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Pipe Filling Problems
(or Tank Filling Problems)
Example 1
Pipe 1 can fill a tank in 3 hours and Pipe 2 can fill a tank in 4 hours.
If both pipes are turned on at the same time, how long will it take to fill the tank?
Let's determine the rate per hour for each pipe.
Pipe 1 fills ⅓ of the tank in 1 hour.
Pipe 2 fills ¼ of the tank in 1 hour.
Working together, they wiil fill how much of the tank in one hour?
(1 / 3) + (1 / 4) = (4 / 12) + (3 / 12) = 7 / 12
Seven twelfths is how much of the tank will be filled in one hour.
To get the total time, we take the reciprocal which is 12 ÷ 7 and so, the entire tank will be filled in 1.7143 hours.
When we have 2 pipes filling a tank, we can use formula "A" to calculate the total time.
Formula "B" is much easier to use and you would probably prefer to use it for 2 pipes.
Example 2
When we have 3 or more pipes filling a pool, we need to use formula "C" to calculate the total time.
For example, if we have 4 pipes that can each fill a pool in 2 hours, 3 hours, 4 hours and 6 hours, how long will it take if all 4 pipes work together?
Total Time = 1 / [ (1/2) + (1/3) + (1/4) + (1/6) ]
Total Time = 1 / [ (6/12) + (4/12) + (3/12) + (2/12) ]
Total Time = 1 / [ (15/12) ]
Total Time = (12/15) = (4/5) = .8 hours = 48 minutes.
Whenever you are calculating 3 or more pipes, it would probably be a good idea to use this parallel resistor calculator.
Example 3
Two pipes can fill a tank in 2.1 hours. One pipe working alone can fill the tank in 7 hours.
Working alone, how long would it take the other pipe to fill up the tank?
We need to use formula D for this problem.
We'll say the total time is 2.1 hours and that the Pipe 1 time is 7 hours.
Pipe 2 Time = (7 * 2.1) / (7 2.1) = 14.7 / 4.9 = 3 hours
Example 4
We have a tank that is filled to the top.
One pipe can fill the tank in 20 minutes and the drain pipe can drain the tank in 15 minutes.
If both pipes are opened how long will it take to empty the tank?
Total Time = (20 * 15) / (20 15) = 300 / 5 = 60 minutes
We have an empty tank.
One pipe can fill the tank in 1 hour and the drain pipe can drain the tank in 2 hours.
If the "fill" pipe is turned on while the drain pipe is open, how long will it take to fill the tank?
Once again, we will use formula "E" to calculate the total time.
Total Time = (1 * 2) / 1 2 = 2 / 1 = 2 hours
