## P & Q

What is the P-Q Curve? How Do You Measure It?

One of the key specifications customers are looking at is the static pressure a fan can perform. Regardless how it is measured, it can be explained more straight forward that you can understand without too much difficulty. Imagine that a fan is installed at one end of an open tube in a way that the fan is drawing air from out side of the tube (the free air) and sending the air flow into the tube (Figure 1). Now, let’s take a plate at the other end of the tube. It will not hard to understand the following situations:
A. We will get zero flow if we seal the other end of the tube with the plate (Figure 1A). B. We will get a little flow if we leave a small gap by slightly moving the plate (Figure 1B). C. We will get more flow if we leave a larger opening (Figure 1C). D. We will get the most flow if we completely move the plate away from the tube (Figure 1D). E. Without any change on the fan and the set up, by no means we can get flow more than that of Case D.

Why we can not get any flow in Case A. Because the tube is pressurized such that the driving force of the fan can not overcome the pressure of the tube. When the tube is “leaking” (Case B), it is not hard to understand that the pressure inside the tube is lower than that of Case A and the fan is able to, though “hard”, to “push” the air out of the tube. When the opening is getting larger and larger, the pressure inside the tube keeps going down. But more and more air flow is coming out of the tube. In other words, the resistance inside the tube is getting smaller and it is easier for the fan to drive the air. When we totally remove the plate, there is no way to pressurize the tube and there is no resistance (assuming Non-viscous flow, no friction and no boundary layer closed to the wall. You do not have to understand this if you are not able to) inside the tube, and therefore we can the most flow out from the fan.

Normally we use the term “static pressure” to evaluate the performance of the fan. You can figure it as the power to overcome the resistance given by the environment. Maximum static pressure is the maximum power a fan can generate. We can start to get flow when the pressure (or, the resistance) of the environment is lower than the maximum static pressure. The higher the number, the more capable the fan can delivery air for cooling.

2. Q – The Air Flow Rate

The air flow rate means the volume of the flow delivered by the fan per unit time. Following the scenario described in previous section, we can get the maximum air flow rate in Case D, in which we got no pressure difference between two sides of the fan. That is, we get the most flow because there can be imagined as no “resistance” in front of the fan when it drives air. When we use the plate to “block” the tube, the resistance increases and there becomes a pressure difference between the two sides. You can take it as a “back thrust” to make the air moving ahead harder. When the “back thrust” equals to the maximum static pressure a fan can generate, we get no air flow out from the tube.

3. Meaning of the P-Q Curve

Understanding the meaning of P and Q described and explained above, you should be able to read, or more, utilize the P-Q curve when trying to select a fan to meet your need. Figure 2 is an example. The ordinate is the static pressure and the abscissa is the flow rate. The most commonly used units for flow rate are CFM (cubic foot per minute) and CMM (cubic meter per minute). The counter part units for pressure are inch-H 2 O and mmH 2 O. From time to time you may use units other than the said ones, Table 1 and 2 are made to help you as a cross reference between different units. A P-Q curve shows, when a fan is selected and used, the maximum flow the fan can deliver (of course, under zero static pressure situation); the maximum pressure the fan can generate to overcome the system resistance (under zero flow rate situation); and all the possible flow rate the fan can produce between these two extremes. You may now have a question in mind that how you know the exact fan operating point when a fan is installed on your system. This is, in fact, a question that needs more knowledge and is not easy to answer straight forward (it will be explained in later section). Owning to this reason, for most of the time people are selecting fans based on the two extremes without involving themselves too much further. It is suggested that you try to get several fans with similar performance and make your own experiment. You may then find the proper one of your wish. The best one that you choose must be having the best operating point (the most flow out of the system).  If you do like to know more about the curve, it is suggested that the shape of the curve the more convex the better. For example, in Figure 3A, curves A and B have the same maximum flow rate (at zero pressure) and maximum pressure (at zero flow rate). However, the fan with curve A is much better than the fan with curve B. Why, because if you need the flow rate of Q*, Fan A has more “power” (higher pressure) to overcome the resistance. Or, you may think, if there is a specific resistance to overcome, Fan A can deliver more air flow than Fan B (Figure 3B). But in reality, it may not be easy to find P-Q curve with a shape so simple (either convex or concave). You may find, from time to time, a curve which concaves down somewhere in the middle. It shows that the fan is reaching its transition stage (close to a so-called “stall” condition) and therefore a drop on pressure. Sometimes the shape of the P-Q curve is even more complicated. This is why it needs deep knowledge of aerodynamics and experiences when designing the profile of the blade for the impeller. But, as a rule of thumb for you when looking at the overall shape of the curve, the more convex the better. In another reality, sometimes you may not be able to find fans that have a similar base for comparison by only comparing the curves. Do not feel frustrated! This gives you the chance to play with them to find the one that can really solve your cooling problem. Have some fun!  4. Measuring method and standard

The performance of a fan is reflected by the performance curve, or the so-called P-Q curve, which is obtained by measuring the flow rate and the corresponding pressure. The measurement is done using the double chamber method based on AMCA standard 210 (85). This method employs a device – a wind tunnel with two chambers (Figure 4) to create environments with dissimilar pressure difference, such that the flow rate can be obtained under each pressure condition. During the measurement, the volume of air flow is obtained by measuring the pressure difference (Pn) between the two sides of the nozzle. The static pressure (Ps) generates by the fan can be measured at the same time. The auxiliary blower is the key to create the intended pressure differences from zero to the highest static pressure a fan can perform. Basically, the pressure, or the pressure difference is measured by using pitot venturi. But the air flow rate is obtained by calculation based on the following:

Q = 60 AV
where
Q = the air flow rate (m3/min)
A = the cross section area of the nozzle = pD2/4 (m2)
D = the diameter of the nozzle
V = the average flow speed at the nozzle
The average flow speed at the nozzle is calculated as:
V = (2g Pn /g)0.5 (m/sec)
where
g is the specific weight of the air in kg/m3 (e.g., g=1.20 at 20?, 1 atmospheric pressure) and g is the acceleration of gravity with the value of 9.8 m/sec2. Pn is the pressure difference in mmH2O.

5. Parallel and Series Operation

Parallel operation is the situation that two or more fans are set up side by side. Figure 5 shows the comparison of P-Q curves of a single fan and of two fans in parallel. It can be seen the air flow rate is increased when using two fans in parallel and the flow is doubled when there is no resistance in the system. However, it can also be noticed that the static pressure of the fan set is not changed. This means you only use this kind of set up when the system resistance is low. Another multiple fan operation is series operation. In this case, you use two or more fans in series. Figure 6 is a comparison of the performance curve of a single fan with that of a two fan in series setup. We can see that the static pressure of the fan series is almost doubled. However, the maximum flow rate is not increased. Series operation can be considered when the resistance of the system is high. Because single fan operation is not able to deliver adequate air flow for cooling. Higher static pressure is needed to overcome the resistance of the system. Series operation is one of the options to get higher static pressure. 