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Concept# Manning formula

Summary

The Manning formula or Manning's equation is an empirical formula estimating the average velocity of a liquid flowing in a conduit that does not completely enclose the liquid, i.e., open channel flow. However, this equation is also used for calculation of flow variables in case of flow in partially full conduits, as they also possess a free surface like that of open channel flow. All flow in so-called open channels is driven by gravity.
It was first presented by the French engineer Philippe Gaspard Gauckler in 1867, and later re-developed by the Irish engineer Robert Manning in 1890.
Thus, the formula is also known in Europe as the Gauckler–Manning formula or Gauckler–Manning–Strickler formula (after Albert Strickler).
The Gauckler–Manning formula is used to estimate the average velocity of water flowing in an open channel in locations where it is not practical to construct a weir or flume to measure flow with greater accuracy. Manning's equation is also commonly used as part of a numerical step method, such as the standard step method, for delineating the free surface profile of water flowing in an open channel.
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 of n are often omitted, however n is not dimensionless, having units of: (T/[L1/3]; s/[m1/3]).
Rh is the hydraulic radius (L; ft, m);
S is the stream slope or hydraulic gradient, the linear hydraulic head loss loss (L/L); it is the same as the channel bed slope when the water depth is constant. (S = hf/L).
k is a conversion factor between SI and English units. It can be left off, as long as you make sure to note and correct the units in the n term. If you leave n in the traditional SI units, k is just the dimensional analysis to convert to English. k = 1 for SI units, and k = 1.49 for English units. (Note: (1 m)1/3/s = (3.2808399 ft)1/3/s = 1.4859 ft1/3/s)
NOTE: Ks strickler = 1/n manning. The coefficient Ks strickler varies from 20 (rough stone and rough surface) to 80 m1/3/s (smooth concrete and cast iron).

Official source

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