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Pelton Wheel Problem

  1. Dec 15, 2012 #1
    Think I posted in the wrong section previously.

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

    The buckets of a Pelton wheel deflect a jet, having a velocity of 60m/s, through an angle of 160o. Assuming that the velocity of the jet relative to the buckets is reduced by 15% as the jet water moves over them, find the efficiency of the wheel if the speed of the buckets is 27m/s and, using this efficiency, calculate the diameter of the jet so that the wheel may develop 200kW.


    2. Relevant equations

    I believe the following are relevant:

    0.5(1+cos θ )

    or 0.5 Rp (1+ cos θ) To be honest I can't find anything in my classroom notes to suggest there should be a Rp in this formula.

    V(bucket) = 0.5 x V(jet)


    3. The attempt at a solution

    Using the equation: 0.5 Rp (1+ cosθ)

    The first problem would give me an efficiency of 0.5 x 60 x (1 + cos 20 degress)

    = 28.691

    V(jet) at 85% = 27 / 0.5 = 54 m/s

    At this speed using again the above formula:

    0.5 x 54 x (1 + cos 20 degrees) = 25.871

    25.871 / 28.691 = approx 90%

    The answer has been given as 89% which is pretty close. However, I don't feel given all the different numerical values given that I have quite grasped the problem and I have just been lucky!!

    Any help would be appreciated.
     
  2. jcsd
  3. Dec 15, 2012 #2

    haruspex

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    That's an expression, not an equation. What does it represent?
    Rp being?
    Always? Why?
    That's a speed, not an efficiency, right? Is this the speed the buckets would move at if the wheel were 100% efficient? And you mean the first equation?
    Where did the 27 come from? 85% of 60 = 51
    I don't understand any basis for calculating the efficiency that way. Efficiency should be a matter of energy, which varies according to squares of velocities typically.
     
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