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Old Apr 17th 2018, 09:25 AM   #1
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Power of a rotor - derivation

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?
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Old Apr 17th 2018, 12:14 PM   #2
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Power of a rotor - derivation

1 rev/sec = 60 rpm
P = 2T.pi.f f = rev/second
f = N/60
P = 2(pi)TN/60
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Old Apr 17th 2018, 12:30 PM   #3
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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.
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Last edited by studiot; Apr 17th 2018 at 01:33 PM.
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