Fan Laws Explained for Real-World Fan Selection & Performance (2025 Guide)
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Understanding how the affinity fan laws affect airflow, pressure, and power consumption is essential when selecting the correct industrial fan for a live application. At Axair, we apply these laws daily to help engineers size and select compliant, efficient fans for industrial, process and ATEX-rated environments.
What are The Affinity Fan Laws?
The Fan Laws describe how key performance parameters, air volume, pressure, and power consumption, change in relation to fan speed and, in certain cases, impeller diameter.
The fan laws are approximations, but in fan selection they offer a highly reliable method for predicting behaviour within normal operating ranges.
Engineers use these fan laws to predict performance changes when:
- Adjusting speed using a VSD (variable speed drive)
- Estimating the effect of system resistance changes
- Comparing similar fans of different sizes
- Assessing energy impact when modifying a ventilation system
It’s important to note that the affinity fan laws are an approximation but do have a greater degree of accuracy when applied to fan selections.
To start we will consider only the effect of a change in the speed of the fan on:
- Volume flow rate/volume of air
- Pressure
- Power consumption
Assumptions Used in These Examples:
To simplify these examples, we assume:
- Air density remains constant
- Fan diameter does not change
- The impeller remains within its safe design speed (typically ≤ 3600 RPM for standard industrial applications
These assumptions ensure the laws apply accurately to most real-world fan selections.
1. The First Fan Law: Air Volume (Flow Rate)
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 therefore, what frequency to set a variable speed drive (VSD) to.
The first law states:
Air volume (m³/hr) varies directly with fan speed (RPM).
If fan speed increases by 10%, airflow increases by 10%.
This is typically used when:
Increasing airflow requirements
Adjusting ventilation rates
Setting a VSD to achieve a target duty point
Where:
Vol1 , m³/hr = Original volume of air
Vol2, m³/hr = New volume of air
RPM1, r/min = Original speed (rpm)
RPM2, r/min = New speed (rpm)
Example: Industrial Warehouse - Increasing Airflow
Problem: A factory of 37,500 m³ requires an increase from 5 to 6.1 air changes per hour due to additional machinery.
Applying the Law: Calculating a change in air volume required, so what speed do we need to run the fan at to achieve more air?
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 to achieve this, at a pressure loss of 185Pa due to ductwork, louvres and other system elements.
20 number 630mm 6 pole short 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 865 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?
Simplifying the data in the above case study:
Original airflow:
Vol₁ = 187,500 m³/hr
Achieved using twenty 630mm axial fans at 865 RPM
New airflow needed:
Vol₂ = 37,500 × 6.1 = 228,750 m³/hr
By re-arranging the above formula like you did in high school maths. (Eq. 1) we find that:
Therefore:
New RPM speed
Result:
New speed required ≈ 1055 RPM
Within safe design limits (max 1470 RPM).
Now we need to determine if the calculated value 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 against our new speed value of 1055.3.
| Curve | qV [m³/h] | pfs [Pa] | Pe [kW] | Po [kW] | nN [r/min] | LWA D,IN [dB(A)] |
| Max. U/min | 236048 | 294 | 44.07 | 39.84 | 1460 | 107 |
| 1470 U/min | 237665 | 298 | 44.98 | 40.66 | 1470 | 107 |
| 1460 U/min | 236048 | 294 | 44.07 | 39.84 | 1460 | 107 |
| 1300 U/min | 210180 | 233 | 31.11 | 28.12 | 1300 | 105 |
| 1000 U/min | 1616677 | 138 | 14.16 | 12.8 | 1000 | 99 |
| 800 U/min | 129341 | 89 | 7.25 | 6.554 | 800 | 94 |
| 600 U/min | 97006 | 50 | 3.058 | 2.764 | 600 | 88 |
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The Second Fan Law: Pressure
This second of the fan laws 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. Therefore if the propeller speed is increased by 10%, the total static pressure will increase by 21%.
Eq. 2
Where:
P2: Pressure 2, Pa
P1: Pressure 1, Pa
Speed RPM1: RPM 1, u/min
Speed RPM2: RPM 2, u/min
Example: Industrial Warehouse
How much additional pressure do we need to achieve?
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:
Old speed = 865
New speed was = 1055.3
Pressure loss = 40Pa
By using the above formula (Eq. 2) we find that:
Substituting in the known parameters gives:
Therefore:
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The Third Fan Law: Power
The third fan law provides the required power needed to achieve a change in fan performance. This law reflects the cubic relationship between power and rotational speed, meaning that even small increases in speed demand significantly more power. Specifically, power (P, kW) varies with the cube of the ratio of the rotational speeds (RPM) of the impeller.
For example, if the impeller speed increases by 10%, the power required to drive the fan increases by approximately 33%.
Where:
P1: Original Power (kW)
P2: New Power (kW)
RPM 1: Original Rotational Speed (u/min)
RPM 2: New Rotational Speed (u/min)
Example: Industrial Warehouse, A Change in Power
Let’s consider an expanding factory scenario. As seen in previous examples, we analyse the impact of increased airflow on fan power consumption.
At the original duty point, each fan consumed 2.12 kW at 18,750 m³/hr @ 40 Pa. With an increase in required airflow, the fan speed is raised.
Given:
- Original RPM = 865
- New RPM = 1055.3
- Original Power = 2.12 kW
Using the third fan law:
With 20 fans, the total additional power consumption is:
So, the total power increase is 34.6 kW, corresponding to an airflow increase of just over 22%.
This results in a power increase of more than 80%, even though the airflow only increased by around 22%, highlighting the steep energy cost of higher speeds due to the cubic relationship.
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