Geoff Edwards, the Business Development Director at Axair Fans UK Limited, explains the three basic fan laws when applied to warehouse ventilation studies.
What are The Affinity Fan Laws?
The Fan Laws are a group of useful equations for determining the effects of a change in:
They are most useful for determining the impact of extrapolating from a known fan performance to a desired performance.
So, in short, the basic fan laws are used to express the relationship between fan performance and power.
To start we will consider only the effect of a change in the speed of the fan on:
We will assume that the fan size and air density are to remain constant.
The first three derivations of the Fan Laws are predicated on a couple of assumptions:
The first law of fans is a useful tool when working out the volumetric flow rate supplied by a fan under speed control or conversely working out what the RPM would be to deliver a required volume of air, and hence what frequency to set a variable speed drive (VSD) to.
Volumetric flow rate (, m³/hr) varies directly proportional to the ratio of the rotational speed (U, r/min) of the impeller.
Eq 1.
Where:
Qv1 , m³/hr – Original volume of air
Qv2, m³/hr – New volume of air
U1, r/min – Original rpm
U2, r/min – New rpm
A Factory of 37500m3 space currently requires five air changes an hour to remove waste heat generated by industrial process machinery. Later additional machines are added to the factory and the required number of air changes per hour increases to 6.1 to maintain the desired maximum air temperature within the factory. The original air flow rate, V1 is 187500 m3/hr at a pressure loss of 185Pa due to ductwork, louvres and other system elements. 8 number 1000mm 4 pole long cased axial fans were used. From the manufacturer’s data sheet we know that to deliver this performance, the RPM (U1) of the fan is 1160 r/min. V2, calculated by multiplying the space by the new air change requirements, is simply 37500m3 x 6.1 which give a new requirement of 228750 m3/hr. So, what is the RPM of the fan required to be to deliver this flow rate increase?
By re-arranging the above formula (Eq. 1) we find that:
Substituting in the known parameters gives:
Therefore:
Now we need to determine if the calculated value for can be delivered by the fan. The first limitation to consider is the maximum RPM ( for the impeller. This can be found from the fan data sheet and in this case the value is 1470 r/min, so this is okay.
Secondly we now determine the VFD frequency to drive the motor at the provide 1415 r/ min.
This is a simple linear relationship and can be expressed by the following,
This second law describes the relationship between the pressure developed by the fan and its rotational speed. From this equation, we can see just how powerful the effect of increasing the rotational speed of the fan is on pressure development, double the speed and you quadruple the pressure development.
Pressure (P, Pa) varies as the square to the ratio of the rotational speed (U, u/min) of the impeller.
Eq. 2
Where:
P2, Pa
P1: Pressure 1, Pa
U1: U, u/min
U2: U, u/min
Example – Industrial Warehouse, a change in air pressure
Continuing with our first situation of the industrial process factory which has added machinery and now requires additional air flow to maintain working conditions what will the pressure development of the fans now be?
This derivation of the first of the Fan Laws is predicated on a couple of assumptions:
By using the above formula (Eq. 2) we find that:
Substituting in the known parameters gives:
Therefore:
Looking at the fan curve above it can be seen that the selection software has a good agreement with the calculation.
The third law provides the required power to deliver the performance change that the system designer is looking for. The cubic nature of this relationship between power and the rotational speed shows how even for small performance gains, large amounts of additional power are needed.
Power (P, kW) varies as the square to the ratio of the rotational speed (RPM, u/min) of the impeller.
Where:
P1: Power, kW2
P2: Power, kW1
U1: RPM 1, u/min
U2: RPM 2, u/min
Example – Industrial Warehouse, a change in power
If look at the situation of the expanding factory as we have done with the previous two examples we can see the effect of the additional air flow on the power consumption of the fan. From the original duty point, we know that the power consumption was 2.12kW at 18750m3/hr @ 40Pa. so what will the total additional power consumption be for all 20 fans?
By using the above formula, (Eq 3.) we find that:
By substituting in the known parameters gives:
Therefore:
From the data sheet again we can see a really good agreement with our calculation.
The total power increase is 18.1kW, for an airflow increase of a little over 22% the power needed has risen by over 80%.
In summary, fan laws are essentially about impellers and what happens to their characteristics when they undergo changes in rotational speed, air density, or are scaled in size. They also help with the understanding of ventilation systems and the relationship between volume air flow rate and system total pressure. Although there are many fan selection software solutions available in the marketplace, it is necessary for engineers to have at least a basic understanding of these basic fan laws to aid their overall awareness of how changes within ventilation systems can influence performance.
If you’re not sure and you’re in the market for industrial fans we’re happy to help you to calculate or further understand the three fan laws. Alternatively, if you’re looking for more educational resources for university and your own understanding, we encourage you to look for more examples online.