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The Drinking Straw, Vacuum and Hydrostatics

  1. Oct 24, 2007 #1
    I am struggling with a mental model of what happens with the water level in a vertical pipe with the top end closed (say by a valve). Given:

    Pipe height = 5000 ft
    Pipe connected at bottom end to a chamber of pressure = 1000 psia
    water density = 62.4 lb/ft^3

    Given a liquid full pipe (5000 ft of water inside), where will the water level stabilize to (remember, top end of the pipe is closed and you've got a 1000psia pressure at the bottom of the pipe)?

    I've gone through some other thought processes (like why the water does not drain out when you've got your thumb on top of a liquid full drinking straw), but will hold back on those so as to not contaminate or lead-on your comments and thoughts.
     

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  3. Oct 24, 2007 #2

    Doc Al

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    If I understand what you're asking: 1000 psi = 144,000 lb/ft^2, so that much pressure can support a column of water of height h = P/D = 144,000/62.4 = 2,310 ft.
     
  4. Oct 25, 2007 #3
    I agree that the pressure can support a water column height of approximately 2310 ft if the top end was open: h = 2.31ft/psi * (P2 - P1) = 2.31*(1000 - 14.7) = 2274 ft. However, with the top end closed, doesn't the falling water level "pull" a vacuum at the top? Using a simple hydrostatic calculation, h=2.31*(1000 - 0), we get 2310 ft. But, I struggle with how the water level can drop 2690 ft once the vacuum has formed at the top, i.e. let's say the liquid full column drops 1 ft and pulls a vacuum (agreed that this is not a perfect vacuum), can the water level continue to drop and this vacuum space just "expand"?
     
  5. Oct 25, 2007 #4

    Doc Al

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    If the top end were open, you'd get a different answer: you'd have to include the downward pressure of the atmosphere (or whatever else the top of the column were exposed to) on the column, which will reduce the height of water that the upward 1000 psi could support.

    Vacuums don't "suck" or create negative pressure. There are only two forces on the column of water when the top is closed and a vacuum is created: its weight and the upward pressure due to whatever's producing the 1000 psi at the base. The vacuum does not exert a force on the water.
     
  6. Oct 25, 2007 #5

    mgb_phys

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    This is easier if you have ever seen a real mercury-in-glass barometer.
    The top of tube is sealed, the height of mercury in the column is held up by the weight of atmosphere pushing on the open pool of mercury at the bottom.
    If the pressure drops (bad weather) there is less force to hold up the column and the height decreases - create a vacuum in the sealed top of the tube.

    This is also why with an ordinary 'suction' pump you can't suck water up a height greater than the height of a column of water supported by air pressure (around 10m). As DocAl says it's not the vacuum pulling, it's the air pushing, all you are doing by sucking is removing the air from the top which was pushing it back down.
     
    Last edited: Oct 25, 2007
  7. Oct 25, 2007 #6

    Doc Al

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    mercury barometer

    Good example. Here's a diagram and brief discussion of how a mercury barometer works: Mercury Barometer
     
  8. Oct 25, 2007 #7

    mgb_phys

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    We had a really nice one outside my lab.
    Somehow it had managed to survive there for 100 years without killing anyone until the safety people found it - then it was the end of the world.
     
  9. Oct 25, 2007 #8

    stewartcs

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    Based on your question and the drawing, I would have to assume that there is some type of barrier at the bottom of the water column that separates it from the 1000 psia pressure initially, correct?

    If so, are you asking how far the fluid column will drop if the barrier is suddenly removed?

    If you are, then the fluid column would only drop a negligible amount. You can take a plastic straw and a cup of water and put your thumb over the end of the straw once it's full and then hold it up. You'll see that the water doesn't fall out. Same principle here.

    This assumes that the fluid column is in a tube and that the tube is strong enough not to collapse, and you are starting from a static condition.
     
  10. Oct 26, 2007 #9

    Doc Al

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    Not if the "straw" is 5000 feet long! Atmospheric pressure alone will support a 34ft column of water, not a 5000 ft one.
     
  11. Oct 26, 2007 #10

    stewartcs

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    Yeah I know, after I posted that and then thought about it for a second, I realized that!
     
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