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Lowest pressure that the student's lungs can create?

  1. Jan 27, 2015 #1
    1. The problem statement, all variables and given/known data
    A student sucks on the end of a long tube which is initially filled with air and whose other end is in a large bucket of water which is open to the atmosphere. They manage to draw the water up a vertical distance of 3.36 m above the surface of the water in the bucket. What is the lowest pressure that the student's lungs can create?

    [P(atmosphere)=105N/m^2, ρ(water)=1,000 kgm-3, g=9.81 m/s^2]

    2. Relevant equations
    Hydrostatic pressure, P = Po +ρgh

    3. The attempt at a solution
    0 + (1000*9.81*3.36) = 33kN/m^2
    This is my attempt at the problem. It's considered partially correct since this is the result of the water being sucked from the bottom of the bucket to the top, but it is not the actual pressure in the student's lungs.
     
    Last edited: Jan 27, 2015
  2. jcsd
  3. Jan 27, 2015 #2

    haruspex

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    Think carefully what each of those variables represents in the context of how you are applying the formula in this question.
     
  4. Jan 28, 2015 #3
    I had another go at the question assuming that Po = 105 (atmospheric pressure) but again, got the wrong. What am I missing?
     
  5. Jan 28, 2015 #4

    haruspex

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    Equations have context. The equation P = Po +ρgh only works if the variables are matched up to the real world according to the relationships the equation assumes. In that equation, what do P, Po etc. refer to? And don't just answer pressure, height etc. What pressures? What height?
     
  6. Jan 28, 2015 #5
    I'm assuming the height is the vertical distance of 3.36m and 33kN/m^2 is the pressure when the water is being sucked from the bottom of the bucket to the surface, and NOT the pressure in the student's lungs. Is there another height that I need to account for? How would I go about finding it?
     
  7. Jan 28, 2015 #6

    haruspex

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    That's not clear - what pressure do you mean? The pressure at the bottom of the bucket? The pressure at the bottom of the tube? The pressure in the tube at the same height as the surface of the water in the bucket? A difference of two pressures?
     
  8. Jan 28, 2015 #7
    The pressure in the tube at the same height as the surface of the water. I just want to know if there's another height that I need to account for?
     
  9. Jan 28, 2015 #8

    haruspex

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    Ok, but it's wrong.
    In the context of the general equation P = Po +ρgh, complete the sentence "where Po is the pressure at point A, P is the pressure at point B, h is the height of ..... above ...., g is acceleration due to gravity and ρ is the density of the fluid at rest and occupying a continuous region including .... and ...."
    Then see if you have used the equation correctly.
     
  10. Jan 29, 2015 #9
    I also used 0 as Po, and have gotten this response from the assignment.

    "This is the pressure difference between the top of the fluid in the tube and the bottom, not the pressure created by the student's lungs."

    I'm not sure where to go from here...
     
  11. Jan 29, 2015 #10

    haruspex

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    Please try to answer my question. Forget the problem posted for the moment, and try to understand what the equation says:
    In the context of the general equation P = Po +ρgh, fill in the blanks in the sentence "where Po is the pressure at point A, P is the pressure at point B, h is the height of .......... above ........., g is acceleration due to gravity and ρ is the density of the fluid; the fluid is at rest and occupying a continuous region including .......... and .........."
     
  12. Jan 29, 2015 #11
    "h is the height of point B above point A, ... , occupying a continuous region including point B and point A."
     
  13. Jan 29, 2015 #12

    haruspex

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    No.
    According to the equation, which is greater, P or Po? So will the pressure be greater at A or at B?
    Which will be higher?
     
  14. Jan 29, 2015 #13
    Well P is just Po plus an added value, so Po is less than P. Pressure will be greater at point B than at point A.
     
  15. Jan 29, 2015 #14

    haruspex

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    So which is higher, A or B?
     
  16. Jan 29, 2015 #15
    In terms of Pressure? Well B of course. I would say point B is lower than point A?
     
    Last edited: Jan 29, 2015
  17. Jan 29, 2015 #16

    haruspex

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    I meant in height, so you agree A is above B. (But that is not what you answered in post 11.)

    Now let's match it to the problem at hand. Pick two points to be A and B. State the equation in terms of pressures at those points.
     
  18. Jan 29, 2015 #17
    So P(B) = P(A) +pgh
     
  19. Jan 29, 2015 #18

    haruspex

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    Sure, but I'm asking you to pick two points in the actual set-up to be A and B for the purposes of applying the equation.
     
  20. Jan 29, 2015 #19
    So point B would be at the bottom of the straw. While point A would be at the top of the straw or the top of the liquid, or does it matter?
     
  21. Jan 29, 2015 #20
    So then would we rearrange the formula to Po = P-pgh, and use this to find the pressure in the lungs of the student?

    Because the pressure in the lungs has to be lower than the pressure of the atmosphere for the liquid to rise, so this equation seems correct to me.

    EDIT: This led me to the right answer, thanks so much for the help.
     
    Last edited: Jan 29, 2015
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