It is shown that the method of hodograph transformation coupled with numerical calculations can be an effective method to account for the effect of gravity on certain two-dimensional potential flow problems. Specifically, the problem of a horizontal channel flow discharging an incompressible fluid through a circular-arc contraction has been worked out to illustrate the procedure. The upstream approaching flow conditions, the opening height, and also the downstream free surface flow must be compatible with each other. They must be determined through iterations. The method of iteration is also presented and discussed.

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