AravindG
  • AravindG
A cylindrical tank of height 0.4 m is open at the top and has a diameter 0.16 m.Water is filled in it upto a height of 0.16 m .Calculate the time taken to empty the tank through a hole of radius 5x10^-3m in its bottom?
Physics
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SOLVED
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jamiebookeater
  • jamiebookeater
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AravindG
  • AravindG
@Vincent-Lyon.Fr , @ash2326 , @waterineyes
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
First, use Torricelli's law to determine speed of water in the hole and rate of flow. \(v=\sqrt{2gh}\)
AravindG
  • AravindG
then?

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More answers

Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
Is the answer 45.80 s ?
AravindG
  • AravindG
i didnt get tht :O
AravindG
  • AravindG
i got 2.8 :P
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
How?
AravindG
  • AravindG
wait
anonymous
  • anonymous
h is variable
AravindG
  • AravindG
hmm
AravindG
  • AravindG
then how ?
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
Total volume is 3.217 L, right?
AravindG
  • AravindG
i got 3.14x10^-4
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
Try again. radius is 0.08m and height is 0.16m
AravindG
  • AravindG
3.21x10^-3
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
ok
AravindG
  • AravindG
so?
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
now escape velocity is \(v=\sqrt{2gh}\)
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
and discharge is v multiplied by area of hole.
AravindG
  • AravindG
v is velocity ryt?
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
yep
AravindG
  • AravindG
so how do we bring in volume?
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
time taken is: volume / discharge you should find 22.9s
AravindG
  • AravindG
hmm
AravindG
  • AravindG
but isnt h varying?
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
Yes, but we can get round this difficulty
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
Do you find the same values?
AravindG
  • AravindG
how/?
Vincent-Lyon.Fr
  • Vincent-Lyon.Fr
initial escape velocity is v=root(2g hmax) discharge is v multiplied by area of hole. time taken is: volume / discharge you should find 22.9s This is the time it would take to empty the tank if initial discharge was constant. Real duration, when h varies, is twice that time.

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