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Homework Help: Radius of gyration/power/rev per minute

  1. Aug 26, 2011 #1
    1. The problem statement, all variables and given/known data
    A water wheel rotates a generator producing power from vertically flowing water onto its blades. Height of water is 100m above blades. init vert velocity is 0.
    I have calc velocity at hitting wheel as 44.3m/s
    calc the mass of water hitting the wheel per second to create 20kW power
    Calc rev/min of gene (wheel and gene combined radius of gyration 3m and mass 120kg)

    2. Relevant equations
    v²=u²+2as
    K.E=0.5mv²
    P.E=mgh
    J=mk²
    g=9.8m/s²

    3. The attempt at a solution
    For mass I have calculated P.E and K.E in terms of m and made equal to 2000 giving answer 10.2Kg? not sure if this is right.
    For rev/min I have worked out J=120x3² = 1080kg m², not sure where to go from here?
     
  2. jcsd
  3. Aug 28, 2011 #2

    rock.freak667

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    Homework Helper

    10.19 or 10.2 kg/s is correct. Remember to put the correct units of mass per second.

    For the second part, remember that you can the kinetic energy of a rotating component as E = Iω2 = mk2ω2.

    or in terms of power P = Mk2ω2 where M is the mass per second and ω is in rad/s.
     
  4. Aug 30, 2011 #3
    Thanks for the help, but I cannot find that equation, I can however find the equation E = 0.5 mk2ω2.
    If I use this then I get 20000=0.5x120x32ω2
    which gives me 6.086rad/s.
    Am I right to use the mass of 120kg, as this is given in the question, and I'm not sure if i need the 0.5 in the equation? Thanks.
     
  5. Aug 30, 2011 #4

    rock.freak667

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    Homework Helper

    That's equating energy with power,

    you need to find E which would normally be the KE+PE but you aren't given a time element so I am not sure if you can get it.
     
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