How can i find the RPM/torque of this electric fan with all of this information?

[thebluser]

an ideal electric fan has: a constant supply of 0.49 HP (367.8 watt), 3 motor poles, 8 blades, radius of 36 cm. based on all of that info. how can i find the torque/RPM or both?
if you know the answer tell me it with the method to find the torque/RPM.
p.s. i just threw in all of the information that i know about so if one of the information pieces is not necessary, that's why. also, i don't have an electric fan that has all of this information so i can't test it, nor build it.

 

[sophiecentaur]

Power is torque times angular frequency

so you need to pick a speed to get the torque or vice versa. Motors with the same power will differ in actual torque, depending on their speed.
Angular frequency, ω is 2pi s/60
where s is the RPM figure

 

[rcgldr]

You'd have to make a lot of assumptions here, such as at the motor running at peak power rpm when driving the fan. Then assuming an efficiency of say 80%, you'd need to find at what rpm the fan consumes .8 x 0.49 hp = .392 hp. An ideal dc motor would have to be designed so that it's peak no load rpm would be double the rpm the fan needs to consume .392 hp. An ideal dc motor produces zero torque at peak rpm, maximum torque when stalled, following a linear formula based on torque = peak torque x (1 - rpm/(peak rpm)). Maximum power occurs at 1/2 peak rpm, 1/2 peak torque x 1/2 peak rpm.

 

[CWatters]

an ideal electric fan has: a constant supply of 0.49 HP (367.8 watt), 3 motor poles, 8 blades, radius of 36 cm. based on all of that info. how can i find the torque/RPM or both?

Unfortunately that's not enough information.

If it was a 60Hz AC motor the rpm might be roughly

Ns = 120 F/p

where

Ns = Synchronous speed, in revolutions per minute
F = AC power frequency
p = Number of poles per phase winding

Ns = 120 * 60/3 = 2400 rpm

power = torque * Angular velocity

so

torque = power/angular velocity

= 367.8/(2*pi*2400/60)

= 1.46 Nm