On the Size of Straws and Atmospheric Pressure

During the last math club meeting one of our members threw out a fun fact that a straw could not be longer than 10.3 meters. This fun fact was met with a hostile argument as to exactly how straws work and how realistic that was. The result was more interesting than expected.

 

Straws

Straws (Photo credit: jeff_golden)

 

To make this clearer, the fact is not that an 11 meter straw is impossible to make. The world record set by a high school group was a 20,000 foot long straw. The claim is that an 11 meter straw would be unable to suck up the liquid to the top. It makes sense that there would be a maximum, but exactly what it is and why there is a maximum were debated points.

The first, obvious argument was that it has to do with the human lungs and the ability to suck in air. Thinking about the energy exerted in the act, running out of breath, and the distance traveled in the straw this reasoning makes sense.

However, it is actually not the issue at all. What happens when you suck on a straw is a vacuum is created. In physics, this refers to space that is empty. The vacuum is subject to forces by atmospheric pressure. The air pressure is pushing the water down into the cup, while the water pressure is pushing against it upward. What happens is that when you suck on a straw you are actually decreasing the air pressure in the straw causing the water to rise.

If you try to pump water up a tube it can only go 32 feet (about 10 meters) before cohesion is lost. It is the highest water can be raised vertically in a vacuum.

The solution comes from the formula

p = ρgd

where

p = atmospheric pressure ( 101,325 Pa)

ρ = density (of water) ( 1000 kg/m^3 )

g = gravity (9.81 m/s^2)

d = depth

When solving for d, the depth of the straw, the answer comes out to 10.3 meters as a maximum water can travel vertically in a perfect vacuum.

There are some ways around the 10.3 meters though, to have even longer straws exist. The first is how deep the body of water is, because the straw could just keep going down in that direction, as long as the length above water is 10.3 or less.

Another solution would be to put the straw at an angle instead of having it vertically. Then a straw could theoretically not have a limit.

Knowing that the limitation here is atmospheric pressure, how do straws operate when at an elevation other than sea level. Higher elevation means less atmospheric pressure, means drinking through a straw is harder to do. Similarly, the pressure at depths underwater would make it harder, not that you could drink underwater anyways. Straws would be completely useless in outer space, because there is no atmospheric pressure at all. While astronauts can use straws aboard their vessels easier than if they were on Earth, they would not be able to do so

outside. (Granted this is hypothetical and a pretty big leap, because astronauts cannot survive outside without their suits, their helmet would prevent them from using a straw, and water cannot exist as a liquid on the moon). The pressure on a spaceship allows astronauts to use straws from a sealed container, but if the water was freely floating about then it would not function properly.

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