Hydraulic Radius of a Trapezoidal Channel (Equal Side Slopes)

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

hydraulic radius of a trapezoid ES 2Hydraulic 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

\(\large{ r_h =  \frac  {  h \; \left( b \;+\; z\; h \right) }  { b \;+\; 2\;h \; \sqrt { 1 \;+\; z_{1}{^2}  }  }   }\) 
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 \(\large{ft}\) \(\large{m}\)
\(\large{ P_w }\) = wetting perimeter \(\large{ft}\) \(\large{m}\)
\(\large{ z_1 }\) = \(\large{ z_2 }\) = width of channel slope \(\large{ft}\) \(\large{m}\)

 

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Tags: Hydraulic Equations