Let R be a lamina of uniform density submerged in a fluid of density w (Figure 27)

Chapter 8, Problem 47

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Let R be a lamina of uniform density submerged in a fluid of density w (Figure 27). Prove the following law: The fluid force on one side of R is equal to the area of R times the fluid pressure on the centroid. Hint: Let g(y) be the horizontal width of R at depth y. Express both the fluid pressure [Eq. (2) in Section 8.2] and y-coordinate of the centroid in terms of g(y)

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