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AravindG

  • 2 years ago

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?

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  1. AravindG
    • 2 years ago
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    @Vincent-Lyon.Fr , @ash2326 , @waterineyes

  2. Vincent-Lyon.Fr
    • 2 years ago
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    First, use Torricelli's law to determine speed of water in the hole and rate of flow. \(v=\sqrt{2gh}\)

  3. AravindG
    • 2 years ago
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    then?

  4. Vincent-Lyon.Fr
    • 2 years ago
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    Is the answer 45.80 s ?

  5. AravindG
    • 2 years ago
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    i didnt get tht :O

  6. AravindG
    • 2 years ago
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    i got 2.8 :P

  7. Vincent-Lyon.Fr
    • 2 years ago
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    How?

  8. AravindG
    • 2 years ago
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    wait

  9. RaphaelFilgueiras
    • 2 years ago
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    h is variable

  10. AravindG
    • 2 years ago
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    hmm

  11. AravindG
    • 2 years ago
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    then how ?

  12. Vincent-Lyon.Fr
    • 2 years ago
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    Total volume is 3.217 L, right?

  13. AravindG
    • 2 years ago
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    i got 3.14x10^-4

  14. Vincent-Lyon.Fr
    • 2 years ago
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    Try again. radius is 0.08m and height is 0.16m

  15. AravindG
    • 2 years ago
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    3.21x10^-3

  16. Vincent-Lyon.Fr
    • 2 years ago
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    ok

  17. AravindG
    • 2 years ago
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    so?

  18. Vincent-Lyon.Fr
    • 2 years ago
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    now escape velocity is \(v=\sqrt{2gh}\)

  19. Vincent-Lyon.Fr
    • 2 years ago
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    and discharge is v multiplied by area of hole.

  20. AravindG
    • 2 years ago
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    v is velocity ryt?

  21. Vincent-Lyon.Fr
    • 2 years ago
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    yep

  22. AravindG
    • 2 years ago
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    so how do we bring in volume?

  23. Vincent-Lyon.Fr
    • 2 years ago
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    time taken is: volume / discharge you should find 22.9s

  24. AravindG
    • 2 years ago
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    hmm

  25. AravindG
    • 2 years ago
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    but isnt h varying?

  26. Vincent-Lyon.Fr
    • 2 years ago
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    Yes, but we can get round this difficulty

  27. Vincent-Lyon.Fr
    • 2 years ago
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    Do you find the same values?

  28. AravindG
    • 2 years ago
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    how/?

  29. Vincent-Lyon.Fr
    • 2 years ago
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    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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