# Manning's Roughness Coefficient

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Manning's roughness coefficient, abbreviated as n, also called Manning's coefficient, roughness coefficient, a dimensionless number, measures the roughness or frictional resistance exerted by a flow against the ground surface in an open channel, culvert or pipe.  The Manning roughness coefficient is one of the most important ways to describe the water flow over the ground surface.

The roughness coefficient is used to calculate the friction factor using a Moody Diagram and the Reynolds number.

## Manning's roughness coefficient formula

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

### Where:

 Units English Metric $$\large{ n }$$ = Manning's roughness coefficient $$\large{ dimensionless }$$ $$\large{ S }$$ = channel slope or energy slope line $$\large{ ft }$$ $$\large{ m }$$ $$\large{ v }$$ = flow velocity in a channel, culvert, or pipe $$\large{ \frac{ft}{sec} }$$ $$\large{ \frac{m}{s} }$$ $$\large{ r_h }$$ = hydraulic radius $$\large{ ft }$$ $$\large{ m }$$

### Solve For:

 $$\large{ v = \frac{1.49 \; r_h^{\frac{2}{3} } \; S^{\frac{1}{2} } }{ n } }$$ $$\large{ r_h = \left( \frac{ v \; n }{ 1.49 \; S^{\frac{1}{2}} } \right)^{ \frac{1}{0.66} } }$$ $$\large{ S = \left( \frac{ v \; n }{ 1.49 \; r^{\frac{2}{3}} } \right)^2 }$$ $$\large{ Q = \frac{ 1.49 }{ n } \; A_c \; r_h^{\frac{2}{3} } \; S^{\frac{1}{2}} }$$

## Related Manning's Roughness Coefficient formula

 $$\large{ n = \frac{ 0.56 }{ Q } \; m_c^{\frac{5}{3} } \; m_l^{\frac{1}{2} } \; Q^{\frac{8}{3} } }$$ (gutter flow rate)

### Where:

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

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

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

$$\large{ m_c }$$ = cross slope of pavement

$$\large{ m_l }$$ = longitudinal slope of pavement