# Pressure generated by a fan

Is there any equation for pressure generated by a fan, specifically a centrifugal blower.

Pressure = 1/2*rho*v^2
where
rho = air density (kg/m3)
v = tip velocity of fan impeller (m/s)
Pressure = pascals

I haven't found additional info on this anywhere else and was looking to confirm if this the correct way of theoretically calculating the pressure.

russ_watters
Mentor
Welcome to PF!

No, there is no single/simple equation -- it is different and highly customized for different types of fans. You must acquire the fan performace data/curve.

Also, in Bernoulli's equation, V is airflow velocity, not fan tip speed.

Welcome to PF!

No, there is no single/simple equation -- it is different and highly customized for different types of fans. You must acquire the fan performace data/curve.

Also, in Bernoulli's equation, V is airflow velocity, not fan tip speed.

Thanks for the welcome Russ.
Does Bernoulli's equation provide a possibly correct way to calculate the pressure generated by a fan?
I'm OK if its a quick way to get a rough estimate of the pressure.

The author I quoted in my post actually wrote the following in his post
Now, the pressure you get from such a blower is limited by the maximum speed of the blade tip, and that in turn is limited by centrifugal forces

I wonder what the relation is for air flow velocity versus the tip speed of the impeller?

russ_watters
Mentor
Does Bernoulli's equation provide a possibly correct way to calculate the pressure generated by a fan?
Sorry, no, pressure and velocity output by a fan are mostly independent of each other. Again: you need the actual fan performance table/curve.....also, I should have said you need the details of the system the fan is blowing through.
I wonder what the relation is for air flow velocity versus the tip speed of the impeller?
None whatsoever. The author of that article does not know what he's talking about.

If you describe in (significantly) more detail what exactly you are trying to accomplish, I may be able to be of more help.

rcgldr
Homework Helper
Eventually the pressure returns to ambient, so it depends on where you measure the pressure. As the pressure decreases to ambient, the speed of the air increases, but this is complicated by the stream from the fan interacting with the surrounding air due to viscosity.

If the fan was similar to a propeller, then the equations in theses NASA articles could be used, although they are idealized.

http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

http://www.grc.nasa.gov/WWW/K-12/airplane/propth.html

http://www.grc.nasa.gov/WWW/K-12/airplane/thrsteq.html

If you describe in (significantly) more detail what exactly you are trying to accomplish, I may be able to be of more help.
I recently purchase a cooling fan for my PC cabinet and there was lot a hype about the static pressure of the fan, basically I found that there were 2 kinds of fans
1. high flow
2. high static pressure.
The fan that finally came to me was an axial fan with a static pressure of about a few mm of H2O.

On further searches on the web I found the centrifugals are better than axials in creating creating greater pressure. So I though If I need higher pressure how do I go about calculating it. Is there any guide of fan blade shap and some definitive calculations for fan pressure.

rcgldr
Homework Helper
What matters is the flow rate through the PC cabinet. Since the ports on a PC cabinet are fixed, the flow rate is related to the pressure. I'm not sure what a high static pressure specification means. The term static thrust refers to the force a fan generates when the fan is not moving (linearly) with respect to the unaffected air, but the fans for a PC cabinet have the flow restricted by the ports on the cabinet, but most or all of those ports will have fans to draw air in or out of the cabinet.

In my case (bad pun?), I found that my desktop ended up quieter when I removed the sides of the cabinet since the internal fans, like the cpu and video card fan, run at a much lower speed with an open case.

escape_velocity
What matters is the flow rate through the PC cabinet
Then how the static pressure rating of the fan come into play. I mean why do pc fan manufacturers now a days advertise this rating?

rcgldr
Homework Helper
russ_watters
Mentor
It's explained at Tom's Hardware. The static pressure fans are good when the flow is very restricted, but a PC cabinet would not be very restrictive, so a high flow fan should be better.

http://www.tomshardware.com/faq/id-2080096/high-airflow-high-static-pressure-fans-air-cooling.html
Agreed. A large, slow spining axial fan will produce a high flow and low static pressure (and low noise), which is it typically best for a PC case fan.

Contrast that with a video card fan: The video card has a small area/volume and a heat sink that covers the entire thing, so the fan needs to be small, yet able to push a large volume of air through a tight restriction. So video card fans are often centrifugal. Also, of course, the centrifugal fan throws the air parallel to the direction of its spin instead of perpendicular like an axial fan.

escape_velocity
It's explained at Tom's Hardware. The static pressure fans are good when the flow is very restricted, but a PC cabinet would not be very restrictive, so a high flow fan should be better.

http://www.tomshardware.com/faq/id-2080096/high-airflow-high-static-pressure-fans-air-cooling.html

Agreed!

Agreed. A large, slow spining axial fan will produce a high flow and low static pressure (and low noise), which is it typically best for a PC case fan.

Contrast that with a video card fan: The video card has a small area/volume and a heat sink that covers the entire thing, so the fan needs to be small, yet able to push a large volume of air through a tight restriction. So video card fans are often centrifugal. Also, of course, the centrifugal fan throws the air parallel to the direction of its spin instead of perpendicular like an axial fan.

Agreed!

No, there is no single/simple equation -- it is different and highly customized for different types of fans. You must acquire the fan performace data/curve.
Now since we don't have a fan performance data/curve as there is no fan to start with. Is there any calculation to start off with?

russ_watters
Mentor
Now since we don't have a fan performance data/curve as there is no fan to start with. Is there any calculation to start off with?
Yes, the way this is done by HVAC engineers is they determine their flow requirement first based on the cooling needs, then calculate the pressure loss for that flow rate based on ducting and other system effects, then select a fan that has a performance curve that intersects with the desired performance. Its not always simple to do, but we can help you through it if you want to try that.

rcgldr
Homework Helper
You could measure the static pressure by ducting the fan output into a sealed container, then measure the pressure inside the container.

russ_watters
Mentor
You could measure the static pressure by ducting the fan output into a sealed container, then measure the pressure inside the container.
Well,
1. There is no fan yet.
2. It sounds like you are suggesting a dead-head (no flow) test. That doesn't provide useful information here because the dead head pressure is not all all related to the operating pressure.

rcgldr
Homework Helper
You could measure the static pressure by ducting the fan output into a sealed container, then measure the pressure inside the container.

2. It sounds like you are suggesting a dead-head (no flow) test.
I'm thinking that is the way the fans are tested when producing the specifications. I see specifications for pressure values ranging from 1.15 mm to 1.5 mm H2O (water) for these type of fans, without a corresponding flow rate.

Last edited:
russ_watters
Mentor
I'm thinking that is the way the fans are tested when producing the specifications. I see specifications for pressure values ranging from 1.15 mm to 1.5 mm H2O (water) for these type of fans, without a corresponding flow rate.
Perhaps, but the dead-head is not necessarily the highest pressure a fan can produce. And even if it is, it is a totally useless piece of information. It's marketing, not engineering. In engineering, you need the whole curve, not just that one point.

rcgldr
Homework Helper
rcgldr said:
ducting the fan output into a sealed container ... the way the fans are tested when producing the specifications.

Perhaps, but the dead-head is not necessarily the highest pressure a fan can produce. And even if it is, it is a totally useless piece of information. It's marketing, not engineering.
I think the key point here is that it's marketing. I found an article:

Maximum Static Pressure is measured with the fan running in chamber A with the (output chamber) nozzle shut.

http://www.sunon.com/uFiles/file/03_products/07-Technology/003.pdf

This may not be the peak pressure possible, but it's how it's defined.

More observations: Most fans mounted on CPU heat sinks are conventional fans due to space issues, perhaps with more blades and/or longer chord blades since diameter is limited. The fans on most video cards enclosed in their own case are centrifugal, and there is a flow path through the card and an exhaust port on the PC case connector (to vent outside the PC case), and I wonder just how much pressure there is in the video card case. As mentioned before, I took the sides off my case, so both the cpu and video card fans are running at low speeds on my system (and the net result is that it's quieter than with the sides on).