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

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Homework Help Overview

The discussion revolves around evaluating the reasonableness of a claim regarding a fan's discharge rate and velocity. The original poster presents a scenario involving a fan that consumes 20W of power and is said to discharge air at a rate of 0.25 kg/s and a velocity of 8 m/s. Participants are examining the calculations and assumptions related to this claim.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to verify the claim by calculating the kinetic energy of the wind produced by the fan. Some participants question the efficiency of the fan and the calculations related to power output. Another participant raises a related question about estimating the "useful power" of the fan and seeks clarification on the logic behind their approach.

Discussion Status

The discussion is ongoing, with participants providing feedback on calculations and exploring different aspects of the problem. There is acknowledgment of potential efficiency considerations, and some guidance has been offered regarding the calculations, but no consensus has been reached on the overall validity of the claim.

Contextual Notes

Participants are navigating assumptions about efficiency and the effects of factors like wind decay and turbulence, which are not fully resolved in the discussion.

a13x
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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??
 
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You probably mean 8J/s - but yes, 40% efficency sounds reasonable.
 
Sorry, I did mean 8J/s.

Thankyou for the reply
 
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?
 

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