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Fluids and Forces

  1. Jan 18, 2008 #1
    [SOLVED] Fluids and Forces

    Hi, I'm new to this site, so I'm not sure if this is the right place to post. I found a year-old entry with the same question that I'm having trouble with, found here:

    https://www.physicsforums.com/showthread.php?t=153538

    For Part a, I followed the same method that PremedBeauty followed, but can't seen to get the correct answer. Is there a force that I am missing?

    For Part b, I integrated to try and find the total force, but, once again, my answer comes out incorrect. My calculations for part b are below.

    F=force
    (atm)= atmospheric pressure (in Pascals)
    p= density of water
    g=gravity
    h= depth of water
    dh= change in depth of water
    A= area = width*h
    D = depth (as defined by problem)

    F=((atm) + pgh)*A
    But because pressure changes with depth, we must integrate
    dF = ((atm) + pgh) * (width*dh)
    Integrating yields:
    F= (atm)(width)(h) + (.5)(p)(g)(h^2) evaluated from 2D to 3D
    Evaulating yields:
    F= 3D^2((atm) + 1/5pgD) - 2D^2((atm) + pgD)

    The answer that I get from this calculation does not agree with the correct answer; is there something I am missing?
     
  2. jcsd
  3. Jan 18, 2008 #2

    stewartcs

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    Not sure what you are missing since you didn't show the calculation for part a.

    For part a you should have:

    [tex]F_A = P_A \cdot A_A [/tex]

    where,

    [tex]F_A[/tex] is the force in Newtons
    [tex]P_A[/tex] is the pressure on face A in Pascals
    [tex]A_A [/tex] is the area of face A in square meters

    If your problem is the same as the picture in the other link then you have,

    [tex]P_A = P_{fluid} + P_{atm} [/tex]

    and

    [tex]A_A = d^2 [/tex]

    Hence the force acting on face A is,

    [tex]F_A = (P_{fluid} + P_{atm}) \cdot d^2 [/tex]

    Now with [tex] P_{fluid} = \rho gh [/tex] and [tex]h = 2d [/tex] you get,

    [tex] P_{fluid} = \rho g \cdot 2d[/tex]

    Which yields,

    [tex]F_A = (\rho g \cdot 2d + P_{atm}) \cdot d^2 [/tex]

    Just plug in the value for [tex] P_{atm} [/tex] in pascals, along with the other missing, but given, values and you'll have the force.


    CS
     
  4. Jan 18, 2008 #3
    Alright, thank you. I meant to refer calculations for part 1 to those that the previous poster did (as I went through those same steps). I came up with the same answer that was displayed here, but it disagrees with the answer given. An error on the part of the book, I think...
     
  5. Jan 18, 2008 #4

    stewartcs

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    Make sure your units are correct.

    BTW, What did the book give for the answer?
     
  6. Jan 18, 2008 #5
    I'm not sure; it's an online homework assignment. It tells me if I'm right or wrong, but won't tell me the actual answer until I've gotten it correct.

    Are you able to help on the second part? (Part b)
     
  7. Jan 18, 2008 #6

    stewartcs

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    You'll have to integrate to find the force.

    [tex]F = P_{atm} \cdot A_B + \rho g \int_{a}^{b} h \cdot dA[/tex]

    where,

    [tex]A_B [/tex] is the area of face B
    [tex]h[/tex] is the height
    [tex]dA[/tex] is the area of some small strip across the face

    The limits of integration, a and b, would be the starting and ending height (depth), i.e. 2d to 3d respectively.

    Hope that helps.

    CS
     
  8. Jan 20, 2008 #7
    Apparently it only wanted the gauge pressure, so I subtracted out the air pressure, and everything worked out great. Thanks for your help.
     
  9. Jan 20, 2008 #8

    stewartcs

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    No problem. I was going to suggest trying that if you were still having problems.

    CS
     
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