# 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 Formula

$$\large{ v = \frac{1.49 \; r_h^{0.66} \; S^{0.5} }{n} }$$

$$\large{ v = \frac{1.49 \; r_h^{2/3} \; S^{1/2} }{n} }$$

Where:

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

$$\large{ S }$$ = channel slope or energy slope line

$$\large{ r_h }$$ = hydraulic radius

$$\large{ n }$$ = Manning roughness coefficient

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