Perfesser Friar Hikes into a Partial Vacuum
I was unpacking some of my hiking gear last night, and I came across my Nalgene water bottle.
And it’s SQUISHED!
Not because I sat on it, but because it’s being crushed by our atmosphere.
You see, the last time I had my water bottle open, it was near the summit of Cascade Moutain in Upstate New York, at an altitude of 4098 feet above sea level. The air was thinner up there, at higher elevation.
Then I closed the bottle, forgot about it, and drove back home to a lower elevation, where the air is thicker.
So basically, there some thin high-altitude thin air trapped inside my water bottle that’s being squished by the thicker low-altitude air outside the bottle, in my living room.
You with me so far?
Let’s do a a quick engineering back-of-the-envelope calculation to figure out the total force squishing my water bottle. (Sorry, I’m a science-geek, I can’t help but wonder about such things!)
1. First we need to know the air pressure as a function of elevation above sea level
This is easy to look up, you can find it in published tables everywhere.
For example, where I live it’s about 500 feet above sea level, and according to the charts, the atmospheric pressure is 14.4 pounds per square inch (psi).
At 4000 feet (roughly the top of Mt. Cascade), the atmospheric pressure is 12.7 psi.
2. Next, let’s determine the pressure difference across the bottle wall
This is easy.
Pressure difference = (Pressure of living room air outside my bottle) – (Pressure of trapped moutain air inside my bottle)
= (14.4 – 12.7) = 1.7 pounds per square inch.
This means that every square inch of the water bottle is being subjected to a net force of 1.7 pounds.
3. Next, let’s determine the surface area of the water bottle
Okay, sorry, folks, I’m going to have to resort to high-school geometry here.
Let’s just focus on the area of the bottle walls (we can ignore the bottom and top of the bottle, they’re pretty small anyways).
For a cylinder:
Surface Area = (Circumference) x (Height)
which, according to my tape measure, is:
= (11 inches) x (10 inches) = 110 square inches.
4. Multiply pressure times area to get force
Force = (1.7 pounds per square inch) x (110 square inches) = 187 pounds.
That’s 187 pounds pressing on the bottle! Holy Jenny Craig, Batman! That’s significant weight!
(No WONDER it’s BENT!)
Just goes to show you, how even a small gain in elevation can result in enough of a pressure difference to be noticeable in everyday life.
And as a side-note, atmospheric pressure at sea level is 14.7 psi. So at 12.7 psi, the top of Cascade moutain is only (12.7 / 14.7) = 87% of an atmosphere!
(So, basically when you hike at 4000 feet, you’re already missing 13% of the air you’d normally breath at sea level)
Gee. Now I don’t feel so bad about puffing and panting so much to get to the top! 🙂