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Hydrostatic force problem

  1. Sep 19, 2014 #1
    1. A vertical plate consists of rectangular and semicircular portion and has dimensions as shown. It is submerged in a liquid such that the upper edge coincides with the free surface of the liquid. What is the ratio of L/R such that force on the rectangular portion is the same as that on the circular portion?


    2. Relevant equations

    3. The attempt at a solution

    For rectangular part, since height of it is L and width of it is 2R
    so force on retangular part is

    for semi circular portion

    Since Fr=Fsc

    2RL2=(L+4R/3∏)∏R2(γ cancelled out)

    now I'm stuck here. Am I doing this right? or did I misunderstand the problem?

    English isn't my first language, so bear me.
  2. jcsd
  3. Sep 19, 2014 #2


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    You're doing just fine. Remember you want an answer for L/R, so if you call that x, all you have to do is rewrite the last equation to get something with x and a few numbers...
  4. Sep 19, 2014 #3


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    Looks good so far. How can you turn this into an equation only involving the ratio L/R? How do you solve a quadratic?
  5. Sep 19, 2014 #4

    er.. so I divide both side with R^2


    since L/R=x


    and this gives me two roots


    so I pick the one bigger than 0; which is x2.

    so L/R should be 1.91832, right?
  6. Sep 19, 2014 #5


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    Looks right, but I would tend to give the answer in surd form, not reduce it to a numerical approximation.
  7. Sep 22, 2014 #6
    whoa.. it is hard to get back to old thread. Thanks!
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