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Air Volume Calculation

Figure 7 is a schematic expression of a system with a heat source inside. This system is to be cooled down by using a fan.

Assume the ambient temperature is Tamb and the ceiling temperature of the system is Tc. The least heat to be removed in order to keep the system temperature less than Tc is calculated as:
H = Cp × M × ∆T
Cp is the specific heat of the air, M is the mass of the air and ?T is the temperature difference between Tc and Tamb.
The mass of the air is the flow rate Q times the density (?)of the air.
Rearrange the above equation we can have:
Q = H / (Cp ×ρ× ∆T)
Cp ≒ 1005 J/Kg℃ andρ≒ 1.18 Kg/m3

Example. For a given heat source of 200 watts with a premises that the temperature of the system can not exceed 80#8451;. If air at ambient temperature of 25#8451; is drawn from outside of the system, the air flow rate Q can be calculated.

Before the calculation, you need to get straight on the units you are using. Check Table 2 for help.

Q = 200 watts/ (1005×1.18×55) = 0.00307 (m3/s) = 0.184 CMM = 6.5 CFM
To help you further, you may use
Q ≒ H / (20×∆T) for CMM (H in watt and ∆T in ℃) or
Q ≒ 1.79×H / ∆T for CFM (H in watt and ∆T in ℃)

Table 3 is an easy look-up table for your reference.

System Impedance Estimation

Now we have to get some idea about how to estimate the system impedance. It should be noted that it is not an easy task to really estimate the system impedance very quick without extra measuring devices. However, basic theory will still be explained for your reference.

When air is introduced into a system, it will encounter resistance due to the layout of the system. It is the pressure drop that causes the resistance. The pressure drop (or, the resistance) goes higher when more flow is trying to pass through the system. As a result, we may envision that there is another P-Q like curve, which is commonly called the system characteristic curve. The curve tells the relation between the system impedance and flow rate.A widely used empirical relation between the two is:

∆P = KQn
where ∆P is the system impedance, Q is the flow rate, K is the system’s characteristic constant and n is the flow factor with value between 1 and 2.
For laminar flow, n=1
For turbulent flow, n =2

Figure 8 shows the relationship between fan performance curve and some typical system characteristic curves with similar flow factor but different Ks. In this figure we can see that curve A reflects a system with higher system impedance than that of curve B and thus curve C. In other words, you may need to use a fan with higher static pressure for system A in order to get the same flow rate as that of using a lower static pressure fan in system C. The intersection of fan performance curve against the system impedance curve is called “operating point”. The same fan installed in systems with different system impedance results in different air flow delivery. Because the fan will not be operating at the same P-Q point.

When you match the system characteristic curve with the P-Q curve of a fan, there can be an intersection point. This point is called “operating point”. That is, the fan is actually operated at the static pressure of that point and delivering the corresponding flow, not the maximum flow rate. This tells you that it is not recommended to select a fan by only compare the extreme values of fans at hand. You should select fans with similar numbers on the data sheet and compare their P-Q curves and examine the operating point of each fan. Of course, it will be more accurate if you can do some real test. Figure 9 shows several situations that tell you the extreme values on the data sheets are only a first check. As Fan 2 and Fan 1 may perform the same in System A, though their extremes differ very much. For system with low impedance like System B, the maximum static pressure of a fan may not be critical. But for system with impedance much higher than System A, Fan 3 may not be suitable, though its maximum flow rate is far more than that of Fan 1. It is better to compare the fan performance curves of different fans with the concept of system impedance in mind

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