2.5 The Actual Manning Equation?

Although Manning published his famous equation in 1890, he was not satisfied with it. The units on either side of the equal sign were not in balance, so the equation was highly empirical. Manning also believed (correctly) that because the formula was based on observed data (measured velocity versus measured depth, area, and slope), it could not be used correctly outside the range of the observed data (Manning, 1890). Consequently, Manning started over to develop an equation that would be dimensionally correct. Manning later proposed a very different equation for velocity:

where	V	=	the velocity (ft/s, m/s)
	C	=	the "pure" surface roughness (not Chézy C), dimensionless
	g	=	the gravitational constant (9.82 ft/s2, 9.81 m/s2)
	S	=	the slope (ft/ft, m/m)
	R	=	the hydraulic radius (ft, m)
	m	=	the height of a column of mercury corresponding to atmospheric pressure (ft, m)

This formula is dimensionally correct, with ft/s (m/s) units resulting on both sides of the equal sign. However, the formula was not greeted with enthusiasm and was not used by the engineering community. What we use today as the Manning equation was not the equation formally proposed by Manning for use in computing channel velocity (Rouse and Ince, 1963). Sometimes, even the "giants" of science and technology don't realize the value of their work!