Force due to pressure on side of a container

  1. Hi gang,

    I'm having an issue with one my homework problems. There is an L shaped tank, 3d in height, 1d in width. The verticle part of the L is 2d in height, and the horizontal part of the L is a 1d box. d = 8m
    _
    | |
    | |_
    |_ _|<--Force due to pressure needed for this side.

    I need to find the pressure on the right wall of the horizontal part of the L. What I have managed to get so far is the equation:
    F=(rho)(g)(width)(height^2)

    Not very far, I know. I'm assuming I have to integrate this somehow, but I am unsure as to how to set it up. I'm not really looking for a solution, just a push in the right direction with regards to the integration, or in the correct direction if I am very, very wrong.

    Thanks, in advance, for the help.
     
  2. jcsd
  3. Fermat

    Fermat 876
    Homework Helper

    Is this a Plan view (a view from on top) or a Side view?
     
  4. From the side, sorry.
     
  5. Fermat

    Fermat 876
    Homework Helper

    Ok, hang on a min.
     
  6. LeonhardEuler

    LeonhardEuler 864
    Gold Member

    OK, I can explain this in general but I didn't completely follow all the dimentions you gave. From equilibrium considerations, the pressure at some depth, h is [itex]P_0+\rho gh[/itex] where [itex]P_0[/itex] is the pressure at the surface. The force at this hieght is PA where A is the area. Along the surface of the wall, the pressure is changing with the depth. At a given depth, h, the force is [itex](P_0+\rho gh)ldh[/itex] where l is the length of the wall. Now it is a matter of integrating the infinitesimal forces at each height to get the total force.
     
  7. We are actually using gauge pressure, so it simplifies the formula you gave a bit. I did get the correct answer using your method, though, so thank you very much.
     
  8. Fermat

    Fermat 876
    Homework Helper

    Arrgh, too late!!

    Oh, well. What LeonhardEuler said.

    I enclose a small piece of work explaining how to do these types of integrals for pressure over a submerged area.

    It may be useful for yourself or anyone else reading these posts.
     

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