A theory of Manning's formula
Abstract
Manning's formula for the mean velocity of gravitydriven, uniform, fully developed turbulent flows in rough open channels is among the better known expressions used by hydrologists, geomorphologists, and hydraulic engineers. Even though it was proposed more than a century ago, the formula has remained purely empirical. Here we show that Manning's formula represents the powerlaw asymptotic behavior of a flow of incomplete similarity in the relative roughness. We then derive the formula based on the phenomenological theory of turbulence. Our derivation yields the correct similarity exponent; it justifies Manning's use of a single parameter, the hydraulic radius, to characterize the geometry of the cross section; and it affords insight into the mechanism of momentum transfer.
 Publication:

APS Division of Fluid Dynamics Meeting Abstracts
 Pub Date:
 November 2003
 Bibcode:
 2003APS..DFD.DB012G