Question

A fan is to accelerate quiescent air to a velocity of 10 m/s at a rate of 4 m3/s. determine the minimum power that must be supplied to the fan. take the density of air to be 1.18 kg/m3. 55

Answer 1

hope it helps..

refer this pic.

Answer 2

Given,

velocity = 10 m/s

rate = 4 m³/s

density of air = 1.18 kg/m³

(Here, all of the physical quantities are SI units, so no unit conversion is required.)

To find,

Minimum power that must be supplied to the fan

Solution,

We can solve this numerical problem by using the following process.

We know that;

The minimum power that must be supplied is the power of the kinetic energy of air:

⇒  $P = m\frac{v^2}{2}$

          = $dV \frac{v^2}{2}$

          = 1.18* 4 * $\frac{10^2}{2}$

          = 236 W

Thus, the minimum power that must be supplied to the fan is 236W.