The Manning Equation
The Manning Equation for U.S. units is: Q = (1.49/n)A(R2/3)(S1/2),
and for S.I. units it is: Q = (1.0/n)A(R2/3)(S1/2), Where
Q = volumetric water flow rate passing through the stretch of channel, ft3/sec (m3/s for S.I.)
A = cross-sectional area of flow perpendicular to the flow direction, ft2 (m2 for S.I.)
S = bottom slope of channel, ft/ft (dimensionless),
n = Manning roughness coefficient (empirical constant), dimensionless,
R = hydraulic radius = A/P in ft (m for S.I.) where
A = cross-sectional area of flow as defined above,
P = wetted perimeter of cross-sectional flow area, ft (m for S.I.)
The Manning Equation can be expressed in terms of flow velocity instead of flow rate. Using the equation, V = Q/A as a definition for average flow velocity, the Manning Equation becomes:
V = (1.49/n)(R2/3)(S1/2), with average flow velocity in ft/sec.
In S.I. units this equation becomes: V = (1.0/n)(R2/3)(S1/2), with average velocity in m/s.
Note that the Manning Equation is an empirical, dimensional equation. With the constant equal to 1.49 for U.S. units (or 1.0 for S.I. units), all of the parameters must have the units given above for the chosen system of units.