# Pressure and variation in pressure due to depth

In my class, we were shown the following problem: 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 ?

• 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. – BowlOfRed Oct 22 '14 at 19:51
• 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. – docscience Oct 22 '14 at 19:51
• I should be clear, negative absolute pressure is not possible - by definition. Negative pressure relative to 1 atmosphere is. – docscience Oct 22 '14 at 19:54
• @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? – Armadillo Oct 22 '14 at 22:53
• @jake , depends on temperature, but yes water can vaporize but that doesn't help Superman get a drink. – docscience Oct 22 '14 at 22:57

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.