5_03 - derive an expression for the horizontal force F per...

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Problem 5.3 Force on sluice gate Sluice gates are used to regulate water level (or flow rate) in open channels. The figure shows a gate that is adjusted so that the upstream depth is maintained at a depth h 1 . The density of water is , and the acceleration of gravity is g . The water flow under the gate may be considered incompressible and inviscid. Suppose the downstream depth is measured as h 2 , that is, the quantities h 1 , h 2 , and g are known. (a) Assuming uniform velocities at the far upstream and downstream stations1 and 2
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Unformatted text preview: derive an expression for the horizontal force F , per unit breadth, required to hold the gate in place. Check your result by showing that it gives zero when h 1 =h 2 and the hydrostatic result gh 1 2 2 when h 2 =0. HINT HINT 2 HINT 3 ANSWER (b) Also obtain expressions for the velocities V 1 and V 2 and the volume flow rate Q per unit breadth in the stream. Show that as h 2 approaches zero, V 2 approaches 2 gh 1 . Explain. HINT ANSWER...
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