Question

A fan is putting 1.0 J of kinetic energy into the air every second. Then the fan speed is increased by a factor of 2. Air moves through the fan faster, so the fan moves twice as much air at twice the speed. How much kinetic energy goes into the air every second?

Answer 1

A fan is putting 1.0 J of kinetic energy into the air every second - This statement gives us the power of the fan.

That is power = 1.0 J/1 s = 1.0 J/s = 1.0 W

Power of a fan/turbine is given by:

Where, A is the area of fan, ρ is density of air and v is the speed of fan.

Here area A and density of air ρ are constants.

Hence, Power is directly proportional to the velocity of air.

Hence, if the velocity is doubled, the power will be come (2)³ times.

P = 8 x (1.0 J/s) = 8.0 J/s

• Therefore, 8.0 Joules kinetic energy goes into the air every second. (P = 8.0 J/s)