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I Which tank fills first

  1. Aug 2, 2017 #1
    upload_2017-8-2_16-57-42.png

    I originally thought tank K because the area in tank J is much larger than the area in the pipe connecting J to I
    But then I realize Bernoulli's equation does not include volume but only includes height.
    H_1, H_2 = height of water tank J, height of water in pipe between tanks J and I
    P, p, V = pressure, density, velocity
    $$P_1+pgH_1+\frac{1}{2}pV_1^2=P_2+pgH_2+\frac{1}{2}pV_2^2$$
    Pressure terms are the same, so is density. Velocity = 0, gravity cancels out ##H_1=H_2##
    So even in the small pipe connecting J to I, the water level is going to be the same as the height of water in the tank J.

    Is this correct?

    Also note the pipe from C to D is blocked off.
    Also I assume A would be trivial solution so water must exit pipe faster than the tap fills tank A
     
  2. jcsd
  3. Aug 2, 2017 #2

    jbriggs444

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    The water is dripping in. Flow velocity will be negligible.
     
  4. Aug 2, 2017 #3
    It really depends on what point do you consider the tank is 'full', let's say that the point full is when the tank is overfilling. I think the tank H would get filled first because the connection JI goes higher than connection JL.
     
  5. Aug 2, 2017 #4
    I say F will fill up (overflowing) first!
     
  6. Aug 2, 2017 #5

    jbriggs444

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    There is no path into tank H.
     
  7. Aug 2, 2017 #6
    whoops that's true. Then my guess is F. Thanks.
     
  8. Aug 2, 2017 #7

    CWatters

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    Tank G fills up first. The water flows A B C D G. No water goes into J. No water goes into E.

    Darn I didn't spot the blocked pipe. Ok so yes it's F.
     
  9. Aug 2, 2017 #8

    phinds

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    It's G
     
  10. Aug 2, 2017 #9

    Nugatory

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    You've missed the blocked pipe C to D.
     
  11. Aug 2, 2017 #10

    Nugatory

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    A and B fill to the level of their outputs; C fills to the level of its outlet into J; J fills to the level of its outlet into L; L fills to the level of the top of F; and F fills and overflows. Once F is full, every drop of water into A causes another drop to overflow from F and the system is in steady state.
     
  12. Aug 2, 2017 #11

    phinds

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    Damn ! Thanks.

    CWaters even SAID it was there and I still couldn't see it. o:)
     
  13. Aug 2, 2017 #12
    So, basically, the area doesn't matter of tank J, it wont push the water through the pipe higher than its own water level? Tank J is roughly 27 times the cross sectional area then the pipe... but it doesn't matter right?
     
  14. Aug 2, 2017 #13

    Nugatory

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    Not as long as the rate at which water enters the tank is small compared with the rate at which a single pipe can carry the water out - the water level will not rise above the height of the lowest flowing pipe. The illustration suggests that we're dealing with a dripping faucet which will easily be handled by a single pipe - think about an air conditioning unit's condensate drain tray.
     
  15. Aug 2, 2017 #14
    It's K
     
  16. Aug 3, 2017 #15

    Nugatory

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    Can't be - nothing flows from J to I because the level in J doesn't rise above the outlet from J to L.
     
  17. Aug 5, 2017 #16
    I choose L due to pressure and flow
     
  18. Aug 5, 2017 #17

    RonL

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    I agree with you, F will overflow before any others :smile:
     
  19. Aug 5, 2017 #18

    davenn

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    no ... look again .... F is at a lower level than L which fills F

    Like phinds and a couple of others, I originally was going for G as I didn't see the block between C and D
     
  20. Aug 5, 2017 #19

    DrGreg

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    Here's the picture for the slow-drip steady-state solution:
    Which tank will fill up first - solution.PNG
     
  21. Aug 8, 2017 #20
    Tank F will fill up first
     
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