# The fan laws

It is usual for a particular type of fan to be made as a set of different sizes, all exhibiting dynamical similarity because it is not a practical proposition to test every single fan made.

Their performances are then related by what are termed the fan laws, which are good enough for all practical purposes, even if not exact. The amount of testing that must be done by a manufacturer is then much reduced.

The laws apply to a given point of rating on the pressure-volume characteristic of the fan and those of most use in air conditioning are as follows:

A. For a given fan size, duct system and air density

1 The volume handled varies directly as the fan speed.

2 The pressure developed varies as the square of the fan speed.

3 The power absorbed varies as the cube of the fan speed.

4 The total efficiency is constant.

The duct system has a pressure loss depending on the square of the volume handled (see equation (15.39)); thus it follows that the first two laws correspond to the law for the system. The consequence of this is that the fan will always operate at the same point of rating, for a particular system, and that this point will move up or down the system curve as the fan speed is changed. We see this in Figure 15.19.

The third law is a consequence of the first two, in accordance with equations (15.19) and (15.20). Hence the fan efficiency must be constant.

B. For a given fan size, duct system and speed

1 The volume handled remains constant.

2 The fan total pressure, fan static pressure and the velocity pressure at fan discharge vary directly as the density.

3 The fan power absorbed varies directly as the density.

4 The total efficiency is constant.

EXAMPLE 15.10

(a) If the case of Example 15.9 is for operation at 0°C and 101.325 kPa barometric pressure with a total efficiency of 84 per cent determine the absorbed fan power.

(b) Determine the air quantity handled, the fan total pressure and the absorbed fan power if the temperature is 35°C and the barometric pressure is 85 kPa.

(a) By equations (15.19) and (15.20) we have

 = 1.527 kW Fan power = 2.11 x 0.463

0.84

(.b) The air quantity handled is unchanged at 2.77 m3 s“1 because the speed is unchanged, in accordance with law Bl.

Using law B2 we have Fan total pressure = 463 x

Hence, since the fan total efficiency is unchanged because the point of rating is not altered, we have, by equations (15.19) and (15.20):

< 2.77 x 0.344 — j i*2 4

Fan power =——————— = 1.134 kw

Alternatively, using law B3, we could have calculated

Fan power = 1.527 x ^73 + 35) X ToB25 = U35 kW

EXAMPLE15.il

For the conditions of example 15.9, at what speed must the fan run to deliver 3 m3 s“1? Answer

The first fan law in group A applies and hence the new speed, n2, is given by

N2 = 1144 x 3.0/2.77 = 1239 rev min-1 = 20.6 rev s_1

The fan curve representing this speed is that shown in Figure 15.19, intersecting the system curve at the point P2. Note that P2 is the same point of rating on the fan curve but shifted up the system curve from position Pb by the speed increase.

Posted in Engineering Fifth Edition