For context, this would be to vent a basement bathroom with a a window in an old house, and I can’t install a bathroom vent.
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Some Youtuber did a video testing this with wind speed meters a while ago and the conclusion was to put the fan a few feet from the window pointing straight at the window at an appropriate height. Iirc the exact distance was 3,5 feet / 106cm but hat of course will vary depending on the model of fan and the size of your window.
Edited for some typos.
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Definitely a little way away. The air flowing out will create a low pressure region sucking additional air from the room and magnifying the effect. You may want to play with the distance based on the size and output of the fan
Using Bernoulli’s principal alone probably won’t be sufficient for an open air environment with so much chaos (in my opinion), so may only give an idea of what to do that then needs fine tuning.
The actual maths of Bernoulli’s principal is basically just energy conservation in a given volume of fluid (air).
Separate to this, we have a basic fluid dynamics model (how air moves) to combine with this principal that says a given stream of air will never cross another stream of air, or in other words, all the different paths of air sort of smoothly move around eachother.
A fan takes air in from one side, then speeds it up. On each side of the fan, however, notice that an equal amount of air must enter it from the back as what comes out the front every second.
If we say a cylinder of fast air is coming out the front, but the air from the back of the fan is slow moving, that means it must be sucking in a wider cone (than the front cylinder) of slow moving air every second.
The only thing this has to do with Bernoulli’s principal is that we can use it to describe the pressure and speed of these cones/cylinders of air, but it’s important to know it will give a very incomplete model. It doesn’t account for drag, turbulence, 3D effects, or anything like that.
To actually answer your question, despite not mentioning Bernoulli’s principal: it depends. An easy solution is to place it against the window, as none of the accelerated air will remain in the room. However, if you wish to remove moisture, perhaps having more internal circulation in the room could be beneficial, so having some of the fast moving cylinder of air be inside could be useful. It’s possible that a weak fan would not pull in air from one side of the room purely through its (slow moving) back-end suction, but using the higher velocity frontal air may help dissipate lingering air, and move it closer to the window/fan’s suction zone faster
It’s a few feet away from the widow, at window height, and pointed out toward the window, perhaps sitting on a stool or table. This creates a current that forces more air out (the damp, musty, stinky, or hot air you’re trying to dispose of). The air will be replaced by new air, either from the rest of the house or from another nearby open window.
There might be reasons not to do things the “optimal” way, though. Powerful fans might blow over and placing them directly in the window allows you to pin it in place with the weight of the window at a cost of a little efficiency. A fallen fan is doing nothing for you, after all.
Putting it directly in the window can help keep out pests, too. You’re not going to be happy to have eliminated the bad air only to have replaced it with a invasion of gnats.
Finally, the reason for venting matters. If you’re, say, trying to fill the room with cold night air, you might want to put fans in windows to pull in the air while vent windows are open to let the hot air out. Doing it the other way could pull more hot air into the room from the rest of the house at the same rate it’s pulling in cool air, which won’t cool the room very efficiently.
Keep it back a bit. This is why:
In short:
Having the fan directly at the window expels the amount of air the fan moves, at the speed the fan moves it. This amount times this speed gives you x volume pr unit of time.
Having the fan back a bit, expels the air the fan moves PLUS a significant amount of air around it (since air is “sticky” – look up “laminar flow vs turbulent flow over aircraft wings” for instance). This reduces the speed of which the air os beeing ejected, but not by as large a factor as the volume being moved is increased. As such, this y volume pr unit time is significantly higher than in the first case, all other things being equal.
I don’t have an answer, but just wanted to say thanks for the great question, I searched “bernoulli” for this exact same reason
Open a door or window.
Put a fan outside of this opening, facing the opening. 3-4 feet back.
Open a window on the opposite side of the area you’re trying to ventilate.
You will be introducing positive pressure into the area and ventilating it through the opening on the back side.
This is the most common way fire fighters ventilate structures to clear them of heat/smoke quickly.
I would guess it would depend on the size of the window. If you remember the concept of vena contracta for orifices you will have something like that (not the same) with the flow field behind the fan. Ideally you’d match that area with the window. So the bigger the window the further away until it stops increasing the flow.
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