Air pressure, vacuum cleaner and a bathroom scale

Updated: September 12, 2012

Atmospheric pressure, what does it really mean? When someone says: standard atmosphere, what is your first thought? Do you think of numbers or the fact you breathe with no difficulty in such conditions? Do you think of values or wonder what happens to submarines 300 m below the sea?

Today, I'd like to run a super cool experiment - and show you how significant air pressure really is, something we take for granted almost every second of our lives. I will demonstrate using some common household appliances, a bathroom weight scale you use to gauge your insecurity, your average vacuum cleaner and one airtight bag. So here's the test - let's see how heavy the air really is. BTW, this experiment's been done quite a lot all around, do not hail me as a genius, merely a super-intelligent entertainer slash educator. There you go.

## Physics behind air pressure

Pressure is nothing but force divided by the area upon which it is applied. It is measured in Pascal (Pa) units, which stands at 1N/m2. In other words, if you were to place an object measuring 1x1 meters and with a mass of approx. 100 grams onto the ground, that object would exert a pressure of 1Pa against it.

The standard atmosphere is a pressure of 101,325 Pa - or 101KPa - at sea level, room temperature and typical air density and humidity. In other words, a force of approx. 100KN, or roughly 10 tons, weighs down on every meter of surface anywhere on Earth. This also amounts to approx. 10N per square centimeter. We're not exempt from this pressure, either. So how come we do not feel this enormous weight?

The reason is quite simple; the column of air that goes up for some 70-80 km or more is not a singular mass, but a gradient. In a way, infinitesimal layers of air are stacked one on top of the other, with the top layers pushing down and bottom layers pushing back up. Therefore, the air pressure difference we feel is always very small, just a few millimeters between our nerve points or less. For someone 2 meters tall, the variation between their toes and the crown of their head is only about 14Pa - see barometric formula for more fun facts. If we assume our total top-down cranial cross-section is about 20 x 20 cm, meaning roughly 400 cm2 or 0.04 m2, then our head feels about 0.5N less weight than our feet. And this is an extreme example, which illustrates why we ignore it.

All right, let's make things a little more dramatic.

## The experiment

To demonstrate that air pressure is significant when it comes to bear against our poor planet, we will use the standard bathroom scales. Only, we will place it inside a vacuum bag and suck the air out of it using the vacuum cleaner. We will place the vacuum cleaner nozzle beneath the scales, for which purpose you might want to use some kind of a prop, and you will see the air gradient sharpen, resulting in a downforce against the scales, translating into ghost weight.

In theory, for a typical scales the size of a 17" laptop, the total area is about 600 cm2. This means that if we can achieve the same atmospheric pressure beneath the scales as that at 80 km altitude, our scales will bear the tremendous force of about 6 KN or roughly 600 kg. All right, let's do it.

First, here's the unencumbered scale, showing 0.0 on the dial:

Now, we place the scales into an airtight bag:

Now we fire up the vacuum cleaner and start sucking the air out. At the lowest setting, we can manage to force the scale to show approx. 16.6 kgf of downforce, or roughly 170N. This amounts to a pressure of about 2.8KPa, which means our appliances manages an altitude difference of about 400 meters.

At the highest setting, we fare a little better, up to 18.9 kgf. Now, the vacuum cleaner is not among the most powerful ones, nor did we achieve a perfect seal with the bag, but it illustrates the point quite nicely. We also know what our appliance is capable of. All in all, some 3.5KPa or roughly 450 m altitude delta, but without the usual human benefit of a gradual change, all concentrated within a few centimeters of space.

So this experiment might have set you wondering - what happens below the sea? Indeed, with the water being some 800 times more dense than the air, you merely need to dive some 10 meters to double the pressure. And if you've ever dived, you will know how tough it gets just a few meters below the surface. Even with a small pocket of air inside your lungs, you will easily float your 60-80 kg of mass. Not trivial when you think about it.

## Conclusion

There you go. Now you can delight your friends and family and even business customers with crazy tricks like these. They might be a little worried if you ask them to bring a vacuum cleaner to a meeting, but they will surely appreciate the physics of the whole deal, if they show up, that is.

Air pressure is a tricky thing. But it can be enjoyed. And if you ever wondered why decompression is needed when you're brought up to surface from deep sea explorations, it's the same like the bathroom scales experiment, only in reverse. Anyhow, I hope you liked this; and if not, it's still ok, I know I enjoyed myself immensely.

Cheers.

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