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Anderson Video - Diving to a Pressure of Two Atmospheres

Professor Anderson
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>> So let's ask a follow-up question to our pressure under water discussion. Let's say you want to go underneath the ocean such that the pressure on you is now twice what it was at the surface. Right. Up here at the surface it is one atmosphere. That is the pressure due to all the air in our atmosphere being pulled down by gravity. So that's kind of weird to think about but you just take all these air molecules and you stack them up as high as our atmosphere is and that's the pressure on you from gravity pulling down on all that air. But now let's go down here and say that we want the pressure to double. Okay. And we know that pressure increases with depth. How deep do I have to go to double the pressure on me? All right. We go back to our equation that we just derived. Pressure under water is this, P naught at the surface plus rho gh. And now this one is going to be 2 P naught. And so I can subtract 1P naught from both sides and this becomes P naught equals rho gh. And now I can solve this thing for h. h is P naught over rho g. What is P naught? Well, it's 1 atmosphere which is 10 to the 5 pascals. Okay. Rho is the density of water which is around 10 to the 3 kilograms per cubic meter. g is of course gravity which is really close to 10. And this works out to be 10 to the 5 over 10 to the 4 which is 10 meters. Okay. So in SI units 10 meters is how deep you have to go in order to double the pressure on you, 33 feet or so. That's pretty deep, right. If you go down 30 feet under water, you definitely know it, right. The bottom of a swimming pool is usually around 10 feet if it's a deep swimming pool and if you go to the bottom of 10 feet, you definitely know it. If you go three times that, you will know it. And certainly is you don't fix the pressure on your ears, it will really, really hurt your ears and could even damage them. So you have to do the Valsalva maneuver as you go down, you have to increase the pressure inside your head.