a Determine the total force on the bottom of a swimming pool

(a) Determine the total force on the bottom of a swimming pool 22.0 m by 6.0 m whose uniform depth is 2.0 m?
_________ N (downward)
Determine the absolute pressure at the bottom of the swimming pool?
______ N/m²

(b) What will be the pressure against the side of the pool near the bottom?
________N/m²

Solution

Pressure at depth 2.0 m = g h

= 1000 * 9.8 m/s² * 2 m

= 19600 N/m² = 1.96 * 10⁴ N/m²

A = (22 m * 6 m) = 132 m²

The force on the bottom of the pool due to the water F = P A = 2.59 x 10⁶ N

F = (101,325 N/m²) x (132 m²) = 13.37 x 10⁶ N

Thus the total force = 13.37 x 10⁶ + 2.59 x 10⁶ = 15960000 N

P = F / A = 15960000 / 132 = 120909 N/m²