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ECONOMIC DESIGN SOLUTION OF TRAPEZOIDAL OPEN CHANNEL SECTION INVOLVIONG PUMPING USING OPTIMUM DERIVATIVE OF WATER BENEFIT FUNCTION 1 Mohamed M.A. Somaida ABSRACT In the present paper, an economic water benefit design mathematical solution has been derived for trapezoidal open channel section involving pumping which is based on hydraulic and economic considerations. The solution utilizes the derivative optimum of water benefit function and maximizes the benefit gained from the delivered water to reach the maximum water benefit MWB design solution. The solution is applied on a channel example and the results obtained are compared with those obtained by an earlier solution based on the minimum construction cost MC design of the channel only. The channel costs in both solutions are found to be of nearer magnitudes with little deviation. It is not necessary that the channel geometry in both cases must be identical, because the MWB solution depends on several factors such as; water benefit variables, pumping cost parameters and channel length, while the minimum cost MC solution depends on the channel cost parameters only. The MWB design solution is advantageous in that it achieves money gains even the delivered water is of cheap price, while this advantage is not satisfied in the earlier solution. However, the present study introduces an analytical solution for developing comprehensive water benefit and costing. The results of the given channel example involving pumping, demonstrate the simplicity and practicability of the MWB design solution as well as water benefit verification KEYWODS: channel geometry, pumping costs, channel construction costs, optimization, maximum water benefit MWB function, optimal economic depth of flow, money gain