Question

An empty swimming pool with a square floor dimension has a volume of 3y2 m3. Given the weight of air in the swimming pool is about 500 N and the air density is 1.29 kg/m3.

(a) Find the length of the swimming pool’s floor, y.

(b) Determine the force exerted by air on the floor of the swimming pool.

Answer 1

Weight of the air and the side:

$$W=mg=\rho Vg=\rho Ahg=\rho a^2hg,\\\space\\ a=\sqrt{W/(\rho hg)}=3.63\text{ m}.$$

The force:

$$F=pa^2=\rho gha^2=500\text{ N}.$$