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Fluid Mechanics Problem

  1. Mar 10, 2014 #1
    The correct answer to this problem is h2 = h1 but I don't get it. According to what I understand,

    F=p/A

    So for the Tube on the left:

    F1 = P/A = ([itex]\rho[/itex]*g*h1)/A1

    For tube on the right:

    F1 = P/A = ([itex]\rho[/itex]*g*h1)/3*A1

    I get h2=3h1 (i know if you think about it this does not make sense, but i don't what i am not getting).
     

    Attached Files:

  2. jcsd
  3. Mar 11, 2014 #2
    I think your solution is wrong... it should come h1=3h2...but it's the last line of the question that's bugging me... i think we gotta understand h2 relative to h1...
     
  4. Mar 11, 2014 #3
    This problem illustrates the concept of a hydraulic piston.

    First of all, a small minor correction in your formula where F=P*A, not F=P/A.

    Next, you have to accept the principle that for a given fixed depth a body of water will always have the same pressure everywhere. This means the pressure where the force F is applied in the left column is the same pressure at the same elevation in the right column. I think you made the mistake of equating forces which is not correct. If you equate the pressures then I think you'll see h1 = h2.

    A hydraulic piston or cylinder is a way to use a small force over a large distance to move a large force over a small distance.
     
    Last edited: Mar 11, 2014
  5. Mar 11, 2014 #4
    Yeah I agree the equation i had was wrong..but how can the height of the water level on system B be equal to System A when the area on the system B is 3 times the area of system A? I mean the volume of water on both system is same..where would the extra water for system B come from?

    Doing math i do get h2=h1

    For system B:

    Fout = 3F1
    P=(3F1)/(3A1) = F1/A1
    ρgh1=F1/A1
    h1=F1/(A1*ρ*g)

    For system A:
    Fout=Fin
    ρgh2=F1/A1
    h2=F1/(A1*ρ*g)

    So h1=h2
     
    Last edited: Mar 11, 2014
  6. Mar 11, 2014 #5
    The volume of water is irrelevant in both systems. It could be the same or they could have added more water, it makes no difference to the answer.

    I think you might still be trying to equate forces so starting with Fout and Fin seems confusing to me and also I think you mixed up h1 and h2 between the two systems.

    Just equate the pressures P1 = P2 and I think it would answer your question immediately.
     
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