FAN LAW AND SYSTEM CURVE

With a basic understanding of these rules. the performance  of a fan can be quickly  calculated  for various conditions.

SYSTEM REQUIREMENT

The three fundamental rules governing fan performance are commonly called the "fan laws."  These rules are only valid within a fixed system with no change in the aerodynamics or airflow characteristics of the system.   For the purpose of this discussion. a system is the combination of duct work, hoods. filters, grills. collectors, etc . through which air is  distributed. Therefore, these rules can also be referred to as "system laws."

VOLUME AND PRESSURE

The motion of any mass causes friction with its surroundings. The movement of air through a system causes friction between the air molecules  and their surroundings  (Ducts walls, filter media, etc.)  and any other air molecules.  Energy is required (to overcome  this friction,  or resistance.   The faster the air moves the greater the resistance to flow and the more energy is required to push or pull the air through the system.

This energy is stated in term  of pressure.  The portion of the pressure  that results  in air velocity is described as velocity pressure (V_P).  The portion necessary to overcome friction in the air and in the system is described as static pressure (S_P). The sum of the two is described as total pressure (T_P).
The law of physics, for motion, is expressed algebraically as:
V  = √(2 gh)      OR         V²    =    2gh
where V =  velocity of flow
g  =  force of gravity
h =  pressure causing flow

As can be seen from the equation, the pressure necessary to cause flow is proportional to the square of the velocity.  In a system,  this  means that  S_P will  vary as the square  of the change  in velocity  or  volume  expressed  in cubic  feet per minute (CFM).  This makes it possible to predict all possible combinations of SP at the corresponding CFM given anyone such calculated relationship of S_P and CFM for a fixed system.

For example, a system is calculated to require a static pressure equal to 2" water gauge at an airflow rate of 1000 CFM.  If it is desired to increase the flow to 1500 CFM without any physical change in the system, the required SP would be:
(1500 ÷ 1000)² x 2" = 4.5" S_P

(CFM_new/CFN_old)   =  S_P(new)/S_P(old)

 The same calculation using any number of varying CFM ratings would result in a plotted curve as shown in Figure 1.

Regardless of fan type, fan size, or volume of flow through a system, the relationship of CFM to S_P will not change unless the system itself is altered in some way. S_P always varies as the square of the change in CFM. The only exception to this rule is found in a laminar flow characteristic where V_P is of far greater importance than S_P. Such circumstances are not typical of fans.

FAN LAWS

In air movement system, it it the fan wheel that does the work. In a sense, the fan wheel act like a shovel. As it revolves, it discharges the same volume of air with each revolution. Working within a fixed system, fan will discharge the same volume of air regardless of air density,(disregarding the effect of compression at high velocity pressures).

If the fan RPM is increased, the fan will discharge a greater volume of air in exact proportion to the change in speed. This is the fist "Fan Law".

1. CFM varies in direct proportion to change in RPM

CFM_(new) = [RPM_(new) x CFM_(old)] / RPM_(old)

2. SP varies in proportion to change in (RPM)²

S_P(new)  = [RPM_(old)/RPM_(new)]²   x S_P(old)

3. BHP varies in proportion to change in (RPM)³

BHP_(new)  = [RPM_(old)/RPM_(new)]³   x BHP_(old)

It is important to remember that each of these "fan laws" relationship takes place simultaneously and can not be considered independently.

FAN CURVE AND SYSTEM CURVE

As stated earlier, a system curve can be plotted to show all possible combination of S_P and CFM for a given fixed system. Any fan used on that system must operate somewhere on that system curve Fan performance is determined by laboratory testing and is presented graphically in the forms of fan curves. Unless it is physically altered in some way, a fan must operate somewhere on its S_P/CFM curve. The relative shape of that curve will not change, regardless of fan speed. Because the fan and system can each only operate somewhere on their own respective curves, a fan used on a fixed system can only have one point of operation. The point of operation, as shown in Figure 3, is the intersection of the system curve and the fan S_P CFM curve. 

 if the fan speed is increased or decreased, the point of operation will move up or down the existing system curve. This shown in Figure 4. 

Example 1: A fan has been selected to deliver 35,530 CFM at 8" SP. The fan runs at 1230 RPM and requires 61.0 BHP. After installation, it is desired to increase the output 20%. 
At what RPM must the fan run? What S_P will be developed? What BHP is required? 

1. CFM varies at RPM 

 (1230) x (1.20) = 1476 RPM 

 2. SP varies as (RPM)2 

 (1476/1230)2 x (8) = 11.52" SP 

3. BHP varies as (RPM)3 

 (1476/1230)3 x (61.0) = 105.4 BHP

 Use of the "fan law" is based on a fixed system and a non-modified fan. Adding or deleting system components such as dampers, or incurring density changes, will create completely new system curves. Changing fan accessories such as inlet boxes inlet dampers will alter the fan's performance curve fro standard. There variable must be considered before the fan laws can be applied.

You can also calculate the following calculation:

1. Fan Power Calculation

2. Raw Mix calculation

3. Ball Mill calculation