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Homework Help: Torque, angular momentum and kinetic energy of water wheels.

  1. Jun 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Calculate the torque, angular momentum and kinetic energy of the water wheels in the table.

    [I'll give one example]

    High breast water wheel:
    Angular velocity/rpm 8
    Head/m 4.65
    Flow rate*/m3 s−1 1.0
    Power/kW 39.4
    Diameter/m 7.0
    Width or height/m 2.5
    Mass/kg 14 143
    Power-to-weight ratio/W kg−1 2.8

    2. Relevant equations

    Torque = Moment of inertia * Angular acceleration
    Moment of inertia of thin solid disc = (mr^2)/2 (about z axis)
    Angular momentum = Moment of inertia * Angular velocity
    Rotational kinetic energy = (Iw^2)/2

    3. The attempt at a solution

    8rpm -> (8/60)*2*pi rad/s = (4pi)/15 rad/s

    Torque = (14143*3.5^2*(angular velocity))/2 = 72572Nm
    Angular velocity has here been used instead of angular acceleration due to explanation found here: https://www.physicsforums.com/showthread.php?t=346163

    However, this means that the angular momentum calculation gives the same answer (minus a direction, which will take the direction of the angular velocity vector). Have I done this correctly?

    Rotational KE = (14143*3.5^2*((4pi)/15)^2)/2 = 60797J

    Do these seem at all right?
  2. jcsd
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