Manning formula

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The Manning formula is an empirical formula for open channel flow, or flow driven by gravity. It was developed by the Irish engineer Robert Manning.

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

Where:

  • V - cross-sectional average velocity (m/s)
  • n - Manning coefficient of roughness
  • Rh - hydraulic radius (m)
  • S - slope of pipe/channel (m/m)

When using English units, the 1/n may be simply replaced by 1.486/n in order to correct for different units, in which cases the units of meters above will be in feet.

The hydraulic radius is:

R_h = \frac{A}{P}
  • A - cross sectional area of flow (m2)
  • P - wetted perimeter (m)

The hydraulic radius is not half the hydraulic diameter, despite what the similarity in the names may suggest. It is actually one quarter the hydraulic diameter. In wide rectangular channels, the hydraulic radius is approximated by the flow depth.

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