A rectangular above-ground swimming pool is 6 m long and 3 m wide. The pool has

Question

A rectangular above-ground swimming pool is 6 m long and 3 m wide. The pool has a constant height of 2 m above the ground. Take atmospheric pressure to be 1 atm = 10^5 Pa and g = 10 m/s^2.

a) Calculate the weight of the air that fills the pool when the pool is empty. ( Take the density of air to be 1.17 kg/m^3)

Weight of air = _______Newtons

b) What is the weight of the water that fills the pool and what is the pressure on the both of the pool due to just the water?

weight of water = _______Newtons

c) What is the pressure on the bottom of the pool due to the water and atmosphere above it?

Total Pressure = _______Pascals

d) What percentage of the total pressure on the bottom of the filled swimming pool is due to just the air above it?

Percentage of air = _______%

Explanation / Answer

(a) swimming pool area , A = 6 m x 3m = 18 m2 pool height , h = 2m volume of the air accupied , V = A x h = 36 m3 (when the pool is empty ) density of the air , = 1.17 kg/m^3 thus, mass of the air ,m = V = (1.17)(36) = 42.12 kg weight of the air , W = mg = (42.12)(10) = 421.2 N (b) weight of the water that fills the pool is , W' = m'g = ' V g where ' is the density of the water , 1000 kg/m3 we ight , W ' = 1000(36)(10) = 360000 N presure at the height , h = 2 m P= h' g = (2 )(1000)(10) = 0.2 x105 N/m2 (c) total presue , P = (1+ 0.2 )x105 N/m2 = 1.2x105 N/m2 (d)      1/ 1.2 x 100 = 83.33 % (c) total presue , P = (1+ 0.2 )x105 N/m2 = 1.2x105 N/m2 (d)      1/ 1.2 x 100 = 83.33 %

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