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. For more than a hundred years, this formula lacked a theoretical derivation. Recently this formula was derived theoretically[1],[2] using the phenomenological theory of turbulence.

The Manning formula states:

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

where:

V is the cross-sectional average velocity (ft/s, m/s)
k is a conversion constant equal to 1.486 for U.S. customary units or 1.0 for SI units
n is the Manning coefficient of roughness (independent of units)
Rh is the hydraulic radius (ft, m)
S is the slope of the water surface or the linear hydraulic head loss (ft/ft, m/m) (S = hf / L)

The discharge formula, Q=A\,V, can be used to manipulate Manning's equation by substitution for V. Solving for Q then allows the calculation of the volumetric flow rate (discharge) without knowing the limiting or actual flow velocity.

The Manning Formula is typically used to estimate flow in open channel situations where it is not practical to construct a weir or flume to measure flow with greater accuracy. Error rates of +/- 20% are common using the Manning Formula while error rates within +/- 5% are possible with properly constructed weirs or flumes.

[edit] Hydraulic radius

The hydraulic radius is defined as:

R_h = \frac{A}{P}

where:

Rh is the hydraulic radius (m)
A is the cross sectional area of flow (m2)
P is wetted perimeter (m)

The hydraulic radius is not half the hydraulic diameter, despite what the similarity in the names may suggest. It is a function of the shape of the pipe, channel, or river in which the water is flowing. In wide rectangular channels, the hydraulic radius is approximated by the flow depth.

[edit] Manning coefficient of roughness

The Manning coefficient of roughness, often denoted as n, is an empirically derived coefficient, which is dependent on many factors, including river-bottom roughness and sinuosity. Often the best method is to use photographs of river channels where n has been determined using Manning's formula.

Values typically range between 0.02 for smooth and straight rivers, to 0.075 for sinuous rivers and creeks with excess debris on the river bottom or river banks.

[edit] References

  • Walkowiak,D (Ed.) Open Channel Flow Measurement Handbook, 6th Ed. Teledyne ISCO; 2006 ISBN 0962275735.
  1. ^ http://www.mechse.uiuc.edu/research/gioia/Art/manning.pdf
  2. ^ http://cee.engr.ucdavis.edu/faculty/bombardelli/PRL14501.pdf

[edit] See also

[edit] External links