Approximating Wetted Perimeter in Power-Law Cross Section

The wetted perimeter is an open-channel parameter that influences surface drag and also influences infiltration in furrows and unlined canals. Various approximations to the wetted perimeter are examined for channel cross sections in which the top width is a power law of depth. Exact solutions are available only for select values of the exponent. Interpolation between exact values, partial sums of series approximations, and numerical integration are compared. A simple nonlinear interpolation scheme or a three-term summation yields results accurate to within 1% of the range of typical channel geometries. Common numerical A approximations are shown to yield errors in excess of a range of from 3 to 10%.