Infinitesimal Cross‐Wave Analysis

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Abstract
The plane cross-wave pattern in open channel flow is investigated. The governing equations for supercritical flow in bends are determined by accounting for the mass and linear momentum balances. An infinitesimal analysis with respect to the wave angle indicates that the solution of Knapp and Ippen must be prefered to von Karman's result for that type of open channel flow. While the first two authors arrive at their solution by experimental evidence the present investigation yields a purely analytical solution. A diagram facilitates the application and yields immediately the lateral surface elevation for given inflow Froude number and deflection angle. A comparison of the analysis with experiments of Poggi indicates a fair agreement for relatively high Froude numbers. Knapp and Ippen hypothesis of constant average velocity through a bend is thus more relevent than von Karman's assumption of constant specific head. The present study, therefore, may clear this particular problem of supercritical open channel flow in bends.

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