Written by Jerry Ratzlaff on . Posted in Fluid Dynamics  Hydraulic radius, abbreviated as $$r_h$$, is the cross-section area of water in a pipe or channel divided by the wetting perimeter.

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

$$\large{ r_h = \left( C \; n \right)^6 }$$

$$\large{ r_h = \frac{1}{m} \; \left( \frac{v}{C} \right)^2 }$$     (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

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

$$\large{ A }$$ = cross-section flow area

$$\large{ v }$$ = flow velocity

$$\large{ n }$$ = Manning 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)

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

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