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8 October, 08:37

A fan that consumes 20 W of electric power when operating is claimed to discharge air from a ventilated room at a rate of 1.0 kg/s at a discharge velocity of 8 m/s. Is the claim reasonable? What if the electric power is 40 W?

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  1. 8 October, 08:55
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    No, the claim is not reasonable for 20 W electric power consumption.

    It is reasonable for 40 W electric power consumption.

    Explanation:

    Power = (1/2) * mass flow rate * (square of velocity)

    mass flow rate = 1 kg/s

    velocity = 8 m/s

    square of velocity = 64 m^2 / s^2

    Power = (1/2) * (1) * (64)

    Power = 32 W

    For a fan that consumes 20 W power it is not possible to deliver more power than 20 W but this one is delivering 32 W hence it is a false claim.

    For a fan that consumes 40 W it is indeed possible to deliver 32 W considering the efficiency. Hence this claim is reasonable.
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