Fans of the same basic design and proportions operate theoretically in accordance with certain fan laws. In practise, these laws do not apply exactly because of design considerations and manufacturing tolerances, but they are useful in estimating approximate outputs of similar fans of different diameters and speeds as applied to normal ventilation work, and can be summarised as follows:

It is important to note, however, that these Laws apply to the same point of operation on the fan characteristic. They cannot be used to predict other points on the fan's curve.

These laws are most often used to calculate change in flow rate, pressure, and power of a fan when the size, rotational speed or gas density is changed. Therefore, in the following Laws the suffice "I" has been used for initial known values and the suffice "2" for the changed values and the resulting calculated value when:

Q = volume flow rate
P = pressure (total, static or dynamic)
p = gas density
n = fan rotational speed
D = impeller diameter
W = impeller power

1.	VOLUME of air flow varies as the (fan diameter)³ and as the rpm or: New Volume = Old Volume × ( new impeller diameter ) ³   × ( new rpm )     old impeller diameter   old rpm   or: Q2 = Q  × ( D2 ) ³   × ( n2 )       D1   n1
2.	PRESSURE developed varies as the (fan diameter)² and as the (rpm)² or: New Pressure = Old Pressure × ( new impeller diameter ) ²   × ( new rpm )     old impeller diameter   old rpm   or: P2 = P1  × ( D2 ) ²   × ( n2 ) ²     D1   n1
3.	POWER ABSORBED by the fan varies (fan diameter)5 and as (rpm)³ or: New Power = Old Power × ( new fan diameter ) 5   × ( new rpm³ )     old fan diameter   old rpm   or: W2 = W1  × ( D2 ) 5   × ( n2 ) ³     D1   n1 Pressure and power calculation should also take gas density into account. (new pressure) or p2 (old pressure)    p1

But if this or any other variable is unchanged they can be omitted from the equation: for example if the fan diameter is constant, only speed variation applies:

or Q2 = Q1 ×	(	n2	)
		n1

P2 = P1 ×	(	n2	)²
		n1

W2 = W1 ×	(	n2	)³
		n1

A simple example of the application of the fan law dealing with volume can be shown using Vent-Axia data. (TX Window model).

FAN LAW VOLUME varies as (fan diameter)³ and as rpm e.g., A 300mm Ø fan running at 1190 rpm delivers 1415m³/h. What will 190mm Ø fan running at 1290 rpm deliver?

1. VOLUME of air flow varies as the (fan diameter)³ and as the rpm

or:	New Volume = Old Volume ×							(	new impeller diameter	)	³   ×	(	new rpm	)
									old impeller diameter				old rpm
or:	Q2 = Q  ×	(	D2	)	³   ×	(	n2	)
			D1				n1
or:	1415	(	190mm	)	³   ×	(	1290	) = Q2
			300mm				1190
or:	1415		6859000		×		1290	= Q2
			27000000				1190
1415 × 0.254 × 1.084 = 389 (Published Figure 395)

This slight variation from our quoted output for the size is negligible from the practical point of view and will be due to small differences in the similarity of the two units being compared, and to the "rounding off" of test figures.

System Resistance Laws

The resistance of a ventilating system is caused by:

a	the loss of energy at the point of entry of the air due to a sudden increase in air velocity from practically zero to the velocity along the duct.
b	the friction between the air and the side surface of the duct.
c	changes of cross-sectional area of the duct, where there are expansions and contractions, or changes of shape (say from square to oblong section). Expansions, contractions and changes of size or shape should be made by gradual taper sections, not abruptly, ideally 15° included in angle.
d	changes of direction, such as bends and Tee-junctions are large wasters of energy. Changes of direction should be by easy bends and well-rounded corners, not by sharp elbows, unless fitted with guide vanes.

The loss of pressure due to all of these sources, known as the system resistance, is for practical purposes proportional to the square of the velocity at the point of loss. Therefore, for a fixed system, it may be said that the pressure required to pass a given volume of air through the system will vary as the (volume flow rate)² i.e. P °C Q².

Therefore, if it is required to double the air flow through a system, the fan must be capable of providing twice the volume flow rate at four times the original pressure! AND EIGHT TIMES THE FAN MOTOR POWER!

If a specified duty requirement does not exactly match the available fan performance, it is advisable to superimpose a system resistance curve onto the fan performance curve to confirm the final anticipated duty. Data points for plotting the system resistance curve may be derived from the following formula:

P₁, Q₁ = Specified system pressure and volume flow.
P₂, Q₂ = New values of pressure and volume flow to be plotted.

(Simply choose a new value for Q₂ and calculate the corresponding new value for P₂. Repeat the procedure until there are enough points to plot the curve - three will usually suffice).

Square Law

Resistance Varies as the Square of the Velocity    P °C Q²

As velocity varies directly as volume, we can say that Resistance varies as the square of the volume. The equation then becomes: