Manning formula

Abstract

The Manning formula is also known as the Gauckler--Manningformula, or Gauckler--Manning--Strickler formula in Europe. Inthe United States, in practice, it is very frequently calledsimply Manning's Equation. The Manning formula is an empiricalformula estimating the average velocity of a liquid flowing in aconduit that does not completely enclose the liquid, i.e., openchannel flow. All flow in so-called open channels is driven bygravity. It was first presented by the French engineer PhilippeGauckler in 1867, and later re-developed by the Irish engineerRobert Manning in 1890. The Gauckler--Manning formula states:where: V is the cross-sectional average velocity (L/T; ft/s,m/s); n is the Gauckler--Manning coefficient. Units for valuesof n are often left off, however it is not dimensionless, havingunits of: (T/[L1/3]; s/[ft1/3]; s/[m1/3]). Rh is the hydraulicradius (L; ft, m); S is the slope of the hydraulic grade line orthe linear hydraulic head loss (L/L), which is the same as thechannel bed slope when the water depth is constant. (S = hf/L).k is a conversion factor between SI and English units. It can beleft out if consistent units are used throughout. However it isstandard practice to use k=1 for SI units, and k=1.49 forEnglish units. (Note: (1 m)1/3/s = (3.2808399 ft) 1/3/s = 1.4859ft1/3/s) NOTE: Ks strickler = 1/n manning. The coefficient Ksstrickler varies from 20 (rough stone and rough surface) to 80m1/3/s (smooth concrete and cast iron). The discharge formula, Q= A V, can be used to manipulate Gauckler--Manning's equation bysubstitution for V. Solving for Q then allows an estimate of thevolumetric flow rate (discharge) without knowing the limiting oractual flow velocity. The Gauckler--Manning formula is used toestimate the average velocity of water flowing in an openchannel in locations where it is not practical to construct aweir or flume to measure flow with greater accuracy. Thefriction coefficients across weirs and orifices are lesssubjective than n along a natural (earthen, stone or vegetated)channel reach. Cross sectional area, as well as n', will likelyvary along a natural channel. Accordingly, more error isexpected in estimating the average velocity by assuming aManning's n, than by direct sampling (i.e., with a currentflowmeter), or measuring it across weirs, flumes or orifices.Manning's equation is also commonly used as part of a numericalstep method, such as the Standard Step Method, for delineatingthe free surface profile of water flowing in an open channel.The formula can be obtained by use of dimensional analysis.Recently this formula was derived theoretically using thephenomenological theory of turbulence.