The Manning formula or Manning's equation is an empirical formula estimating the average velocity of a liquid in an open channel flow (flowing in a conduit that does not completely enclose the liquid). 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  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.