A cylindrical air duct in an air conditioning system has a length of 3.5 m and a radius of 5.00 X 10^-2 m. A fan forces air (ç = 1.8 X 10^-5 Pa·s) through the duct, such that the air in a room (volume = 242 m3) is replenished every 12 minutes. Determine the difference in pressure between the ends of the air duct.

Answer 1

Your value of ç = 1.8 X 10^-5 Pa·s is called the viscosity.

Get the volume flow rate from
Q = 242 m^3/720 s = 0.336 m^3/s

Get the duct velocity from
V = Q/(pi r^2)
I get 43 m/s, which seems much too high for a well designed A/C system. Pressure drops will be high.

Compute the dimensionless Reynolds number of the flow, which is

(density*diameter*V/ç)

Use pipe flow charts to compute the friction factor, f, which is a function of the Reynolds number.

pressure drop = f*(L/D)*(1/2)(density)*V^2