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I just noticed today that the curtains in my room behave weirdly when fan is switched on. Let me give a rough sketch of what happens before and after the fan is switched on. Below is the side-view.enter image description here

The window wall has four curtains and this is the case for the middle two curtains.

Before switching on the fan in the room, the curtain is nearly parallel to the window wall behind it. But when the fan is switched on it starts behaving weirdly and three things happen mostly, some times in order then without order:

  1. The curvature of the curtain becomes as in the fig. 2 that is a bulge in middle appears and the lower part kind of goes nearer.
  2. Sometimes the bulge gets sucked inwards with the lower part still being near.
  3. The entire curtain middle and lower both get swept away as shown in fig. 3

I thought that Bernoulli's equation would be able to explain this and below is the diagram for the application for the same.
enter image description here $$\mathrm{P_0 + 0 = P + \frac{1}2\rho v^2}$$This comes with the assumption that the velocity of air behind the curtains is 0. Now the outward pressure difference is: $$\mathrm{\triangle P = \frac{1}2\rho v^2}$$ but this can only explain the outer bulge and nothing else. Thus I have got two questions here;

Why does this happen?Also is it possible mathematically to find out the curvature of the curtain in fig.2?

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2 Answers 2

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The air currents in the room due to the ceiling fan cause pressure variations on both sides of the curtain. If instantaneously the curtain is very close to the wall with a "film" of air in between at rest, then the fast moving air on the fan-facing side creates a lower-pressure region in that side. The relatively higher-pressure air on the other side pushes the curtain toward the fan. This is broadly what is occurring: the higher pressure region pushes the lower pressure region.

Deducing the exact behavior of the curtain would require knowledge of a large number of variables, such as the exact pattern of airflow created by the fan, its speed, the ambient temperature and pressure, etc.

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I would imagine that as the fan is creating downwards movement of air in the middle of the room, there must also exist an upward movement of air along the walls (and the window). This updraft would move the curtain in fairly unpredictable way, but probably starting as you described in Fig. 2, by pushing the bottom end of the curtain towards the wall/window. Then probably some kind of oscilation would occur but, as Yejus has said above, a lot of factors would have to be taken into consideration - weight, elasticity, length of the curtain, speed of the updraft, etc. I have no idea how to put that into anything resembling an equation.

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