope or energy slope line

$$\large{ k }$$ = unit conversion factor ($$k = 1.49$$ English units ft/sec) ($$k = 1.0$$ SI units m/sec)

$$\large{ v }$$ = velocity of flow in a channel, culvert, or pipe

$$\large{ P_w }$$ = wetted perimeter