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Determine the diameter of a piston

  1. Nov 19, 2016 #1
    1. The problem statement, all variables and given/known data
    Determine the diameter of a piston if the working stroke of a piston is ##h## and if a working cylinder ##(720^\circ )## describes the following ##p(V)## diagram, where on the ##x## axis is a ratio between the current volume of a piston and the total volume (swept + clearance volume). The compression rate is 7.5:1.
    graf.png

    2. Relevant equations


    3. The attempt at a solution
    I was able to calculate the height of the clearance volume (assuming it has the same shape as swept volume) by the following equation $$\frac{V_{clearance}+V_{swept}}{V_{clearance}}=7.5$$ so $$a=6.5 h.$$ And I honestly tried to calculate the diameter but everything I do leads me only to a ratio of some volumes, ergo the diameter falls out of the equation. I simply don't have an idea how to calculate the diameter of a piston.
     
  2. jcsd
  3. Nov 20, 2016 #2

    haruspex

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    I see your difficulty. It makes no sense to me either.
    Btw, I believe the given h is Vswept, so your a = 6.5h is backwards.
     
  4. Nov 21, 2016 #3
    I apologize, I misread the problem statement. The swept volume ##V_{swept}## is also given. In that case, this is all a trivial problem.
     
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