Power of a rotor - derivation

Atom · Apr 17th 2018, 10:25 AM

I'm trying to understand the equation P = 2(pi)TN/60, where T=torque, N=rpm...

So far I understand:

E = F.d = F.(2.pi.r)*(no. of revolutions) = 2T.pi.n
And
P = E/t = 2T.pi.n/t - but n/t is revolutions per second, so:
P = 2T.pi.f f = rev/second

This is where I'm having trouble, because
1 rev/sec = 60 rpm, so I'd say:
P = 2T.pi.60.N
but in the textbook and online it says P = 2(pi)TN/60 so I'm not sure what's going on...

Anyone know what's going on?

YellowPeril · Apr 17th 2018, 01:14 PM

1 rev/sec = 60 rpm
P = 2T.pi.f f = rev/second
f = N/60
P = 2(pi)TN/60

studiot · Apr 17th 2018, 01:30 PM

This is where I'm having trouble, because
1 rev/sec = 60 rpm, so I'd say:
P = 2T.pi.60.N
but in the textbook and online it says P = 2(pi)TN/60 so I'm not sure what's going on...

I'm glad you realise where your difficulty lies since your foregoing analysis is correct if somewhat roundabout.

However your intial data says the shaft is running at N rpm

By definition this is N/60 rps.

So your f = N/60 and you must substitute this for f in the equation you have developed, not the other way round.