Question

A backyard swimming pool with a circular base of diameter 6.00 m is filled to depth 1.50 m. (a) Find the absolute pres- sure at the bottom of the pool. (b) Two persons with com- bined mass 150 kg enter the pool and float quietly there. No water overflows. Find the pressure increase at the bottom of the pool after they enter the pool and float.

Answer 1

Answer

given,

diameter = 6 m

depth = h = 1.5 m

Atmospheric pressure = P₀ = 10⁵ Pa

a) absolute pressure

P = P₀ + ρ g h

P = 10⁵ + 1000 x 10 x 1.5

P = 1.15 x 10⁵ Pa

b) When two person enters into the pool

mass of the two person = 150 Kg

    weight of water level displaced is equal to the weight of person

    ρ V g = 2 m g

     $V = \dfrac{2 m}{\rho}$

     $V = \dfrac{2\times 150}{1000}$

            V = 0.3 m³

Area of pool = $\dfrac{\pi}{4}d^2$

                    =$\dfrac{\pi}{4}\times 6^2$

                    = 28.27 m²

height of the water rise

        $h = \dfrac{V}{A}$

        $h = \dfrac{0.3}{28.27}$

               h = 0.0106 m

pressure increased

           P = ρ g h

           P = 1000 x 10 x 0.0106

           P = 106.103 Pa