A theory of Manning's formula
Abstract
Manning's formula for the mean velocity of gravity-driven, 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 power-law 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