$\"\"$

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The circular plate of radius is $\"\"$ submerged vertically in a tank of fluid that weights $\"\"$ .

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The center of the circle is $\"\"$ $\"\"$ feet below the surface of the fluid.

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Consider the depth of the tank is $\"\"$ .

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The standard form of circle equation is $\"\"$ .

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Consider the center of the circular end of the tank is at origin.

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The horizontal length of the tank is $\"\"$ .

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Therefore, $\"\"$ .

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The $\"\"$ ranges from $\"\"$ to $\"\"$ .

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$\"\"$

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The fluid force is $\"\"$ .

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

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$\"\"$

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$\"\"$

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The second integral is zero because its integrand is odd and the limits of integration are symmetric to integral is the area of a semi circle with radius $\"\"$ .

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Therefore, $\"\"$ .

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$\"\"$

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Apply formula: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Fluid force on a circular plate is $\"\"$ .

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$\"\"$

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Fluid force on a circular plate is $\"\"$ .