Manning formulation¶

The application of Manning's formula uses a friction slope:

\[ I_{f} = fq\left|q\right| \]

Equation: Friction slope in Manning resistance formulation as a function of discharge and flow properties.

with the friction factor:

\[ f = \frac{1}{M^2 A_{fl}^2 R^{4/3}} \]

Equation: Manning friction factor relating resistance to Manning coefficient, flow area, and hydraulic radius raised to 4/3 power.

where M is the Manning resistance number, A~fl ~the flow area, and R the hydraulic radius. Conveyance is defined as

\[ K = M A_{fl} R^{2/3} \]

Equation: Conveyance as the product of Manning coefficient, flow area, and power of hydraulic radius.

The unit of the Manning M is \(m^{1/3} / s\). The Manning number, M, is equivalent to the Strickler coefficient. It is the inverse of the Manning n, i.e.

\[ \begin{array}{r}{M=\frac{1}{n}}\end{array} \]

Equation: Manning M coefficient defined as the reciprocal of Manning n roughness.

The value of n is typically in the range 0.01 (smooth) to 0.1 (thickly vegetated/very rough bottom). The corresponding values for M are from 100 to 10.