An air-conditioning system is designed to fill a room of 10.0 m * 8.0 m * 6.0 m with fresh air every 20 minutes. If the circular air duct has a radius of 13 cm, calculate the speed of airflow in the duct.
A) 30.0 m/s
B) 450 m/s
C) 2.4 m/s
D) 7.5 m/s
E) 1.0 m/s

Question

Quizplus · Accepted Answer

The volume of the room is 480 m³. The air duct's cross-sectional area is π*(0.13)² m². The airflow rate is 480 m³/20 min = 24 m³/min = 0.4 m³/s. The speed of airflow is the flow rate divided by the cross-sectional area, which gives approximately 7.5 m/s.

An Air-Conditioning System Is Designed to Fill a Room of 10.0