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Safety Valve/Pressure System question

  1. Mar 23, 2012 #1
    1. The problem statement, all variables and given/known data
    A valve for a pressure system has a discharge hole whose diameter is 50mm. The spring has a free length of 250mm (if you stretched the spring out), a coiled length (measured top to bottom while spring is coiled) of 207mm and a spring constant of 120kN/m. At what pressure will the valve open?


    2. Relevant equations
    Not 100% but I think
    a) p = F/A
    b) F = kx

    3. The attempt at a solution
    Area of discharge hole = ∏r2 = 1.963x10-3m2
    Force exerted by spring to keep hole closed = length of spring x spring constant = .207m x 120kN/m = 24.84kN
    Therefore valve open pressure = 24.84kN/1.963x10-3m2 = 12.65 kPa.

    How does that look? There is a diagram with some other info attached but I'm not sure it's relevant.

    Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Mar 23, 2012 #2

    gneill

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    Staff: Mentor

    Hook's Law requires the change in length of the spring from its equilibrium point (relaxed condition). You've used the compressed length only. What if the spring were compressed to nearly zero length? Would the force then be nearly zero? :wink:
     
  4. Mar 27, 2012 #3
    Aha! So the resistance force due to the spring is F = -kx where x = 250mm - 207mm and k is as given.
    I feel like they are giving me a little more info in the picture than is necessary. Specifically the 400mm diameter of the tank (not the discharge hole) and the 25mm thickness of the walls. My solution doesn't involve these numbers. Is that correct?
    Thanks for the help :)
     
  5. Mar 27, 2012 #4

    gneill

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    Staff: Mentor

    Yes, sometimes you'll find extraneous information given, particularly on diagrams. This may be because: It's placed there to confuse you; To get you used to picking the required data out of actual engineering diagrams; Simply because the diagram originally came from some other question entirely. Pick one or more :smile:
     
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