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 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
h_{2}, that is, the quantities
h_{1}, h_{2},
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 h_{1}=h_{2}
and the hydrostatic result when h_{2}=0.
