Manning Equation

Manning equation, expressed in numerous ways, is a commonly used equation for the uniform flow in open channels.

 

Manning Equation formulas

\(\large{ v =  \frac{ k }{ n } \; \left( \frac{A}{p_w} \right)^{\frac{2}{3}} \; S^{\frac{1}{2}}  }\)
\(\large{ v =  \frac{ 1 }{ n } \; r_h^{\frac{2}{3}} \; \sqrt{i}  }\)
\(\large{ v =  \frac{1.49 \; r_h^{2/3} \; S^{1/2} }{n}   }\)
\(\large{ v =  \frac{ k }{ n }  \; r_h^{2/3} \; S^{1/2}   }\)
\(\large{ Q=  \frac{ k }{ n } \; A \; r_h^{2/3} \; S^{1/2}  }\)
\(\large{ Q =  \frac{ 1.49 }{ n } \; A \; r_h^{\frac{2}{3}} \; S^{\frac{1}{2}}  }\)
\(\large{ Q =  \frac{ k \; A \; r_h^{\frac{2}{3}} \; S^{\frac{1}{2}} }{ n }  }\)

Where:

\(\large{ v }\) = flow velocity in a channel, culvert, or pipe

\(\large{ Q }\) = flow rate in a channel, culvert, or pipe

\(\large{ A }\) = area cross-section flow in a channel, culvert, or pipe

\(\large{ S }\) = channel slope or energy slope line

\(\large{ i }\) = hydraulic gradient

\(\large{ r_h }\) = hydraulic radius

\(\large{ n }\) = Manning's roughness coefficient

\(\large{ k }\) = unit conversion factor (\(k = 1.49\) English units ft/sec) (\(k = 1.0\) SI units m/sec)

\(\large{ P_w }\) = wetted perimeter