Manning formula

Estimates the average flow velocity of water in an open channel, such as a river or canal, from the channel's roughness, hydraulic radius and slope. It is an empirical formula widely used in hydraulic engineering.

V = \frac{k}{n} R_h^{2/3} S^{1/2}

What the symbols mean

mean flow velocity (m/s)
conversion constant depending on unit system (1 in SI, 1.49 in US customary units)
Manning roughness coefficient of the channel surface
hydraulic radius (m), cross-sectional flow area divided by wetted perimeter
hydraulic gradient, the slope of the energy line (dimensionless)

About this formula

  • FieldEngineering
  • TopicFluid mechanics
  • LevelUniversity
  • Also calledManning's equation, Gauckler-Manning formula, Gauckler-Manning-Strickler formula, open channel flow velocity, Manning equation velocity, flow velocity in open channel
  • SourceWikidata Q1428692

Write it in Obsidian

MathLive is a free visual math editor for Obsidian. Run Find a formula, type “manning formula”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.

Related formulas