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 formula

 $$\large{ r_h = \frac { A_c } { P_w } }$$

### Where:

 Units English Metric $$\large{ r_h }$$ = hydraulic radius $$\large{ ft }$$ $$\large{ m }$$ $$\large{ A_c }$$ = area cross-section of flow $$\large{ ft^2 }$$ $$\large{ m^2 }$$ $$\large{ P_w }$$ = wetting perimeter $$\large{ ft }$$ $$\large{ m }$$

## Related Hydraulic Radius formulas

 $$\large{ r_h = \frac{1}{m} \; \left( \frac{v}{C} \right)^2 }$$ (Chezy Formula) $$\large{ r_h = \left( \frac{ v \; n }{ 1.49 \; S^{\frac{1}{2}} } \right)^{ \frac{1}{0.66} } }$$ (Manning's Roughness Coefficient) $$\large{ r_h = \left( C \; n \right)^6 }$$ (Roughness Coefficient)

### Where:

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

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

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