A tank holds 100 gallons of water. Its inlet is 7 inches in diametre and fills the tank at 5 gallons/min. The outlet of the tank is twice the diametre of the inlet. How many minutes will it take to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diametre) (a) 7.14 min (b) 10.0 min (c) 0.7 min (d) 5.0 min
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Answer:
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Given : A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5 gallons/min.
The outlet of the tank is twice the diameter of the inlet.
To Find : How many minutes will it take to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened
(Hint: Rate of filling or emptying is directly proportional to the diameter)
(a) 7.14 min (b) 10.0 min (c) 0.7 min (d) 5.0 min
Solution:
considering Hint as given fact
Rate of filling or emptying is directly proportional to the diameter
=> 5 gallons/min. ∝ 7 inches
=> 5 / k = 7 / (2 * 7)
=> k = 10 gallons/min
Hence rate of emptying is is 10 gallons/min
Tank = 100 gallon
Time taken = 100/10 = 10 mins
In Actual Rate of filling ∝ cross section Area hence ( diameter )²
Considering that
=> 5 gallons/min. ∝ 7²
=> 5 / k = 7² / (2 * 7)²
=> k = 20 gallons/min
Hence rate of emptying is is 20 gallons/min
Tank = 100 gallon
Time taken = 100/20 = 5 mins
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