Dimensionally Homogeneous Manning's Formula

Abstract

Manning was looking for a dimensionally homogeneous velocity equation but did not achieve it. Later the coefficient in one of his equations was related to Kutter's n. The dimension of n is reviewed here. If n is indeed a boundary roughness geometry measure, its dimension should be length to the one-sixth power. Subsequently, a new coefficient ng = (✓g/Kn) n is defined such that an improved, dimensionally homogeneous Manning formula is introduced. A short table of values of ng is provided. Finally, an equation to evaluate the error in using Manning's formula for fully-developed turbulent, steady, uniform flow in rigid boundaries is given.