SOLUTION: Water is pumped into the pool through a pipe with a 2-in diameter at a velocity of 1.5 feet per second. Another pipe is attached at the bottom of the pool, which is used to drain

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Question 1065751: Water is pumped into the pool through a pipe with a 2-in diameter at a velocity of 1.5 feet per second. Another pipe is attached at the bottom of the pool, which is used to drain water from the pool. The pipe has a diameter of 3 inches and the pump at its end sucks water out at a velocity of 0.25 ft/sec. One day, when the pool was empty, both the inlet and outlet pipes were opened simultaneously. How many hours will it now take to fill the pool? The volume of the pool is 7200.
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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"The volume of the pool is 7200."

7200 OF WHAT ? of which units ?? DIMENSION ???


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Comment from student: 7200 ft^3, amount of water in it
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My response: OK, very good. 

1.  Calculate the inflow rate through the pipe of the diameter d%5B1%5D = 2 inches.
    For it, first convert the diameter of 2 inches to feet:   2%2F12 = 1%2F6 ft.

    Then calculate the inflow rate  V1 = pi%2Ad%5B1%5D%5E2%2Av%5B1%5D = 3.14%2A%281%2F6%29%5E2%2A1.5 ft%5E3%2Fs = 0.1308 ft%5E3%2Fs.


2.  Calculate the outflow rate through the pipe of the diameter d%5B2%5D = 3 inches.
    Again, convert the diameter of 3 inches to feet:  3%2F12 = 1%2F4 ft.

    Then calculate the outflow rate  V2 = pi%2Ad%5B2%5D%5E2%2Av%5B2%5D = 3.14%2A%281%2F4%29%5E2%2A0.25 ft%5E3%2Fs = 0.049 ft%5E3%2Fs.


3. Next, calculate net flow as the difference V1 - v2 = 0.1308 - 0.049 = 0.0818 ft%5E3%2Fs.


4.  As the last step, calculate the time = 7200%2F0.0818 = 88051 seconds = 24.46 hours = 24 hours and 30 minutes approximately.

Which of these steps was so difficult to you that you could not make it on your own ?