# Manning Equation

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

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