$\"\"$

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The fluid force on the vertical side is $\"\"$ , where $\"\"$ is depth of the liquid, and $\"\"$ is the horizontal length of the region at $\"\"$ .

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Observe the figure :

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The Depth is $\"\"$ .

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The radius of the circle is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Length of the circle is $\"\"$ .

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The weight density of water is $\"\"$ .

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The limits range from $\"\"$ to $\"\"$ .

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$\"\"$

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The fluid force is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Take derivative with respect to $\"\"$ .

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$\"\"$ .

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If $\"\"$ then $\"\"$ .

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if $\"\"$ then $\"\"$ .

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$\"\"$

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$\"\"$

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Therefore, the fluid force is $\"\"$ .

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$\"\"$

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The fluid force is $\"\"$ .