A room has a volume of 120 m3 An airconditioning system is t

A room has a volume of 120 m^3. An air-conditioning system is to replace the air in this room every twenty minutes, using ducts that have a circular cross-section (i.e., the ducts have the shape of a hollow cylinder). The speed of the air in the ducts is 3 m/s.

a) What is the volume flow rate of the air in the ducts?

b) What is the radius of the ducts?

Solution

Here ,

Volume of room , V = 120 m^3

speed of flow , u = 3 m/s

a)

volume flow rate = volume of room/time

volume flow rate = 120/(20 * 60)

volume flow rate = 0.1 m^3/s

the volume flow rate is 0.1 m^3/s

b)

radius of ducts is r

volume flow rate = u * pi * r^2

0.1 = 3 * pi * r^2

r = 0.103 m

the radius of the duct is 0.103 m