Question

A swimming pool of depth 2.2 m is filled with ordinary (pure) water (ρ = 1000 kg/m3).

(a) What is the pressure at the bottom of the pool?

(b) When the pool is filled with salt water, the pressure at the bottom changes by 8.8 x10³Pa. What is the magnitude of the difference between the density of the salt water and the density of pure water?

Answer 1

Given that :

height of the swimming pool, h = 2.2 m

density of pure water, _w = 1000 kg/m³

(a) The pressure at the bottom of the pool which is given as :

using an equation,     P = P_atmos + _w g h                                                                 { eq.1 }

where, P_atmos = atmospheric pressure = 101325 Pa

inserting the values in above eq.

P = (101325 Pa) + [(1000 kg/m³) (9.8 m/s²) (2.2 m)]

P = (101325 Pa) + (21560 Pa)

P = 122885 Pa

P = 1.22 x 10⁵ Pa

(b) When the pool is filled with salt water, the pressure at the bottom changes by 8.8 x 10³Pa, then the magnitude of the difference between the density of the salt water and the density of pure water is given as :

(Combined pressures) = (Atmospheric Pressure) + [(2.2 m) (9.8 m/s²) ]

(Combined pressures - Atmospheric Pressure) = (2.2 m) (9.8 m/s²)

(Combined pressures - Atmospheric Pressure) = (21.5 m²/s²)

= (Combined pressures - Atmospheric Pressure) / (21.56 m²/s²)

= [(122885 Pa) - (101325 Pa)] / (21.56 m²/s²)

= (21560 Pa) / (21.56 m²/s²)

= 1000 kg/m³