Ductwork elements
In the design of a ductwork system it is the practice to add the resistance of all the elements in the index leg together, to determine the total (or static) pressure loss. The fan must develop this pressure at the design flowrate. The system and fan will then be in harmony. (See Chapter 4.)
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Where: |
The resistance of duct fittings and straight ducting is invariably determined from the Guides produced by CIBSE or ASHRAE. Both bodies have a similar approach and treat the pressure losses as a function of the local velocity pressure. This function is usually regarded as a constant and thus the loss becomes:
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PLf |
= pressure loss (Pa) |
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KF |
= constant |
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P |
= local air density (kg/m3) |
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(usually taken as standard 1.2) |
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V |
= local velocity (m/s) |
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1 9 Pl =kF X2PV Equ3.26 |
Whilst this may be reasonably true in the normal working range, it is important to know that kF has a Reynolds Number dependence and that at low Reynolds Numbers kF can increase enormously, whilst in fully turbulent flow, if ever attained, the value could be less.
There are very few textbooks which even admit this variation. The only one of note is Idelchik’s Handbook of Hydraulic Resistance which gives a very detailed exposition of the subject and is noteworthy for its comprehensiveness. Miller’s Internal Flow Systems is also recommended.
It might be thought that the topic is somewhat esoteric, but it is suggested that with the increasing use of inverters and other variable flow devices, it is important to know that at high turndown ratios, the system resistance curve diverges ever more from the oft quoted pL °c Q2. Thus power absorbed is not x fan speed N3, even if there were no bearing, transmission and control losses.
In like manner, the loss in straight ducting is usually quoted as
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Diameter D M |
Average Velocity V M/s |
Reynolds No R.= P* N |
Relative Roughness K D |
Friction Factor F |
Flow quality |
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0.1 |
2.5 |
16492 |
0.0015 |
0.0076 |
Tr |
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5 |
32985 |
0.0067 |
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10 |
65970 |
0.0063 |
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15 |
98955 |
0.0059 |
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20 |
131940 |
0.0057 |
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0.25 |
2.5 |
41231 |
0.0006 |
0.006 |
Tr |
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5 |
82463 |
0.0055 |
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10 |
164926 |
0.005 |
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15 |
247388 |
0.0048 |
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20 |
329851 |
0.0047 |
|||
|
0.315 |
5 |
103903 |
0.00048 |
0.0051 |
Tr |
|
10 |
207806 |
0.0047 |
|||
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15 |
311710 |
0.0046 |
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20 |
415613 |
0.0045 |
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25 |
519516 |
0.0044 |
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0.63 |
5 |
207806 |
0.00024 |
0.0043 |
Tr |
|
10 |
415613 |
0.0042 |
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15 |
623419 |
0.0039 |
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20 |
831226 |
0.0038 |
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25 |
1039032 |
0.0036 |
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1 |
5 |
329851 |
0.00015 |
0.0039 |
Tr |
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10 |
659703 |
0.0037 |
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15 |
989555 |
0.0036 |
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20 |
1319406 |
0.0035 |
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25 |
1649258 |
0.0034 |
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2 |
10 |
1319406 |
0.000075 |
0.0033 |
Tr |
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15 |
1979109 |
0.0032 |
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20 |
2638812 |
0.0031 |
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25 |
3298516 |
0.003 |
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30 |
3958218 |
0.00295 |
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2.5 |
15 |
2473887 |
0.00006 |
0.00295 |
Tr |
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20 |
3298516 |
0.0029 |
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25 |
4123144 |
0.00285 |
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30 |
4947773 |
0.0028 |
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40 |
6597031 |
0.0028 |
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Table 3.1 Friction factors versus duct size and velocity Note 1 : Values apply to standard air Note 2: All values are in the transitional range |
FL 1 o
Pls = ^ Pv Equ 3.27
M 2
And — is taken to be a constant ks m
Where:
L = length of straight duct (m)
M = mean hydraulic depth (m)
~ — for circular cross-sections 4
F = friction factor
Again, as L and m are constants and f is assumed to be constant, the loss is taken to be
PLs=ks^Pv2 Equ 3.28
And thus another problem is created, for f is not a constant but rather a function of absolute roughness and Reynolds Number.
The Moody chart shown in Figure 3.13 shows that in the transitional and lower zones f * constant, and that again, as flow enters the critical zone there are significant increases in f, then a sudden drop, before climbing again in the laminar zone.
Referring now to Table 3.1, this covers the range of sizes and velocities encountered in HVAC practice. Assuming an absolute roughness applicable to g. s.s. (galvanised sheet steel), it can be seen that in all these cases the flow is transitional. The relative roughness and friction factor therefore vary enormously as shown. Thus with decreasing flow, and therefore velocity, the reducing velocity pressure is partially offset by the increase in f.
A system resistance curve is likely to be of the form shown in Figure 3.14 although for most HVAC systems the flow at which instability occurs is very close to zero flow. For mine ventilation, where the size of roadways can be considerable and the
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Figure 3.14 A system resistance curve |
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0,025 |
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0,004 |
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0,002 |
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7 89 2 34567 89 Iff 104 |
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2 3 4 5 6 789 |
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105 |
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2 3 4 5 6 789 |
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106 |
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2 3 4 5 6 789 |
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10: |
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2 3 4 5 6 789 |
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108 |
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P vd Reynolds number Re = —— Figure 3.13 Friction factor versus Reynolds number — Moody chart |
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Reynolds Number is higher, this shape of system resistance curve has been recognised for at least 50 years. Somewhat later in Section 3.4.1 it will be shown how the formula has been tailored to fit the facts by reducing the index of v velocity from 2 down to 1.9 or even less.
Vigilant readers of this text will have detected that the author is somewhat cynical and he would suggest that it hardly seems worth the struggle to reach the truth, if there is any! Better to go back to basics. In this computer age, it should be possible to develop a programme to give the correct f for the velocity, diameter and roughness. Whether the effort is applauded, however, may still be debatable.
Norman Bolton at NEL, East Kilbride, was responsible for a programme of work which measured the resistance of supposedly identical ducts and fitting from three different manufacturers. The variation in pressure loss pL was enormous, thus proving that quality is everything. It also suggests that so-called balancing of systems is not enough and that, to use “management speak”, a full system audit should be carried out.
The results should be fed back into the company design database. Some aspects of ductwork design are rarely mentioned in
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^v2 VA2y |
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1- |
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— Ps1 + Pv1 |
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+ Pv2 |
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A, |
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Eps |
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1- |
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So, the static regain psr or addition to the initial fan static pres- V2 |
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Which is exactly the same as |
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Sure psi is the term pv1 (Pv1~Pv2> As the efficiency of conversion is never 100%, the actual regain will be: |
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1- |
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VA2 |
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Because velocity pressure is inversely proportional to area2. Then “ ,2" |
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A, |
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Pv1 Pv1 |
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+ Pv2 |
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Ps1 Pv1 Ps1 " |
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