Question

The return-air ventilation duct in a home has a cross-sectional area of 900 cm^2. 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. What is the speed of the air in the duct? (Express your answer to two significant figures.) (m/s)

Answer 1

0.86 m/s

Step-by-step explanation:

A = cross-sectional area of the duct = 900 cm² = 900 x 10⁻⁴ m²

v = speed of air in the duct

t = time period of circulation = 40 min = 40 x 60 sec = 2400 sec

V = Volume of the air in the room = volume of room = 7 x 11 x 2.4 = 184.8 m³

Volume of air in the room is given as

V = A v t

inserting the values

184.8 = (900 x 10⁻⁴) (2400) v

v = 0.86 m/s