An empirical formula used to estimate the average velocity and discharge of open channel flow based on channel geometry, slope, and roughness. It is one of the most widely used equations in hydraulic engineering.
The Manning equation (also called Manning's formula or Gauckler-Manning equation) is an empirical relationship used to calculate the mean velocity of water flowing in an open channel or partially full conduit under uniform, steady-state conditions. The equation relates velocity to the hydraulic radius, the energy slope, and Manning's roughness coefficient (n), which accounts for boundary friction caused by channel bed material, vegetation, channel irregularities, and obstructions. Manning's n values have been tabulated for a wide range of natural and artificial channel surfaces, ranging from about 0.010 for smooth concrete to 0.100 or more for heavily vegetated floodplains. The equation is used extensively in hydraulic engineering for designing channels, culverts, storm sewers, and irrigation systems, as well as in flood modeling and floodplain analysis. Despite being an empirical formula, it provides reliable results for turbulent flow conditions in channels of moderate to steep slope. The Manning equation is the basis for water surface profile calculations in widely used software such as HEC-RAS. Limitations include its inapplicability to laminar flow, rapidly varied flow, and situations where the roughness coefficient varies significantly with depth.