Question

Dimensions of a swimming pool are 34.0 m by 9.5 m and its uniform depth is 1.8 m . The atmospheric pressure is 1.013×105N/m2.

A) Determine the absolute pressure on the bottom of the swimming pool.

B) Calculate the total force on the bottom of the swimming pool.

C) What will be the pressure against the sideof the pool near the bottom?

Answer 1

A)

Dimensions of the swimming pool are 34.0 x 9.5 m x 1.8 m .

Atmospheric pressure,

Density of water is

Increase in pressure at depth pressure is .

Given that h = 1.8 m. .

= 0.176 x 10⁵ N/m².

Absolute pressure at bottom of pool is

P = P_atm + P₁ = (1.013 +0.176) x 10⁵ = 1.189 x 10⁵ N/m².

B)

Total force on the bottom of the swimming pool is

F = P x Area of the bottom = 1.189 x 10⁵ x 34 x 9.5 = 3.840 x 10⁷ N.

C)

Pressure in any direction (i.e. on the wall) near the bottom will be nearly the same as that on the bottom.

So, pressure on side wall near bottom is

P_w = P =  1.189 x 10⁵ N/m².