Air flow: pressure increase over a constriction and fan

[Imolopa]

Homework Statement

So a fan sucks air through a pipe, and the outlet is near the fan, and thus the inlet where the air starts to travel is furthest away.

If the diameter is constant the speed would be constant due to the continuity equation, and I assume we neglect compression effects in ambient temperature within a building (assuming the air sucked in is from the inside air). So that means if the velocity is constant due to energy equation the pressure must decrease if we assume the height difference is zero.

Now by the Bernoulli equation and combined with the idea that the diameter of the pipe right before and after, and everywhere else is the same, so that the speed has to be the same (if incompressibility applies). Which from Bernoulli returns us a higher pressure right after the fan, because the speed can't increase (continuity equation and incompressibility). But the fan itself occupies area, all the blades that turn, so speed increases at the fan itself (continuity equation). But maybe at the location of the fan the area increases because the fan is bigger than the pipe, so then pressure would have to increase due to lower speed right where the fan is (Bernoulli) and the return to same old speed when area gets the same as for the pipe before the fan.

Now let's say that there is an adjustable outlet, which means that a door can be adjusted vertically to adjust air flow out behind the fan. And assuming the fan runs at constant speed. Now the more closed this door is the more pressure the fan would have to work against, thus you would achieve a max increase of pressure over the fan for the lowest volumetric flows (the door is more closed) because the fan has to "work harder" to keep blowing/turning at the same speed, while at the highest volumetric flows like when the door is more open or completely open the pressure increase over the fan would be minimal because the fan has to face least resistance when pushing the air.

If we add a constriction (1 mm thick) to the middle of this pipe, where the constriction has lower diameter than the pipe on both sides. Now the pressure actually increases at the constriction itself and is higher after the constriction than before (this especially notable when the above mentioned door is allowing higher volumetric flows). Now my Bernoulli argument does not hold here, because pressure would decrease due to higher speed through the constriction according to this energy equation. So I guess compressibility plays a role here.

Homework Equations

Bernoulli and continuity equations

The Attempt at a Solution

My gut feeling contradicts the following given data/results: Why exactly is the pressure higher going through the constriction and after, and this increase of pressure seems to go up with increasing airflow. And it seems like the pressure increase over the fan is at it's biggest when the door is fully open.

How to intuitively think of this situation, what is actually happening?

My beliefs that contradict the results:
I would believe that the pressure goes up when the fan blows at the same speed towards a more closed door. Also over the constriction I'd guess there would be a pressure drop which would increase with increasing volumetric flow. In addition I wouldn't believe that the pressure stays very high after the constriction, but rather reset to a more or less equal state (at the least lower pressure due to energy loss) than prior to the constriction.

 

[nilesh_pat]

I'm guessing the pressure is higher at the constriction and afterwards because of the compression of the air molecules at the area of constriction, but I don't get the fact that the pressure increases with increasing volumetric flow.