# Fluid Volume Calculation

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The end plates (isosceles triangles) of the trough shown below were designed to withstand a fluid force of 6000 lb. How many cubic feet can the tank hold without exceeding this limitation?

Assuming the density is 62.4 lb/ft^3, the maximum volume is ? ft^3.

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##### Solution Summary

In this solution, we show how to compute the volume of water in a tank given the fluid force it exerts on the walls of the tank.

##### Solution Preview

The fluid force acting on each end plate is given by

F_0 = integral_S(P(y) dx dy),

where S is the surface the water makes with an end plate and P(y) is the water pressure at height y. We have

P(y) = rho(d-y), where rho = 62.4 lb/ft^3 is the density of water. Thus we ...

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