Hydraulic Radius of a Trapezoidal Channel (Unequal Side Slopes)

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Tags: Hydraulic Open Channel

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 trapezoid US 2

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 \(\large{ft}\) \(\large{m}\)

 

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Tags: Hydraulic Open Channel