Water Channel Flow Calculator

Manning equation describes steady uniform flow, the condition in which the water surface, the energy grade line, and the channel bed all run parallel, so gravity exactly balances boundary friction and depth stays constant along the reach. In customary units, velocity equals 1.49 divided by n, times hydraulic radius to the two-thirds power, times slope to the one-half power, where hydraulic radius is flow area divided by wetted perimeter. The 1.49 is not physical; it is the conversion that carries the metric coefficient of 1.0 into feet and seconds, numerically the cube root of 3.281, the number of feet in a metre. Because hydraulic radius appears to the two-thirds power, sections that minimize wetted perimeter for a given area carry the most flow, which is why the half-hexagon trapezoid is the most hydraulically efficient shape. Roughness values in common use are 0.012 to 0.014 for finished concrete, 0.022 to 0.027 for corrugated metal pipe, 0.022 to 0.030 for clean earth channels, and 0.05 to 0.10 for vegetated natural streams. The Froude number, velocity divided by the square root of g times hydraulic depth, sorts the result into subcritical flow below 1.0, which is controlled by downstream conditions, and supercritical flow above 1.0, controlled from upstream. Designs are normally kept away from Froude numbers between about 0.9 and 1.1 where the water surface becomes unstable. Manning equation does not apply to rapidly varied flow at drops, gates, or hydraulic jumps, and for a circular pipe it returns full-flow capacity only, since a pipe actually peaks near 93 percent of full depth.

Open channel resistance formulas begin with Antoine Chezy, a French engineer who in 1769 derived velocity as proportional to the square root of hydraulic radius times slope while investigating the Yvette canal proposed to supply water to Paris. Chezy's coefficient, however, was not constant, and the nineteenth century produced a long sequence of attempts to describe how it varied, most prominently the elaborate Ganguillet and Kutter formula of 1869. Robert Manning, chief engineer of Ireland's Office of Public Works, presented a far simpler alternative to the Institution of Civil Engineers of Ireland in 1889 and published it in 1891. He arrived at it by fitting several existing formulas against gauging data, and he was reportedly uneasy about its dimensional inconsistency. Philippe Gauckler had reached an equivalent exponent in France in 1867, and Albert Strickler in Switzerland related the roughness coefficient to bed grain size in 1923, so the relation is properly the Gauckler-Manning-Strickler formula. Its dominance in English-language practice was cemented by Ven Te Chow of the University of Illinois, whose 1959 textbook Open Channel Hydraulics compiled the extensive tables of n values, illustrated with photographs of real channels, that engineers still consult when selecting roughness. The equation remains embedded in modern software including the U.S. Army Corps of Engineers HEC-RAS model.