Fluid dynamics (continuity equation), pressure on gate

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xzi86
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Homework Statement


Consider the cross section of a sluice gate, which is a device for controlling the flow of water in channels. Determine the force on the gate per unit width of the gate.

Hint: think of each line as a surface, with the length given above, and 1 foot of depth in the direction normal to the plane of the paper. The hydrostatic gauge pressure field p equals ρgh. That is, the gauge pressure at any point in the flow will linearly vary with the depth of the water, h. Use the average values of the pressure (at half-depth) for the pressure forces.

Homework Equations


Continuity equation integral form

The Attempt at a Solution


The answer is : V =16.667 ft/sec, Force in the x- direction on the gate = 1708 lb per foot of width in the direction normal to the plane of the paper. No idea how this was reached. How do you apply the continuity equation to this problem? And what does the hint mean? Any help would be greatly appreciated. Thanks.
 

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