Manning Formula

The Manning formula, known also as the Gauckler–Manning formula, or Gauckler–Manning–Strickler formula in Europe, is an empirical formula for open channel flow, or free-surface flow driven by gravity. It was first presented by the French engineer Philippe Gauckler in 1867, and later re-developed by the Irish engineer Robert Manning in 1890.

The Gauckler–Manning formula states:

where:

V	is the cross-sectional average velocity (L/T; ft/s, m/s)
k	is a conversion factor of (Length1/3/Time), 1 m1/3/s for SI, or 1.4859 ft1/3/s U.S. customary units, if required. (Note: (1 m)1/3/s = (3.2808399 ft) 1/3/s = 1.4859 ft1/3/s)
n	is the Gauckler–Manning coefficient, it is unitless
Rh	is the hydraulic radius (L; ft, m)
S	is the slope of the water surface or the linear hydraulic head loss (L/L) (S = hf/L)

The discharge formula, Q = A V, can be used to manipulate Gauckler–Manning's equation by substitution for V. Solving for Q then allows an estimate of the volumetric flow rate (discharge) without knowing the limiting or actual flow velocity.

The Gauckler–Manning formula is used to estimate flow in open channel situations where it is not practical to construct a weir or flume to measure flow with greater accuracy. The friction coefficients across weirs and orifices are less subjective than n along a natural (earthen, stone or vegetated) channel reach. Cross sectional area, as well as n', will likely vary along a natural channel. Accordingly, more error is expected in predicting flow by assuming a Manning's n, than by measuring flow across a constructed weirs, flumes or orifices.

The formula can be obtained by use of dimensional analysis. Recently this formula was derived theoretically using the phenomenological theory of turbulence.