Next, consider the representative rectangle of width ∆y and length L(yi), where yi is in the ith subinterval. To determine the total force against one side of the region from depth c to depth d, you can subdivide the interval into n subintervals, each of width ∆y. in a fluid of weight-density w (per unit of volume), as shown in Figure 7. Y Calculus methods must be used to find the fluid force on a vertical metal plate. Consider a vertical plate that is submerged x L(yi) h(yi) Δ y d c This problem is more difficult because the pressure is not constant over the surface.
Consider a surface that is submerged vertically in a fluid.
In Example 1, the fact that the sheet is rectangular and horizontal means that you do not need the methods of calculus to solve the problem. The fluid force would be the same in a swimming pool or lake. This result is independent of the size of the body of water. pounds square foot (12 square feet) = 4492 pounds. Because the total area of the sheet is A = ( 3 )( 4 ) = 12 square feet, the fluid force is F = PA = ̳74. Solution Because the weight-density of water is 62 pounds per cubic foot and the sheet is submerged in 6 feet of water, the fluid pressure is P = (62)( 6 ) P = wh = 374 pounds per square foot. 506 Chapter 7 Applications of Integration Fluid Force on a Submerged Sheet Find the fluid force on a rectangular metal sheet measuring 3 feet by 4 feet that is submerged in 6 feet of water, as shown in Figure 7.
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