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

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 of a Trapezoidal Channel (Unequal Side Slopes) formula

$$\large{ r_h = \frac { \frac {h} {2} \; \left( b \;+\; w \right) } { b \;+\; h \; \left( \sqrt { 1 \;+\; z_{1}{^2} } \;+\; \sqrt { 1 \;+\; z_{2}{^2} } \right) } }$$
Symbol English Metric
$$\large{ r_h }$$ = hydraulic radius $$\large{ft}$$  $$\large{m}$$
$$\large{ A_c }$$ = area cross-section of flow $$\large{ft^2}$$ $$\large{m^2}$$
$$\large{ b }$$ = bottom width of fluid $$\large{ft}$$ $$\large{m}$$
$$\large{ h }$$ = depth of fluid $$\large{ft}$$ $$\large{m}$$
$$\large{ g }$$ = gravitational acceleration $$\large{\frac{ft}{sec^2}}$$ $$\large{\frac{m}{s^2}}$$
$$\large{ w }$$ = top width of fluid $$\large{ft}$$ $$\large{m}$$
$$\large{ P_w }$$ = wetting perimeter $$\large{ft}$$ $$\large{m}$$
$$\large{ z_1 }$$ = width of channel slope $$\large{ft}$$ $$\large{m}$$
$$\large{ z_2 }$$ = width of channel slope $$\large{ft}$$ $$\large{m}$$ 