Duct friction
The friction loss of straight ducting is not usually the most important element in determining the resistance of a ventilation system. Why then has so much effort been expended over the years in producing equations for its determination?
The classical equation is:
Pls = 
TL 1 2 — x — pv M 2 
Where: 

Pls 
= pressure loss in a straight duct (Pa) 
F 
= dimensionless friction factor 
L 
= length of straight duct (m) 
M 
= hydraulic mean “depth” (m) 
P 
= air density (kg/m3) 
V 
= mean air velocity (m/s) 
The hydraulic mean depth is defined as: 

M 
< loll 
















Where:
A = crosssectional area of duct (m2)
P = perimeter of duct (m)
Ltd2
For a circular crosssection A =—— and P = nd
4
For any other air density, the pressure loss due to friction at the same air velocity was obtained by multiplying the “standard” density value by:
0.0751
A M = — = P 
Equ3.39 
Pls 
XV 
Where: d = Thus: 
Diameter of duct
Ttd2 . d
— — hud = —
4 4
And
4fL 1 2
P — = ^X2PV
Here it should be noted that in American and some German texts, the pressure loss is defined for a circular duct and their formula becomes
FL 1 2
: —— X — DV
D 2
No difficulty should be encountered provided one realises that their values of f, the friction factor, are four times the value, to compensate.
It has frequently been assumed that f is a constant and this leads to the conclusion that:
Pl <xQ2
This is very far from the truth, especially at low velocities. In fact f oc fn. Re and the relative roughness of the duct. The relationship is best shown on the Moody chart in Figure 3.13. Numerous formulae have been produced to make the necessary corrections to the classical equation, these usually resulting in an index to v of less than 2 and an index to d of more than one.
As stated earlier, due to the numerous formulae having been produced, the author will content himself with examples from the preSI units era.
In the 1930s the then ASHVE (American Society of Heating and Ventilating Engineers, nowASHRAE), put forward the following empirical formula for the American market:
0. 75fL ‘ • x184
Pls — ,1.31 x
4005
At about the same time the then IHVE (Institution of Heating and Ventilating Engineers, now CIBSE), was giving its formula for the British user as:
0. 0001577 L
Pls =
ASHVE gave suitable charts for the coefficient of friction, whilst this was included within the IHVE equation. In both of these formulae:
PLs = frictional resistance (ins. w.g.)
L = length of straight duct (ft)
D = diameter (ins)
V = mean air velocity (ft/min)
There were some differences in the air density assumed, the American data being for dry air at 70°F and 29.92 ins Hg barometric pressure whilst the British values were based on the then standard air at 60 °F, 29.53 ins. Hg and 60% relative humidity. For “average” sheet metal construction IHVE specified an addition of 20%.
Where:
Air density at stated conditions lb/ft3
It will be noted that in both American and British formulae, the friction was shown to vary as 1.84 to 1.852 the power of the velocity. Most practical engineers, however, continued to calculate friction losses as varying as the square of velocity. Provided the changes in velocity on a given system were relatively small (say less than 10%), the error was negligible and likely to be less important than variations due to manufacturing tolerances. Also, the friction loss was taken as directly proportional to air density, again without serious error.
The fact that the Fan Laws defined similar variations in fan performance was an added advantage. Indeed such assumptions were in order, because the calculated values can never be more than estimates, due to the inexact knowledge of constructional roughness, covered, as already noted by a 20% addition. Normal roughness does not necessarily mean bad workmanship, but essential constructional features such as circumferential joints which at that time were as many as 40 per 100 ft. Nevertheless, the variations in calculated resistance from the ASVE 1930s data to the most recent formulae, of more than 30% can never be justified. It has not, however, deterred the researchers, and Loeffler’s formula of the 1980s, whilst showing similarities with the historical formula has increased the velocity index to about 1.9.
The formulae for galvanised steel ducts with an absolute roughness of:
Ј = 0.0001524 m (0.0005 ft)
LQ1
Pl
D
Where:
A = 1.717 E02 (for SI units)
Or
A =3.534 E09 (for Imperial units) where:
PL = total pressure loss (Pa or in. wg)
Q = flow rate (m3/s or cfm)
D = duct diameter (m or ft)
(or equivalent diameter of rectangular ducts)
L = duct length (m or ft)
To repeat, duct friction is usually a very small item in the overall resistance of a typical ventilation plant. In a dust extract or wood refuse collection plant, the frictional resistance is usually much higher as the air velocity in such systems is also higher.
Posted in Fans Ventilation A Practical Guide