Manning's Emerical Formula
On December 4, 1889, at the age of 73, Manning first proposed his formula to the Institution of Civil Engineers (Ireland).
The Manning equation is a widely used and very versatile formula in water resources. It can be used to compute the flow in an open channel, compute the friction losses in a channel, derive the capacity of a pipe, check the performance of an area-velocity flow meter, and has many more applications.
It is an empirical equation because it is not based on first principles formed from theories of science and physics, but rather it is derived from curve fitting "observed data". There is nothing wrong with using such an equation in engineering, so long as we keep in mind that it is empirically derived and that there are limitations to its use.
Most pipes and channels flow under turbulent conditions. And we do not yet have a sufficient scientific understanding of turbulence to derive equations based on first principles.
The Manning’s value is a unitless coefficient that represent the roughness or friction factor of the conduit. Rougher conduits with higher friction have a higher value, and smoother conduits with lower friction have a lower value.
Manning's workbook
Data input can be in SI, Imperial or US units, input data required is pipe size (or estimated open waterway dimension) and slope (gradient or "fall"). Slope is expressed as a Fall/Length dimension, eg 1:100 or 2:100 which is a common standard for minimum fall in gravity fed pipes used for drainage
Data outputs are produced in table and graph format with Flow Volume and Flow Velocity given across the range of "% Pipe Fill"