Question

An Olympic pool has dimensions 50.0 m × 25.0 m × 3.00 m (length × width × depth). The density of the pool water is 1008 kgm-3. Atmospheric pressure (1.00 atm) is acting on the surface of the water. 100 If a child dives down to the bottom of the pool what pressure is exerted on the child? tion Pa Check The child now pulls his air filled blow up toy to the bottom of the pool. The toy is compressible and has a volume of 2.05 L on the surface of the pool. What volume does it have on the bottom of the 1.00 pool? The air around the pool is at thermal equilibrium with the water in the pool. tion Check

Answer 1

Dimension of Olympic pool {length = 50 m width = 25 m depth(h) = 3 m} density of pool water (p) = 1008 kg/m^3 Pressure on the surface of water (p_o) = 1 atm = 101325 pascal A child dives down to the bottom of the pool * pressure at the bottom of the pool = p_0 + pgh where h is the depth of the pool p = (101325) + (1008 times 9.8 times 3) p = (101325) + (29635.2) p = 130960.2 pascal Note Rightarrow This calculation is done assuming negligible height of the child \r\n The tag is compressible V_surface = 2.05 L The air around the pool is at thermal equilibrium with the water in the pool By the above statement it is clear that the process of pulling the toy to the bottom of the pool is isothermal and hence, we can write p_surface v_surface = P_bottom V_bottom (101325) (2.05) = (130960.2) V_bottom Therefore V_bottom = 1.586 Litter