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A power-law channel is a generalized form of a channel and includes parabolic an triangular sections. A method is developed to design power-law channels for any given side slope. Using Lagrange.s method of undetermined multipliers it is possible to determine the optimum exponent of the power law channel and a hydraulically efficient channel can be designed. The existing parabolic design of Pehur High Level Canal in Pakistan is compared with and optimum power-law channel with the same side slope.