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 inground 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 1.30 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. Answer in meters. Please list all the steps to get to the answer. Assume I know nothing (which is kinda true since I have to ask in the first place).

Explanation / Answer

let the depth of the pool be h

now we know that pressure at a depth of height h will be rho *g * h

the upper part will have atmospheric pressure ( Po= 101325 Pa) while the bottom part will experience atmospheric + water pressure

now , let area at the top be1.3 A0 and at the bottom be Ao

now we know that force = pressure * area

and it is fiven that force on top = force on bottom

so ,

1.3*Po * A0 = (Po + rho* g*h) * (Ao)

1.3* P0 = Po + 1000kg/m3* 9.8* h

=> 0.3 * Po = 1000kg/m3* 9.8* h

=>0.3 * 101325 = 1000kg/m3* 9.8* h

=> h = 3.10 m

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