Find the fluid force on the vertical plate submerged in water, where the dimensi

Question

Find the fluid force on the vertical plate submerged in water, where the dimensions b = 3 and a = 9 are given in meters and the weight-density of water is 9800 newtons per cubic meter. newtons The figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Determine the force on this part of the concrete form. lb Rectangle A square porthole on a vertical side of a submarine (submerged in seawater) has an area of 1 square foot. Find the fluid force on the porthole, assuming that the center of the square is 15 feet below the surface. (Assume the weight-density of seawater is 64 pounds per cubic foot.) lb

Explanation / Answer

Solution:(4)

The weight-density of water is 9800 newtons per cubic meter and the sheet is submerged in b = 3m of water, the fluid pressure is

P = (9800) (3) = 29400 N/m^2

Because the total area of the sheet is A = 9 * 9 = 81 m^2 , the fluid force is

F = PA = 29400 N/m^2 * 81 m^2 = 2381400 N

Solution:(5)

To get the total force on the rectangular end, we use Force = Pressure * Area.

Since the pressure varies, we have to integrate to get the value. In this case, the pressure function is 140.7x where x measures the depth (0 to 4) and the differential area is 6dx (cutting the rectangle into thin horizontal slices).

The total Force = 04 (140.7x) * 6dx

                       = 04 844.2 x dx

                       = 844.2 x2/2 evaluated from 0 to 4

                       = 844.2 (16)/2 = 6753.6 lb

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