
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.]