Example_3_9_Cylindrical_Gate

# Example_3_9_Cylindrical_Gate - below the curved surface It...

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Example Problem – Hydrostatic Pressure Force on Curved Surfaces (Example Problem 3-9, Ç engel and Cimbala) Projected horizontal face Projected vertical face Calculate the horizontal force F x acting on the projected vertical face. W is the weight of the water in the shaded volume. Calculate the vertical force F y acting on the projected horizontal face. Draw a free body diagram around this volume of water, as shown to the right.

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The centroid of the projected vertical surface is located at a depth of s + R /2 from the water surface. The centroid of the projected horizontal surface is located at a depth of h bottom from the water surface. ( P is constant along this surface since it is at a constant depth.) We subtract weight W since the shaded volume is
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Unformatted text preview: below the curved surface. It turns out that for cylindrical surfaces (a circular arc shape), the resultant hydrostatic force acting on the surface always passes through the center of the circular arc. We take the moment about point A , using counterclockwise as positive. As shown in the sketch to the right, there are only two moments acting about point A : (1) the weight of the cylinder times its moment arm, which is the radius of the cylinder, and (2) the net hydrostatic force acting on the portion of the cylinder that is in contact with the water times its moment arm. Its force is F R and its moment arm R sin θ which is the perpendi distance from A to the line of action of the force. W cyl A F R R R sin is cular...
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Example_3_9_Cylindrical_Gate - below the curved surface It...

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