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A swimming pool is 20 ft wide and 40 ft long and its bottom is an inclined plane, the shallow end having a depth of 3 ft and the deep end, 9 ft. If the pool is full of water, find the hydrostatic force on (a) the shallow end, (b) the deep end, (c) one of the sides, and (d) the bottom of the pool.

(a) 5625 $\mathrm{lb}$

(b) 50625 $\mathrm{lb} \quad$ (or $5.06 \times 10^{4} \mathrm{lb} )$

(c) 48750 $\mathrm{lb}$ \quad$($ or $4.88 \times 10^{4} \mathrm{lb}\right)$

(d) Net force $=1.347 \times 10^{6}$ Newtons $=3.03 \times 10^{5} \mathrm{lb}$

Applications of Integration

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Missouri State University

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Boston College

Mhm. Okay. The final problem, we are asked to find the force that's going to be based on the hydrostatic force is gonna be on the show on the deep end one of the sides and the bottom of the pool. Mhm. Well, we know that the deeper we go um there's going to be greater hydrostatic force because there's going to be a higher amount of pressure. Remember that pressure is equal to force over the area. In that case we know the force or we're trying to find the force, knowing what we have already about the pressure. So what this is going to look like is we're going to find the force, the hydrostatic force. And at the shallow end we're going to get 5.63, I'm 10 to the 3rd lbs. Then we're going to get 5.06 times 10 to the 4th lbs. That's going to be um at the deep end and then 4.88 times 10 to the 4th, that's gonna be um at one of the sides. And then lastly, we'll have the bottom of the pool which will be 3.3 times 10 to £15

California Baptist University

Applications of Integration