Fan Laws

The relationships of discharge Q , head H and Power P with the diameter D and rotational speed N of a centrifugal fan can easily be expressed from the dimensionless performance parameters determined from the principle of similarity of rotodynamic machines as described before . These relationships are known as Fan Laws described as follows

	(40.1)

	(40.2)

	(40.3)

where and are constants.

For the same fan, the dimensions get fixed and the laws are

and

For the different size and other conditions remaining same, the laws are

and	(40.4)

These relationships are known as the Fan-laws. The Fan-lows can be summarized as

For the same fan:

Discharge Speed
Head developed (Speed)2
Power (Speed) 3

For the fans of different sizes:

Discharge (Diameter)3
Head developed (Diameter)2
Power (Diameter)5

Performance of Fans

For all three cases (backward, radial and forward swept blades) in Figure 39.3, we can write

	(40.5)

The work done is given by Euler's equation (refer to Modue-1) as

	(40.6)

Noting that (zero whirl at the entry) we can write

or,		(40.7)

The volume flow rate (assuming no density change between the inlet and outlet)

Thus

By substitution in (40.7)

	(40.8)