### Question

If Bernoulli's equation is true, then wouldn't the passengers in a car die of suffocation (because of the lower pressure system outside of the car creating a vacuum inside the car) if they had their windows down while driving?

Well, I think a major problem in your reasoning here is that you are neglecting the proportionality this effect has to velocity, and you're also overlooking what would happen to the 'high' pressure inside the car as it is evacuated (think about equilibrium).

However, before talking about that, it probably is useful to mention that those windows should only be rolled down an inch or less. If they are rolled down too far, you will get too much flow separation, and the 'lift' that you are expecting (think about smooth laminar flow -- layered flow lines that go from one point to another without swirling in between) would not occur. By only cracking the window, the streamlines can continue across the entire car and 'rejoin' at the back of the car. When this occurs, you do experience a lower pressure outside of the car, and if you place a piece of paper by the crack in the window, that paper might be sucked (or blown, that is) out the window.

However, there are a number of things which will prevent the car from becoming a vacuum. One in particular has to do with the vents. When you crack the window of a car, you may notice that the air through the vents starts to increase. This is because as the pressure differential across the crack in the window causes much of the pressure inside the car to be converted to faster low pressure air escaping from the car, this causes a pressure differential across the vents which brings air in through the vents to substitute for the air which is being evacuated.

However, if the vents were completely shut, the car would still not be entirely evacuated of its air.

As that air rushes outside of the car, the pressure does start to decrease inside the car. Pressure is nothing but another form of potential energy, and when there is a pressure difference (just like when there is a gravitational difference (height) or an electric potential difference (voltage)), the higher pressure body will convert that excess pressure into kinetic energy which will result in air being moved from inside the car to outside the car to try to balance things out. As this occurs, the amount of moles of air inside the car decreases which will end up decreasing the car's internal pressure.

What I'm trying to show here is that there is a point where the pressure inside the car will become so low that even the fast moving air outside of it will not be at a lower pressure. There is a transient time when these two may be different, but they will quickly come to equilibrium. If the car starts to increase in speed or decrease in speed, there will again be a transient time when there is a difference maintained, but, again, this will quickly come to equilibrium.

When air escapes from a balloon, you see this sort of equilibrium dance. The high speed air causes the air coming out of the balloon look like much lower pressure. The outside pressure clamps up on the balloon, causing no air to escape -- this lowers the velocity of that air, brings it up to a higher pressure, and causes it to force the mouth open again . . . and the mouth starts opening and shutting back and forth until there is no high pressure air left inside the balloon. As the car travels, air does rush out, but if there are absolutely no vents, the inside air comes back to a point where it is at an equal or LESSER pressure than the outside air. However, most cars have vents, which allow for a constant stream of air to move outside the car (provided no flow separation due to windows being completely open).

To help explain what I mean by flow separation . . . Imagine an airplane wing with a bunch of holes in it -- like swiss cheese -- or made out of a big wire mesh. Would it surprise you that this wing had no lift?

If you're simply not convinced that Bernoulli's equation is true, there are a number of other good examples. Let's take that same balloon from before, but fill it with water. Now squeeze the water filled balloon. If you have sealed the mouth of the balloon, think about what happens inside . . . The water which was vibrant before, like any liquid, starts to get squished and its kinetic energy slowed. However, at that temperature that water wants to be energetic, so it fights to be motive again, and this 'fighting' feels like higher pressure. Newton's tells us that the water will 'fight' as hard as you will squeeze.

Now open the mouth of the balloon and squeeze. We know the squeezing puts a high pressure inside the balloon, and now we see that that water starts coming out of the balloon very fast, and it continues very fast through the air. This occurs because the air is at a lower pressure than the water inside. The water inside had more pressure exerted on it, and that was a source of energy. It stored the energy in pressure (like a capacitor stores energy in voltage), and now was being forced to a lower pressure environment. The new water which was placed in the lower pressure environment had no choice but to exert all that energy as kinetic energy, and move faster.

It's all a question of conservation of energy.

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