Hydraulic Radius of a Trapezoidal Channel (Unequal Side Slopes)

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.

Hydraulic Radius of a Trapezoidal Channel (Unequal Side Slopes) formula

$$\large{ r_h = \frac { \frac {h} {2} \left( b + w \right) } { b + h \left( \sqrt { 1 + z_{1}{^2} } + \sqrt { 1 + z_{2}{^2} } \right) } }$$

Where:

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

$$\large{ b }$$ = bottom width of fluid

$$\large{ h }$$ = depth of fluid

$$\large{ g }$$ = gravitational acceleration

$$\large{ w }$$ = top width of fluid

$$\large{ z }$$ = width of channel slope