System curves
Just as fans have characteristic curves, so also do systems.
It has been shown that fan performance cannot be adequately described by single values of flowrate and pressure. Both quantities are variable, but have a fixed relationship with each other.
This relationship, demonstrated in Chapter 1, is best described graphically in the form of a fan characteristic. Volumetric flowrate is normally plotted along the base with the fan pressure, absorbed power and efficiency as ordinates. Such characteristic curves are specific to:
• a given fan design and size (usually based on impeller diameter)
• impeller rotational speed
• air/gas conditions (temperature, barometric pressure, humidity, chemical composition and, therefore, gas density)
Chapter 2 showed how to calculate the system pressure caused by the resistance of a system to the required volumetric flowrate. The resistance can also be plotted along the base with the system pressure as ordinate. For a specific system the pressure for a number of points may be calculated and these points would be joined be a curve — the system characteristic. Again, it is specific to the air/gas conditions. In general, the more air required to be circulated, the more pressure required. As noted in Section 5.2, a typical system will comprise a number of components connected by a ducting system comprising straight ducting, bends, junctions, etc.
The head loss in metres of fluid flowing in straight ducting:
Equ 5.1
H fL v‘
M 2g
= friction factor = length of duct (m)
= air/gas velocity (m/s)
= mean hydraulic depth cross — sectional area
M
M
Perimeter For a circular crosssection duct:
47id = —
4 4
Head loss may be converted to pressure loss for:
HL=^ = ^
W pg
Or
Pl = hL pg
Or
FL 1 2
Pl = ZT x 9 pv m 2
Note: In some literature, mostly of German or American origin, pL is defined in terms of circular crosssection ducting, i. e.
FL 1 2
Pi = — xpv L d 2
As m = , the value off has to be 4 times larger in this literature,
For in the UK 4fL 1
XpV2 d 2
Q
If we define v = —, and if we assume that the flow is fully turbulent, then we may also assume that f is a constant, then
PL ocQ2
In like manner, the pressure loss in fittings
^ 1 2 = kxpv
Again if we assume fully turbulent flow, kmay betaken as a constant and
1 2
Pl *2pV
Oc V2 ocQ2
Thus overall pL ocQ2 and the system line may be plotted accordingly.
If we draw both fan characteristic and system characteristic to the same scales of flowrate and pressure, they may be plotted on the same grid.
The intersection of the two curves will be the point of fan operation on that particular system, again assuming the same gas conditions for each (see Figure 5.2).
Note that Q w P A N W 
= flowrate through duct of fitting (m3/s)
= weight of gas per unit volume (kg m/s2)
= density of air or gas (k/m3)
= crosssectional area of duct (m2)
= fan rotational speed (rev/s or rev/min)
= absorbed fan power (W or kW)
A change in fan speed alters the point of operation from A to B ie along the system curve. This is because, as shown in the “Fan Laws”, (Chapter 4), for a given fan and system:
QocN
P ocN2
And.p ocQ2 for the fan as well.
Thus if a fan is applied to a system and its speed is changed from ^ to N2 then:
QocN
N. Equ 5.5
IeQ^CV^
The fan “law” still applies to the fan alone at a near constant fan efficiency. It does not however apply to the attached system, over a range of volumetric flowrates greater than say 10%. Where the fan speed is reduced over a turndown ratio of say 10:1 (e. g. with inverter control), the expected power savings <x N3 will not be achieved as claimed in many catalogues.
Table 3.1 in Chapter 3, shows the Reynolds numbers for a range of duct sizes and air/gas velocities. The corresponding friction factor for straight smooth ducting is shown as taken from the Moody chart, (Chapter 3, Figure 3.13), for typical galvanized sheet steel ducts, f is far from constant and is in fact a function of Reynolds Number and relative roughness.
It is a similar situation for duct fittings. Whilst the pressure loss through these is normally assumed to be
. 1 2
PL =kxpv^
Where k is a constant, it is known that k in fact varies with the duct Reynolds number.
The supporting experimental evidence for this statement is sparse, although the work of Idelchik and Miller, is perhaps the most valuable. Turbulence in a right angled circular bend leads to dead areas as shown in Figure 5.3, with a resultant value for k typically as detailed in the graph in Figure 5.4.
P ocN
Equ 5.6
Ie p2 = p.
N,
W ocNJ
Equ 5.7
Ie W2 = W, x ^2
2 ‘ N.
An increase of 10% in fan rotational speed will therefore increase volumetric flowrate Q by 10%, pressure developed by the fan and the system pressure by 21 %, but power absorbed W by 33%, assuming air/gas density is unchanged and that the friction factor for straight ducting and fittings remains virtually constant.
Unless large motor margins over the absorbed power are available, therefore, the possibility of increasing flowrate by a speed increase are usually limited unless substantial overdesign is incorporated. Speed increase also leads to increased stresses within the fan impeller (and other parts) also oc N2.
Most importantly, it has been assumed that the friction factor f is also constant. Whilst this is almost true for small changes in duct velocity, it is not true for large changes.
Reference to the Moody chart in Chapter 3, Figure 3.13, shows that this is not the case in the laminar and transitional zones. Only in the fully turbulent zone is it remotely close to the truth. In general f increases in all systems from design flow down to near zero flow where, by definition, the flow is laminar.
Thus Pl is not oc Q2 over a wide range of flows and thus:
N,
Q2 * Q, :
Ni
"dead" areas Figure 5.3 Crosssection through a right angled circular section bend showing "dead" areas 
Figure 5.4 Values of k against Reynolds number 
It will therefore be appreciated that for a typical system p cc Qn where n < 2. Typically it will be between 1.7 and 1.9. For systems incorporating absolute filters and little else, n > 1. For the flowthrough granular beds such as grain, n will lie between 1.25 and 1.4 according to its variety and moisture content.
P2 * Pi: 
W2 * W, x 
There will be very few systems where the flow is fully turbulent and consequently f * a constant. There will always be a flowrate where there is a change from transitional to laminar. At this point it is likely that the system pressure will increase. In all systems the velocity index will change from around 1.8 down to 1.0 with decreasing flow. Areal system pressure curve is likely to be as shown in Figure 5.5. 



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