Question

A fan uses a rotating blade to moves 2m3 of air each second at a speed of 3 m/s. Assumes air is initially at rest and has a density of 1 kg/m3. Fans are inefficient; assume an efficiency of 10%.What is the acceleration of the air? m/s2What is the mass of the air? kgWhat is the force the fan applies? NWhat is the power output of the fan? WWhat is the power input of the fan? W

Answer 1

Given that velocity of air, v = 3 m/s and initial velocity of air, u=0 m/s.

Also time, t = 1 seconds

Volume of the air, V = 2m^3

Density of the air , D = 1 kg/m^3

Efficiency, n = 10 %

Acceleration can be obtained by the formula

$\begin{gathered} a=\frac{v-u}{t} \\ =\frac{3-0}{1} \\ =3m/s^2 \end{gathered}$

Mass of the air is given by the formula,

$\begin{gathered} m=D\times V \\ =2\times1 \\ =2\text{ kg} \end{gathered}$

Force is given by the formula

$\begin{gathered} F=\text{ ma} \\ =2\times3 \\ =6\text{ N} \end{gathered}$

Power output is given by the formula,

$\begin{gathered} P_o=F\times v \\ =6\times3 \\ =\text{ 18 W} \end{gathered}$

Power input is given by

$\begin{gathered} P_i=\frac{P_o}{n}\times100 \\ =\frac{18}{10}\times100 \\ =180\text{ W} \end{gathered}$