Question

2 Pascal’s Principle
An Olympic swimming pool is 50 m long, 25 m wide, and 2 m deep.
(a) Make a plot of pressure as a function of depth in the pool, for 0 ≤ y ≤ 2 m.
(b) What is the pressure on the bottom of the pool?
(c) What is the total force on the bottom of the pool — the 25 m × 50 m surface?
(d) What is the total force on one end of the pool — one of the 25 m × 2 m surfaces?
(e) What is the total force on one side of the pool — one of the 50 m × 2 m surfaces?

Answer 1

Pascal’s principle (also known as Pascal’s law) states that when a change in pressure is applied to an enclosed fluid, it is transmitted undiminished to all portions of the fluid and to the walls of its container. In an enclosed fluid, since atoms of the fluid are free to move about, they transmit pressure to all parts of the fluid and to the walls of the container. Any change in pressure is transmitted undiminished. Assuming it is a swimming pool it is exposed on the surface to the atmosphere, so the top of the water will be at atmospheric pressure, and, as you descend, the pressure will increase due to the weight of the water above it.

(a) The pressure (P) as a function of depth (h) in the pool is given by

Where, P_atm is the atmospheric pressure, d is the density of the liquid in the swimming pool and g is the acceleration due to gravity. The graph of pressure vs the depth of the liquid will be

(b) The pressure at the bottom will be

the total force on the bottom of the pool is given by

(c) Average pressure on the side wall is half of the pressure at the bottom. Hence, P_Side = P/2 = 6.045 x 10⁴ N/m². The total force on one end of the pool — one of the 25 m × 2 m surfaces is given by

(d) Average pressure on the side wall is half of the pressure at the bottom. Hence, P_Side = P/2 = 6.045 x 10⁴ N/m². The total force on one end of the pool — one of the 50 m × 2 m surfaces is given by