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Fluid Pressure problem

  1. Feb 25, 2012 #1
    Hi I have a midterm study guide question. This one has stumped me for a while and probably the only one undone.

    1. The problem statement, all variables and given/known data
    Suppose there is a semi-circular plate of radius 5 ft that rests on its
    diameter and is tilted at 45 degree angle to the bottom of a tank lled with water to depth
    6 feet. Find the force exerted by the water against one side of the plate. (The
    weight-density of water is 62.4 lb=ft^3)


    2. Relevant equations
    So I'm reading the book and I know that to solve the problem Force is weight-density of water (62.4) times the depth (6-y) and the area.

    Now the problem is I'm not quite sure how to approach the area. I just can't seem to grasp the image of the tank. Not to mention the 45 degree angle really confused my approach. I was under the assumption that its a 6ft tall cylinder with length 10ft and a plate on the bottom tilted at 45 degrees

    3. The attempt at a solution
    Problem seems simple, but I can't seem to figure out the 45 degree plate to find the area.

    What i have is:

    Integral from 0 to 6 of (62.4)(6-y)(area)

    Now this is assuming that I approached this correctly.:confused:
     
  2. jcsd
  3. Feb 25, 2012 #2

    tiny-tim

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    Welcome to PF!

    Hi NoobDoingMath! Welcome to PF! :smile:
    Yes, that's basically correct.

    You seem to be confused about the area …

    I suggest in future you always use the slicing method.

    In this case, slice the plate into horizontal slices of vertical distance dy …

    then find the area of that slice (it'll be dy√2 times the width, won't it?) :wink:
     
  4. Feb 25, 2012 #3
    Still a little bit confused, and I want to see if I'm understanding correctly. My "math English" isn't too good. :shy:

    So √2 is a result of the 45-45-90 triangle right?
    Therefore the slice is √2dy*width

    The width is 10ft since its radius is 5 and the plate rest on its diameter?

    Resulting my solution to be:

    ∫(62.4)(6-y)(10√2)dy a=0, b=6

    My answer would become:

    11232√2
     
  5. Feb 26, 2012 #4

    tiny-tim

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    Hi NoobDoingMath! :smile:

    (just got up :zzz:)
    Nooo, you're not thinking straight. :redface:

    Or, rather, you are thinking straight, and you should be thinking circular! :biggrin:

    The width has to be the width of the slice

    that's the whole point of slicing …

    you add the area of each slice, and that depends on y, doesn't it? :wink:

    Try again! :smile:
     
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