Torque, angular momentum and kinetic energy of water wheels.

  • #1

Homework Statement



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


Homework 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

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?
 

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