Approximate solution of gravity flow from a uniform channel over triangular bottom for large Froude number

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An approximate method is applied to solve the problem of steady free-surface flow of an ideal fluid over a semi-infinite triangle in the bottom of an open channel. The solution is based on the combined use of the conformal mapping and the Hilbert solution of a mixed boundary value problem in the upper half-plane. The obtained integral equations have been approximated for large Froude number. The perturbation technique is used as a basis for the approximate solution of the problem for small inclination interior angles of the triangle. Application of such approximations results in equations in integral form for any order of approximation. Solution up to first-order approximation is obtained and is dependent on the triangle height and the bottom shape. The distribution of the pressure coefficient along the bottom boundaries has been studied, and the results are plotted for different Froude number values. Favorable agreement with the results of different methods suggests that this method is effective in dealing with flow problems at large Froude number.