Abstract
We show that Manning's empirical formula for the mean velocity of turbulent flows in channels 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.
- Received 21 June 2001
DOI:https://doi.org/10.1103/PhysRevLett.88.014501
©2001 American Physical Society