Gauckler-Manning Equation

The Gauckler-Manning calculator computes the cross-sectional average velocity of a liquid in an open channel based on a coefficient, the slope and the hydraulic radius.

INSTRUCTIONS: Enter the following:

• (Ks) Strickler Coefficient (20 for rough surfaces to 80 for smooth)
• (S) Slope of Hydraulic Grade
• (R) Hydraulic Radius

Velocity of Liquid Flow (V):  The calculator returns the velocity in meters per second.  However this can be automatically converted to other velocity units via the pull-down menu.

The Math / Science

This calculator is based on a form of the Gauckler-Manning formula using Ks strickler = 1/n manning. The coefficient Ks strickler varies from 20 (rough stone and rough surface) to 80 m1/3/s (smooth concrete and cast iron).

The Manning formula is also known as the Gauckler–Manning formula, or Gauckler–Manning–Strickler formula in Europe. In the United States, in practice, it is very frequently called simply Manning's Equation. The Manning formula is an empirical formula estimating the average velocity of a liquid flowing in a conduit that does not completely enclose the liquid, i.e., open channel flow. All flow in so-called open channels is driven by gravity. It was first presented by the French engineer Philippe Gauckler in 1867, and later re-developed by the Irish engineer Robert Manning in 1890.

The Gauckler–Manning formula states:

V =k\n*R_h ^2/3* S^1/2
 where:

• V is the cross-sectional average velocity (L/T; ft/s, m/s)
• k is a conversion factor of (L1/3/T), 1 m1/3/s for SI, or 1.4859 ft1/3/s U.S. customary units, if required. (Note: (1 m)1/3/s = (3.2808399 ft) 1/3/s = 1.4859 ft1/3/s);
• n is the Gauckler–Manning coefficient, it is unitless
• R_h is the hydraulic radius (L; ft, m);
• S is the slope of the hydraulic grade line or the linear hydraulic head loss (L/L), which is the same as the channel bed slope when the water depth is constant. (S = hf/L).

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