Let R be a lamina of uniform density submerged in a fluid of density w (Figure 29).

Question:

Let R be a lamina of uniform density submerged in a fluid of density w (Figure 29). 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. Let g(y) be the horizontal width of R at depth y. Express both the fluid pressure [Eq. (2) in Section 9.3] and y-coordinate of the centroid in terms of g(y).

Fluid level R y (depth) g(y) Centroid