Question

Consider a fan located in a 3 ft by 3 ft square duct. Velocities at various points at the outlet are measured, and the average flow velocity is determined to be 22 ft/s. Taking the air density to 0.075 lbm/ft3, estimate the minimum electric power consumption of the fan motor.

Answer 1

Answer:

minimum electric power consumption of the fan motor is 0.1437 Btu/s

Explanation:

given data

area = 3 ft by 3 ft

air density = 0.075 lbm/ft³

to find out

minimum electric power consumption of the fan motor

solution

we know that energy balance equation that is express as

E in - E out  = $\frac{dE \ system}{dt}$    ......................1

and at steady state  $\frac{dE \ system}{dt}$ = 0

so we can say from equation 1

E in = E out

so

minimum power required is

E in = W = m $\frac{V^2}{2}$ = $\rho A V \frac{V^2}{2}$  

put here value

E in =  $\rho A V \frac{V^2}{2}$  

E in =  $0.075 *3*3* 22 \frac{22^2}{2}$  

E in = 0.1437 Btu/s

minimum electric power consumption of the fan motor is 0.1437 Btu/s