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A rectangular duct section of 500mm x 350mm size carries 75 m^3/min of air having density of 1.15 kg/m^3 . Determine the equivalent diameter of a circular duct if-

1) The quantity of air carried in both the cases is same and

2) The velocity of air in both the cases is same

3) If f = 0.01 for sheet metal, find the pressure loss, per 100m length of duct.

Subject:- Refrigeration and Air Conditioning

Topic:- Duct Design, Controls & Applications

Difficulty:- Medium

1 Answer
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Given: a=500mm=0.5m

b=350mm=0.35m

Q=75/60=1.25 m3/sec

ρ=1.15kg/m3

Calculating equivalent diameter of circular duct

1) The quantity of air carried in both the cases is same

D=1.265[(a3b3)(a+b)](1/5) D=0.46 m=459.23 mm

2) The velocity of air in both the cases is same

D=2ab(a+b)

D=0.4117 m=411.76 mm

Also, pressure loss P_f=\frac{f.l.v ̅^2.ρ}{2m}…(1)

Where v ̅=\frac{Q}{A}=\frac{1.25}{(0.5×0.35)}=7.14 m/sec, f=0.01, l=100, ρ=1.15 kg/m^3

Hydraulic mean depth, m =\frac{(cross-section area of flow)}{(wetted perimeter)}

=\frac{(a×b)}{2(a+b)} (for a rectangular duct)

=0.1029

Substituting all values in equation (1) we get, P_f=284.76 Pa

Dividing by 9.81, P_f=29.03 mm of W.C. {Since 1\frac{N}{m}^2 =\frac{1}{9.81} mm of W.C.}

[Tip: In duct designing it is a general practice to write pressures in mm of W.C.]

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