Hydraulic Radius of a Trapezoidal Channel (Equal Side Slopes)

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 (Equal Side Slopes) formula

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

Where:

Units	English	Metric
\(\large{ r_h }\) = hydraulic radius	\(\large{ft}\)	\(\large{m}\)
\(\large{ A_c }\) = area cross-section of flow	\(\large{ft^2}\)	\(\large{m^2}\)
\(\large{ b }\) = bottom width of fluid	\(\large{ft}\)	\(\large{m}\)
\(\large{ h }\) = depth of fluid	\(\large{ft}\)	\(\large{m}\)
\(\large{ P_w }\) = wetting perimeter	\(\large{ft}\)	\(\large{m}\)
\(\large{ z_1 }\) = \(\large{ z_2 }\) = width of channel slope	\(\large{ft}\)	\(\large{m}\)