Is the Claim About the Fan's Discharge Rate and Velocity Reasonable?

[a13x]

Homework Statement

Been at this question for some time an needing a double check to see if things are right.

A fan that consumes 20W of eletric power when operating is claimed to discharge air from a ventilaed room at a rate of 0.25 kg/s at a discharge velocity of 8 m/s. Determine if this claim is reasonable?

Homework Equations

KE of wind = 0.5 mv^2
20W = 20 j/s

The Attempt at a Solution

When i worked it out i calculated it would be 8J. This seems to be posible for a 20W fan to do this work. Is this correct??

 

[mgb_phys]

You probably mean 8J/s - but yes, 40% efficency sounds reasonable.

 

[a13x]

Sorry, I did mean 8J/s.

Thankyou for the reply

 

[noamholz]

Another question, related to the written above -
Is that correct to estimate the "usefull power" of a fan in the following way:

0- Estimating Force applied on fan. we get F.
1 - Estimating the velocity of the wind near the fan. we get Vo.
2 - using this estimation alone (ignoring wind decay & turbulences & whatever happens far from fan) to look at the picture from the wind's frame of reference- where the fan is moving with speed of -Vo, thus calculating P=Vo*F.

It's stage 2 I'm not completely sure of .. is that stage's logic OK?