Problem 5.3: Force on a 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 h1. The density of water is r, 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 h2, that is, the quantities h1, h2, r, and g are known.
(a) Assuming uniform velocities at the far upstream and downstream stations1 and 2 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 h1=h2 and the hydrostatic result when h2=0.
|(b) Also obtain expressions for the velocities V1and V2 and the volume flow rate Q per unit breadth in the stream. Show that as h2 approaches zero, V2 approaches . Explain.|