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In my class, we were shown the following problem:

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Using the equation $P_1$ = $P_0$ + $\displaystyle\rho$gh, where $P_1$ is the pressure at Superman's mouth and $P_0$ is the pressure at the surface of the container he's drinking from, I can find the height that he could pull the fluid up through the vacumn. The first thing my professor said was to assume that the pressure in Superman's mouth can be 0. At this point I'm already lost because I don't understand why the pressure in his mouth would be 0, or what it would mean to have a pressure of 0. Can anybody help me out ?

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  • $\begingroup$ It's just saying that superman can create an arbitrary (non-negative) pressure. If instead we had a powerful vacuum pump, we could do something similar. We can set $P_1$ to a value arbitrarily close to 0. A pressure of zero would be an ideal or perfect vacuum. $\endgroup$ – BowlOfRed Oct 22 '14 at 19:51
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    $\begingroup$ Absolute pressure of zero is a hard vacuum. Standard atmospheric pressure is about 760 mm Hg above vacuum pressure, and in terms of a water column that's about 10 meters. Superman is super, but he can't violate physical laws. In other words the largest water column he could maintain by sucking to zero pressure is about 10 meters. So 12 meters is out of the question - even for Superman. $\endgroup$ – docscience Oct 22 '14 at 19:51
  • $\begingroup$ I should be clear, negative absolute pressure is not possible - by definition. Negative pressure relative to 1 atmosphere is. $\endgroup$ – docscience Oct 22 '14 at 19:54
  • $\begingroup$ @docscience couldn't the water column exceed 10 meters? At 10 meters the free liquid surface will be cavitating/boiling and then you would have a water column in the gaseous phase climbing beyond 10 meters, correct? Super man would be intaking these water molecules, no? $\endgroup$ – Armadillo Oct 22 '14 at 22:53
  • $\begingroup$ @jake , depends on temperature, but yes water can vaporize but that doesn't help Superman get a drink. $\endgroup$ – docscience Oct 22 '14 at 22:57
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People who say this is impossible are assuming that Superman drinking from a straw is a static situation. When nothing is moving, the best S. can do is create a perfect vacuum (pressure of 0 psi / Pascals / atmospheres / krypton standard pressure units). HOWEVER...

If he creates a perfect vacuum at the top of a thick straw, the water that gets pushed up will have a certain amount of work done on it - in fact the pressure difference between the top and the bottom of the column is at all times equal to the length of the column. So when the column has reached a height $h$, the work done by the pressure $P$ is $PAh$ But the potential energy of the column of water is $\rho Agh/2$. Keep sucking like that and water could in principle reach a height of 20 meters before the column of water stops moving. So Superman can take a good sip, the let the water settle and repeat.

Another technique to suck water over a greater height (and one that can be maintained indefinitely since it doesn't rely on dynamics) adds bubbles from time to time. pull the straw out of the water and draw a bit of air into it; then put it back and keep sucking. If you make sure there is at least 2 meters' worth of air in the straw you can drink to your heart's content. You will have changed the effective (apparent) density of the water in the straw. You might get a little gassy...

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  • $\begingroup$ Also, considering the static situation, wouldn't the water (H2O) boil/cavitate and super man would still be drinking the fluid (the water vapor)? $\endgroup$ – Armadillo Oct 22 '14 at 21:46
  • $\begingroup$ @jakemcgregor that depends on the temperature. "Nice cold water" has very low vapor pressure - single digit millimeters of mercury at 0C if I'm not mistaken. But yes that would give him a chance to extract water - by lowering the density in yet another way. $\endgroup$ – Floris Oct 22 '14 at 21:57
  • $\begingroup$ from the limited information given in the question about the environment in which super man is drinking the water it got me thinking about what all information would need to be explicitly defined to truly answer the problem? I was thinking environmental parameters such as atmospheric pressure, temperature, mass of planet or local gravitational field, and depth of drinking straw below the reservoir's free (liquid) surface. What else would need to be defined? $\endgroup$ – Armadillo Oct 23 '14 at 1:54
  • $\begingroup$ All those are good parameters to add for a reasonably complete answer. I suppose from temperature and gravity we can derive viscosity of liquid (which can limit validity of dynamic solution) and you would have to know the diameter to compute viscous drag - but that's getting quite far from the original intent of the question (which I'm afraid was almost certainly the static on-mother-Earth scenario. Boring, I know!) $\endgroup$ – Floris Oct 23 '14 at 4:09

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