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=(v-u)/(t) \\ =(3-0)/(1) \\ =3m/s^2 \end{gathered}`

Mass of the air is given by the formula,

`\begin{gathered} m=D* V \\ =2*1 \\ =2\text{ kg} \end{gathered}`

Force is given by the formula

`\begin{gathered} F=\text{ ma} \\ =2*3 \\ =6\text{ N} \end{gathered}`

Power output is given by the formula,

`\begin{gathered} P_o=F* v \\ =6*3 \\ =\text{ 18 W} \end{gathered}`

Power input is given by

`\begin{gathered} P_i=(P_o)/(n)*100 \\ =(18)/(10)*100 \\ =180\text{ W} \end{gathered}`