# 2.25 Problem Sets - Section 5

## Problem 5.3: Force on a sluice gate

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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 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 _{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 h=0._{2} |

(b)
Also obtain expressions for the velocities Vand
_{1}V_{2} and the volume flow rate Q per unit
breadth in the stream. Show that as h_{2} approaches
zero, V approaches
. Explain. _{2} |
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