Question

For modeling and calculation purposes, architects treat air as an incompressible fluid. As an architect's intern, you are doing the specs on a dorm air conditioning system that is designed to replace the air in each room every thirty minutes. If the rooms each have a volume of 205 m³ and they are supplied by ducts with a square cross section, determine the following.

(a) the length of each side of a duct if the air speed in the duct is to be 4.0 m/s
m

(b) the length of each side of a duct if the air speed at the duct is to be a value twice this speed.
m

Answer 1

Part A.

We know that Volume flow rate is given by:

Q = V*A

V = Speed of sir through duct = 4.0 m/sec

Given that duct have square cross-section, So Suppose length of duct is L, then

A = Cross-section area = L^2

Q = flow rate of air = 205 m^3 per 30 min = 205 m^3/(30*60 sec) = 0.1139 m^3/sec

So,

Q = V*A = V*L^2

L = sqrt (Q/V) = sqrt (0.1139/4.0)

L = 0.169 m = length of each side of duct

Part B.

Now when air speed is doubled, than

V = 2*4.0 m/sec = 8.0 m/sec

So, Now

L = sqrt (Q/V) = sqrt (0.1139/8.0)

L = 0.119 m = length of each side of duct

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