the owner of a company that manufactures drinking cups decides it would be impre

Question

the owner of a company that manufactures drinking cups decides it would be impressive to build an underground swimming pool that is a scaled up version of her best selling cup. for this particular cup, the area of the circular opening at the top is 1.20 times the area of the circular bottom. her pool contractor informs her that when the pool is full of water, the magnitude of the force acting on the top surface will be the same as the magnitude of the force acting on the bottom surface. determine the depth of the pool.

Explanation / Answer

Let the depth be 'h'

Top = R ; Bottom = r

pi*R*R = 1.2 * pi*r*r => R^2 = 1.2 * r^2

force on top = Pa * Area top ; Pa = Atmospheric Pressure

force on bottom = (Pa + rho*g*h) * Area bottom

equating,

rho = density of water

Pa * area top = (Pa + rho*g*h) * area bottom

1.2 Pa = Pa + rho*g*h

h = 0.2 * Pa / rho*g

Pa = 10^5 Pascal

rho = 1000 kg/m^3

g = 10 m/s^2

h = 2 m

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