With Bernoulli’s principle in mind (I think that’s the right one), is it more efficient to vent a room by putting a fan back from a window a bit, or right up next to it, and if so, is there a general sweet-spot as to how far back it should be?

Question

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.

In: 857

Answer 1

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