The performance of a fan is standardly expressed in terms of three affinity laws stated as under : AL-I The air delivery rate is proportional to its rotation speed and varies as the cube of its diameter. AL-II The total or static pressure is proportional to the square of the diameter, the square of the rotation speed and the density of the air. AL-III The total power is proportional to the cube of the rotation speed, the fifth power of the diameter, and is proportional to the density of air.

FAN LAWS The fan laws are a set of proportionalities relating each of the following parameters of airflow with fan speed (n), air density () and impeller diameter (d). o Air pressure (p) o Airflow quantity (Q) o Power developed (Ppow)

Through extensive experimentation and derivation the following direct proportionalities have been arrived. For varying speed but with constant air density and impeller diameter: - Quantity varies directly as the speed - Pressure varies as the square of the speed - Power varies as the cube of the speed - Efficiency is constant For varying density but with constant speed and impeller diameter: - Quantity remains constant - Pressure varies directly as the density - Power varies directly as the density - Efficiency is constant For varying impeller diameter but with constant speed and air density: - Quantity varies as the cube of the impeller diameter - Pressure varies as the square of the impeller diameter - Power varies as the fifth power of the impeller diameter - Efficiency is constant The above statements of fan laws can be presented in the form of table as given in Table 1. Table 1 Fan Laws Parameters Variable n Speed Variable Density Variable d Impeller Diameter

p n2 d2

Q n Independent d3

Ppow n3 d5

Thus, for two fans A and B, having the above mentioned parameters as (pA, QA, Ppow,A) with variables ( nA, A, dA) and (pB, QB, ppow,B) with variables ( nB, B, dB), the fan law equations can be written as follows:

The major function and utility of fan laws is to provide a prediction of performance of one fan when the performance of a similar fan is known to a reasonable level of accuracy.

The first three fan laws are the most useful and are stated as follows:1. The capacity is directly proportional to the fan speed.2. The pressure (static, total, or velocity) is proportional to the square of the fan speed.3. The power required is proportional to the cube of the fan speed.

Basics of fansFans are devices used to produce a gas flow. Centrifugal fan behaviour is characterized by theaffinity laws, which are:- flow is linearly proportional to the fan speed (if no counter-pressure)- pressure changes with square of the ratio of speeds- power demand (product of pressure and flow) changes with cubic of the ratio of speeds