A 2-ft-high and 5-ft-wide rectangular plate is submerged vertically in the water so that the top is 1 ft below the surface. Express the hydrostatic force against one side of the plate as an integral.

Question

Jovanni

Physics

3 April, 12:19

A 2-ft-high and 5-ft-wide rectangular plate is submerged vertically in the water so that the top is 1 ft below the surface. Express the hydrostatic force against one side of the plate as an integral.

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Mason · Answer 1

63393.8 lbfeet/sec^2

Explanation:

Recall that the weight density of water is 62.5 lb/ft3

F = PA P = hρg = h x 62.5 x 32.2 A = 5 x dh force = integral of (hρg3 x dy) / / 3 is width of plane force = integral of (62.5 x 32.2 x 3 x hdh) from 2 to 5 force = 62.5 x 32.2 x 3 x (5^2-2^2) / 2 = 63393.8 lbfeet/sec^2