understanding correlation between fan air pressure and air flow

[m4rtin]

..and is it correct to think that high air-flow fan creates a narrow channalized air-flow because of its fan-blades design and thus it has lower pressure? And high-pressure fan "pumps" air into wider area and thus creates a higher pressure?

No, that's not it.

The power of a fan can be measured as pressure rise times air flow (just as electrical power can be measured as voltage times current flow).

If a fan motor has a given power rating, then it can either move more air through a lower pressure rise, or less air through a higher pressure rise, so that the product remains about the same. The shape of the fan blades can be designed to optimize for one case or the other.

Ok, thanks! I didn't know that Bernoullis principle works only in case the flow is constrained by the walls.
When a fan has higher pressure and slower air-flow, then how do air molecules move differently than in case the fan has lower pressure and faster air-flow?

[IanB]

When a fan has higher pressure and slower air-flow, then how do air molecules move differently than in case the fan has lower pressure and faster air-flow?

Fan designers use computer simulation software that models the exact flow of air through the fan (a bit like a circuit simulator, but modeling fluid flow instead of electricity).

If you want to know what the equations look like, see here: https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations

These equations, together with a description of the shape and movement of the fan blades, allow the precise performance of a fan to be predicted. All you have to do is solve the equations and you can tell how the air molecules move. Simple! 

I don't design fans, so I can't tell you more than that. The simple answer is it depends on the shape, size and geometry of the fan. If you examine a fan carefully, you will see that the blades have a complex curved shape. They are not simply flat rectangles.

[Mechatrommer]

Ditto.. bernoulli's and aerofoil's myth are only for kindergarden storytelling.. if u are serious about this, go for navier stoke equation. Its not a one answer solution, i'm guessing its like maxwell's equation... trying to understand air pressure and flow is like trying to understand the shape and strength of a magnetic field around a working cicuit on a pcb..

[Mechatrommer]

Let alone the linear and angular forces that act on every tiny segments of a blade for high efficiency blade design that only can be simulated through FEA.

[m4rtin]

IanB and Mechatrommer, thank you for your answers!  However, it is counterintuitive to imagine that air molecules with higher speed have smaller penetration(for example, penetration to radiator with thin fin gaps) ability than the ones with lower speed.. Or is it once again because of complexity of air flow dynamics and indeed the air flow with slower speed has for some (weird) reason better penetration abilities?

[f5r5e5d]

yes there are better sites for fluid mechanics - the airfoil/lift relations are popular: http://www.av8n.com/how/htm/airfoils.html#sec-airfoils for some good physics

3.16  Consistent (Not Cumulative) Laws of Physics

We have seen that several physical principles are involved in producing lift. Each of the following statements is correct as far as it goes:
• The wing produces lift “because” it is flying at an angle of attack.
•The wing produces lift “because” of circulation.
•The wing produces lift “because” of Bernoulli’s principle.
•The wing produces lift “because” of Newton’s law of action and reaction.

We now examine the relationship between these physical principles. Do we get a little bit of lift because of Bernoulli, and a little bit more because of Newton? No, the laws of physics are not cumulative in this way.

There is only one lift-producing process. Each of the explanations itemized above concentrates on a different aspect of this one process. The wing produces circulation in proportion to its angle of attack (and its airspeed). This circulation means the air above the wing is moving faster. This in turn produces low pressure in accordance with Bernoulli’s principle. The low pressure pulls up on the wing and pulls down on the air in accordance with all of Newton’s laws.

See section 19.2 for additional discussion of how Newton’s laws apply to the airplane and to the air.

[Mechatrommer]

• The wing produces lift “because” it is flying at an angle of attack.

99% true

•The wing produces lift “because” of Bernoulli’s principle.

99% myth...

https://www.grc.nasa.gov/www/k-12/airplane/wrong1.html
http://warp.povusers.org/grrr/airfoilmyth.html

99% of lift is generated by the net drag or friction forces acting on the blade/wing surface... and the proper angle of attack is one important role in this case...

However, it is counterintuitive to imagine that air molecules with higher speed have smaller penetration(for example, penetration to radiator with thin fin gaps) ability than the ones with lower speed.. Or is it once again because of complexity of air flow dynamics and indeed the air flow with slower speed has for some (weird) reason better penetration abilities?

you need to get the imagination right... and this can be quite complicated... first, air is a compressible fluid, not like water or electrons that are assumed to be incompressible, ie changes at one point will result on changes on another point instantaneously, air is not like that. kinetics from adjacent air molecules will create drag or suction effect, thats what you see as "low pressure" effect. penetration is not proportional to spatial pressure but more to kinetics energy, you move faster, you penetrate, you stay still nothing happened, only pressure... in ee we have skin effect, in fluid mechanics we have exactly that. air adjacent to aluminum fin are stand still, the farther they are from the surface the faster they go pushed by adjacent molecules, they form parabolic shape in term of speed.... to summarize.... its complicated...

[Mechatrommer]

if you want the poorman's way... you can blindly design a fan, put the outgoing air into a enclosed box with pressure sensor in it, you read the pressure and write it down in your spec. to get the airflow speed spec, you put the outgoing air in an open tunnel with flow meter in it, voila! if you are not happy with the spec, redesign the fan and redo until satisfactory...

[f5r5e5d]

argue with Denker http://www.av8n.com/how/htm/author.html - after reading his really excellent site

[suicidaleggroll]

When a fan has higher pressure and slower air-flow, then how do air molecules move differently than in case the fan has lower pressure and faster air-flow?

Once again...the fan does not control the relationship between pressure and air flow, the heatsink does.  The fan specs just [indirectly] tell you the heatsink density that fan has been optimized for.

Think of the fan like a 10W power supply.  You have unit A rated at 1V and 10A, and unit B rated at 10V and 1A.  Sure they're both "10W" supplies, but they're designed for very different loads.  If you stick a 10 ohm load on unit A, you won't get anywhere near the rated 10W, and similarly of you stick a 0.1 ohm load on unit B you won't either.  Just replace current with air speed and voltage with pressure, and it's basically the same as these "high pressure" and "high flow" fans.