Question

The return-air ventilation duct in a home has a cross-sectional area of 900 cm². The air in a room that has dimensions 7.0 m ×× 11.0 m ×× 2.4 m is to be completely circulated in a 40-min cycle.

1. What is the speed of the air in the duct? (Express your answer to two significant figures.) (m/s)

Answer 1

The total volume of air that needs to be circulated = 7 x 11 x 2.4 m = 184.8 m^3 of air.

All this air has to pass through the vent in 40 mins as per given in question.

1 min = 60 sec hence 40 min = 2400 seconds.

so in 2400 seconds 184.8 m^3 has to go through the vent

hence in 1 second air that has to go through vent = 184.8 / 2400 =0.077 m^3.

area of cross section = 900 cm^2 which in meters is 0.09 m^2

now velocity = volume flowing per unit time / area = 0.077 / 0.09 = 0.85 m/s

hence air speed in vent = 8.5 m/s