Chapter 6, Problem 23RE

In each part, set up, but do not evaluate, an integral that solves the problem.

(a) Find the fluid force exerted on a side of a box that has a $3\text{ m}$ square base and is filled to a depth of $1\text{ m}$ with a liquid of weight density $\rho {\text{ N/m}}^{\text{3}}$ .

(b) Find the fluid force exerted by a liquid of weight density $\rho {\text{ lb/ft}}^{\text{3}}$ on a face of the vertical plate shown in part (a) of the accompanying figure.

(c) Find the fluid force exerted on the parabolic dam in part (b) of the accompanying figure by water that extends to the top of the dam.