Hydraulic Radius of a Triangular Channel

Hydraulic radius, abbreviated as \(r_h\), is the area cross-section of water in a pipe or channel divided by the wetting perimeter.  The hydraulic radius (R) of an open channel, including a triangular channel, is a measure of the channel's efficiency in conveying flow.  It is defined as the cross-sectional area of flow divided by the wetted perimeter.

 

Hydraulic Radius of a Triangular Channel Formula
\( r_h \;=\;  \dfrac{ A_c }{ P_w  }\)     (Hydraulic Radius of a Triangular Channel) \( A_c \;=\;  r_h \cdot P_w   \) \( P_w \;=\;  \dfrac{ A_c }{ r_h  }\)
Symbol	English	Metric
\( r_h \) = Hydraulic Radius	\(ft\)	\(m\)
\( A_c \) = Flow Area Cross-section	\(ft^2\)	\(m^2\)
\( P_w \) = Wetting Perimeter	\(ft\)	\(m\)

        

Hydraulic Radius of a Triangular Channel Formula
\( r_h \;=\;  \dfrac{ z \cdot h^2 }{ 2 \cdot h \cdot \sqrt{1 + z^2 } }\)
Symbol	English	Metric
\( r_h \) = Hydraulic Radius	\(ft\)	\(m\)
\( z \) = Width of Channel Slope	\(ft\)	\(m\)
\( h \) = Fluid Depth	\(ft\)	\(m\)