An electric motor powered fan is used to accelerate quiescent air to a velocity

Question

An electric motor powered fan is used to accelerate quiescent air to a velocity of 10 m/s at a volume flow rate of 4 m3/s. The density of air is 1.18 kg/m3. The efficiency of the fan in transferring the mechanical work of the fan to kinetic work of the air is 90%. The efficiency of the motor in converting the electrical work to mechanical work is 95%. Ignoring the change in the potential energy of air, please Draw a schematic diagram of this system to show the transfer of electrical work to the kinetic work of the air. The mass flow rate of the air? The kinetic energy per kg of the air entering and exiting fan, respectively? The rate of kinetic energy of air exiting the fan? The consumption rate of the electricity? (Tips: you need find the power output of the motor first)

Explanation / Answer

b) mass flow rate = (vol flow rate) = 1.18 x 4 = 4.72 kg/s

c) Kin = 4.72 x v2 x 0.5 = 236 J/kg

10% of 236 = 23.6 J/kg [energy loss ]

Kout = 212.4 J/kg

d) Kout = 0.5mv2

212.4 = 0.5 x 1 x v2

v = 20.61 m/s

K = 0.5 x 4.72 x 20.612 = 1002.528 J/s

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