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 1.50 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. 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 1.50 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. 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 1.50 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

Pressure at top be P and Area be A
Then force = P*A

At depth h:
P' = P +rho*g*h
= P + 1000 Kg/m^3 * 9.8 m/s^2 * h m
= P + 9800 *h
Area A' = A/1.5
Force = P'*A'

Since force is same at both top and bottom
P*A = P'*A'
P*A = (P+9800*h) * (A/1.5)
1.5*P*A = P*A +6533.3*A*h
6533.3*A*h = 0.5*P*A
6533.3*h = 0.5*P

At top, P = 10^5 N/m^2
so,
P = 10^5 N/m^2

6533.3*h = 0.5*P
6533.3*h = 0.5*10^5
h= 7.65 m
Answer: 7.65 m

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