Anderson Video - Longest Straw Superman can Drink Through

Professor Anderson
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>> Okay, Superman is drinking water through a long straw. All right. Let's draw the picture. Here is Superman, flying along, that's his cape. Okay, he has got this straw, and he dips it into the ocean. And he is drinking liquid water through this straw. And we will say that the straw is length H. What is the longest straw that he could use? Anybody have any thoughts on that? >> Depends on how much [inaudible]? >> Somebody hand the mic to Richie [assumed spelling]. Let's have a chat, Richie. Richie, what do you think? >> It depends on how much air his lungs can hold before he actually gets to the water? >> Okay, well let's think about what you do when you drink through a straw. What do you do when you drink through a straw? >> I inhale some air, and then some water. >> Okay, you inhale a little bit of air, maybe, what you're really doing is creating a vacuum at the other end of the straw. Okay? You are, in fact, removing air out of your mouth and out of the straw, in order to force liquid up the straw. Okay? So the reason he is Superman is he can do miraculous things, like create a perfect vacuum at that end of the straw. He can suck all the air out of that end of the straw. Okay? You and I can't do that, but Superman can do that. So, what do you think, Richie? How long could that straw be? A foot? Two feet? A thousand feet? Infinite? What do you think? Give me a ballpark guess, Richie. >> Uh...I'd say up to atmosphere, or something? >> Okay, so the atmosphere. >> Yeah. >> So that would be 100,000 feet? Yeah? >> Yeah. >> Okay. It's not quite right for our atmosphere, but let's just pick some number, 100,000. Anybody else have a thought on that? Does that sound like a good guess? Too small? Too big? What do you think? All right, how do we attack this problem? The way we attack this problem is Bernoulli's equation. This is region one, down here, this is region two, up at the other end of the straw. Bernoulli said the following. P1 plus one-half rho V1 squared, plus rho GY1, equals, P2, plus one-half rho, V2 squared, plus rho GY2. This is Bernoulli's equation. What is P1? Well, we're at the surface of the ocean. So P1 is atmospheric pressure, which we're calling P naught. One atmosphere. What is V1? Well, that stuff is not really moving. We can say it's zero, right? We'll pick the static case where he just gets the liquid to the top. What about Y1? Well, let's measure from the surface of the ocean? So that's zero. What is P2? P2 is the pressure at that end of the straw. But he is Superman, so he can suck all the air out of it, so the pressure there is zero. There is no air left in the straw. V2, is zero. Y2 is the height. H. And so look what happens. Most of these things go to zero, and all we're left with is P naught equals rho times G times H, and these are all constants that we know. H is equal to P naught, over rho G. And now you can plug in those numbers. Okay? You know what P naught is. It's one atmosphere. You have to put it in Pascals. You know rho, it's about 1,000 kilograms per cubic meter. You know G, it's 9.8. So let's put them in. We've got 10 to the 5, in SI units, 10 to the 5 Pascals for 1 atmosphere. We've got rho, which is 10 to the 3, right? It's 1,000 kilograms per cubic meter, and we have G, which is another 10. Okay. It's really 9.8, but we're going to say it's 10. And so we get 10 to the 5, over 10 to the 4, which is 10, 10 meters is about 33 feet. That is the longest straw that Superman could use to actually get liquid up, is 33 feet. Which is not very long. Right? Nowhere near the atmosphere, 100,000 feet. It's only 33 feet. Why is that? Because the pressure of the atmosphere is in fact what pushes fluid up the straw. Okay? And that is a fixed number. It is gravity pulling down on all the air out here, that is going to force the liquid up the straw when you lower the pressure at the other end of the straw. This is exactly what you do when you drink through a straw. You lower the pressure on one end. Atmospheric pressure takes over, and pushes the fluid up the straw. But it can only do that to a certain height, and that height is 33 feet. Kind of cool, huh? All right, go out and buy a Big Gulp, and experiment yourself.
>> Okay, Superman is drinking water through a long straw. All right. Let's draw the picture. Here is Superman, flying along, that's his cape. Okay, he has got this straw, and he dips it into the ocean. And he is drinking liquid water through this straw. And we will say that the straw is length H. What is the longest straw that he could use? Anybody have any thoughts on that? >> Depends on how much [inaudible]? >> Somebody hand the mic to Richie [assumed spelling]. Let's have a chat, Richie. Richie, what do you think? >> It depends on how much air his lungs can hold before he actually gets to the water? >> Okay, well let's think about what you do when you drink through a straw. What do you do when you drink through a straw? >> I inhale some air, and then some water. >> Okay, you inhale a little bit of air, maybe, what you're really doing is creating a vacuum at the other end of the straw. Okay? You are, in fact, removing air out of your mouth and out of the straw, in order to force liquid up the straw. Okay? So the reason he is Superman is he can do miraculous things, like create a perfect vacuum at that end of the straw. He can suck all the air out of that end of the straw. Okay? You and I can't do that, but Superman can do that. So, what do you think, Richie? How long could that straw be? A foot? Two feet? A thousand feet? Infinite? What do you think? Give me a ballpark guess, Richie. >> Uh...I'd say up to atmosphere, or something? >> Okay, so the atmosphere. >> Yeah. >> So that would be 100,000 feet? Yeah? >> Yeah. >> Okay. It's not quite right for our atmosphere, but let's just pick some number, 100,000. Anybody else have a thought on that? Does that sound like a good guess? Too small? Too big? What do you think? All right, how do we attack this problem? The way we attack this problem is Bernoulli's equation. This is region one, down here, this is region two, up at the other end of the straw. Bernoulli said the following. P1 plus one-half rho V1 squared, plus rho GY1, equals, P2, plus one-half rho, V2 squared, plus rho GY2. This is Bernoulli's equation. What is P1? Well, we're at the surface of the ocean. So P1 is atmospheric pressure, which we're calling P naught. One atmosphere. What is V1? Well, that stuff is not really moving. We can say it's zero, right? We'll pick the static case where he just gets the liquid to the top. What about Y1? Well, let's measure from the surface of the ocean? So that's zero. What is P2? P2 is the pressure at that end of the straw. But he is Superman, so he can suck all the air out of it, so the pressure there is zero. There is no air left in the straw. V2, is zero. Y2 is the height. H. And so look what happens. Most of these things go to zero, and all we're left with is P naught equals rho times G times H, and these are all constants that we know. H is equal to P naught, over rho G. And now you can plug in those numbers. Okay? You know what P naught is. It's one atmosphere. You have to put it in Pascals. You know rho, it's about 1,000 kilograms per cubic meter. You know G, it's 9.8. So let's put them in. We've got 10 to the 5, in SI units, 10 to the 5 Pascals for 1 atmosphere. We've got rho, which is 10 to the 3, right? It's 1,000 kilograms per cubic meter, and we have G, which is another 10. Okay. It's really 9.8, but we're going to say it's 10. And so we get 10 to the 5, over 10 to the 4, which is 10, 10 meters is about 33 feet. That is the longest straw that Superman could use to actually get liquid up, is 33 feet. Which is not very long. Right? Nowhere near the atmosphere, 100,000 feet. It's only 33 feet. Why is that? Because the pressure of the atmosphere is in fact what pushes fluid up the straw. Okay? And that is a fixed number. It is gravity pulling down on all the air out here, that is going to force the liquid up the straw when you lower the pressure at the other end of the straw. This is exactly what you do when you drink through a straw. You lower the pressure on one end. Atmospheric pressure takes over, and pushes the fluid up the straw. But it can only do that to a certain height, and that height is 33 feet. Kind of cool, huh? All right, go out and buy a Big Gulp, and experiment yourself.