Question

A swimming pool has dimensions 32.0 m x 12.0 m and a flat bottom. The pool is filled to a depth of 2.30 m with fresh water. (a) What is the force exerted by the water on the bottom? 8.65E6 was right but B and C are wrong

(b) What is the force exerted by the water on each end? (The ends are 12.0 m.) i got 311 but its wrong

(c) What is the force exerted by the water on each side? (The sides are 32.0 m.) and 829 was also wrong

Answer 1

(a) As we know that static water pressure is the same in all direction.

Also, the hydrostatic pressure at a given height is represented by the formula -

P = ρ x g x h.

This means, at 'h' meters from the surface the pressure is the same in all directions. This is also called pascal's rule.  

Also,

Force = Pressure x Area.

Therefore, pressure exerted by the water on the bottom (at point 2.30 m) = 1000 x 9.80 x 2.30

= 22540 Pa

Area = 32.0 x 12.0 = 384 m^2

So, force exerted on the floor = Pressure x Area = 22540 x 384 = 8655360 N = 8.65 x 10^6 N

(b) Area of one side = 2.30 x 12.0 = 27.6 m^2

So, force exerted on the side = 22540 x 27.6 = 622104 N

(c) Area of other side = 32.0 x 2.30 = 73.6 m^2.

Therefore, total force exerted on that side = 22540 x 73.6 = 1658944 N