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Fluid force - Applications of Integration

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NOTE: We are supposed to find the fluid force using integrals. I have attached a word document with the fluid force formula we are supposed to use. Please use the US system of measurement (i.e. pounds)

Now here is the problem:

A vertcial gate in a dam has the shape of an isoceles trapezoid. The top of the gate measures 10 feet across, the gate is 11 feet below the surface of the water, the gate is 7 feet high, the bottom of the gate is 8 feet across. Find the fluid force on the gate.

the weight density (w) of the water in pounds per cubic foot is 62.4

Thanks.

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Solution Preview

Put the origin of y at the bottom of the dam (trapezoid), the height of the water above at point y is given by (this will produce the liquid pressure, and hence the force)

h(y) = 11 - y

so that it starts at ...

Solution Summary

Integration is used to find the fluid force on a dam shaped like an isoceles trapezoid.

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