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Title: APPROXIMATING WETTED PERIMETER IN A POWER-LAW CROSS SECTION

Author
item STRELKOFF, T - UNIV OF AZ, TUCSON
item Clemmens, Albert

Submitted to: Journal of Irrigation and Drainage Engineering
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 10/25/1999
Publication Date: N/A
Citation: N/A

Interpretive Summary: Surface irrigation is used in about half of the irrigated lands in the U.S.; in other parts of the world this figure approaches 100%. In terms of such performance indicators as application efficiency and uniformity of distribution, most of these systems are not living up to their potential, which in some cases can rival that of pressurized systems. Efficient surface irrigation depends on proper design and management, which is established most security with the aid of mathematical simulation of the surface irrigation process. Irrigation water is often supplied to fields by furrows, channels formed in the soil to confine the flow to specific paths, in between which the plants are grown on raised beds above the water surface. A physically based mathematical model of the flow in the furrows requires some knowledge of the wetted perimeter, both because infiltration to the surrounding soil takes place through that perimeter and because resistance to the flow from the rough soil surface is applied at the wette perimeter. The documented research compares different approximations for calculating wetted perimeter, and recommends several procedures. The ultimate beneficiaries of these developments would be the growers, who with the advice on proper design and operation can conserve water and protect the environment from excessive contamination by agricultural and soil chemicals in excess irrigation water running off into surface water supplies or percolating into the groundwater supplies.

Technical Abstract: Wetted perimeter is an open-channel parameter that influences surface drag and also infiltration in furrows and unlined canals. Various approximations to the wetted perimeter are examined for channel cross sections in which 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 3- term summation yields results accurate to within 1% in the range of typical channel geometries. Common numerical approximations are shown to yield errors exceeding 3 to 10%.