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The Quarterly Journal of Mechanics and Applied Mathematics 1952 5(4):395-407; doi:10.1093/qjmam/5.4.395
© 1952 by Oxford University Press
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THE FLOW OF WATER UNDER A SLUICE-GATE

A. M. BINNIE

( Trinity College Cambridge )

The analysis of the two-dimensional free motion of a perfect liquid under a sluice-gate in an open horizontal channel is simplified by introducing the Froude number, F, of the stream. The relation is obtained between F1 and F2, the values of F on the upstream and downstream sides of the sluice-gate. If, as is usual, F1 < 1, then F2 > 1. Dimensionless expressions for the depths of the stream, the discharge, and the horizontal force on the gate are found in terms of F1. Experimental and theoretical investigations into the necessary gate opening are correlated by plotting them on a base of F1. and Rayleigh's result for flow under pressure through an aperture is shown to hold good up to a remarkably large value of F1. An explanation is put forward for the absence of waves on both sides of the sluice-gate, from which it is deduced that a Scott Russell wave of depression is impossible.


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