A cylindrical air duct in an air conditioning system has a lengthof 5.5 m and a
ID: 1756646 • Letter: A
Question
A cylindrical air duct in an air conditioning system has a lengthof 5.5 m and a radius of 7.2 x 10^-2 m. A fan forces air ( n = 1.8x 10^-5 Pa·s) through the duct, such that the air in a room(volume = 280 m^3) is replenished every ten minutes. Determine thedifference in pressure between the ends of the air duct.a. 14 Pa
b. 1.1 Pa
c. 0.023 Pa
d. 4.4 Pa
e. 0.47 Pa
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Explanation / Answer
Given: L = 5.5 m R = .072 m n = 1.8e-5 Pas Volume flow rate : Q = (280 m^3 / 10 min) x (1 min / 60 sec) = .467 Difference in pressure (Poiseuille's law) P2 - P1 = 8LQn/R^4 = 8(5.5)(.467)(1.8e-5) / (.072^4) = 4.38 Answer: D: 4.4
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