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.

Conclusion:

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! 🙂

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23 Comments on “Perfesser Friar Hikes into a Partial Vacuum”

  1. Writer Dad Says:

    I wanted to laugh but this was one of your thinking ones. Your lucky you’re good at both.

  2. Friar Says:

    @Writer Dad

    Let’s see how this one goes. Maybe it’s a bit too dry for the non-science-geek crowd.

    (But I LOVE to see water bottles squish after hikes!) 🙂

  3. panchitah Says:

    My brain hurts…

    Dont get me wrong, I can appreciate the wonder surrounding the squished water bottle… Its just that my brain slows to a crawl when I see numbers. 😛

    Great blog by the way! Today I needed to laugh, and I came across some of your posts. I’m now your newest fan.

  4. Allison Day Says:

    This is how you know I’m such a science nerd – my eyes lit up and I kept grinning more and more as I read the post. 😀 I love it, love it, love it when you write these sorts of posts! These and the pumpkin drawings… definitely my favorite posts of yours. 🙂

  5. Brett Legree Says:

    Hey, I’ve seen that bottle recently 😉 good blog post Friar. It would be fun to do a follow-on post about aerosol cans showing how strong they are and why they won’t explode on airplanes (and why the airlines are full of crap for telling you they will).

    And if no one believes me, well, I’ve put *full* aerosol cans in a fire before and it takes a very long time before they go *boom*…

  6. Peter Says:

    The 1.7 psi pressure differential applies only if the bottle was still at full size. When the bottle is in its semi-collapsed state, the internal volume is very close to the density ratio of 12.7/14.4, and the delta P becomes very small. The actual force in this static state is exactly sufficient to fold in the plastic walls, not to overcome any significant pressure difference. I’d say it is about 15-20 lbs, the equivalent of a small daschund standing on an (open) bottle.

    Sorry for being an asshole.

  7. Steph Says:

    Friar: As I said at Brett’s, I. Love. Your. Mind. You intrigue me, and so few people can do that.

    Peter: Yeah, baby! Bring it on! I want to hear how Friar addresses this. Nerd *discussions* are even better!


  8. Friar,

    I might have accidently learned some math with my morning coffee.! You sneak you!
    Funny and educational. Holy Jenny Craig!!!!!
    I’m packing my suitcase and coming up there to be your full time harrassing coach, marketing agent and pain in the neck. We need to bottle you.

  9. Friar Says:

    @Panchitah

    Don’t feel TOO bad about the numbers…most of my other posts are math-free! 🙂

    @Allison
    This is just good ol’ PV = nrT (if you remember your chemistry).

    @Brett
    Aerosol cans in the fire. Heh heh. Been there. Done that. (During my “Darwin Years”).

    Peter
    Okay….good point. I stand corrected.

    My calculations were based on the assumption that the bottle had ridgid walls that didn’t collapse, and the bottle was perfectly sealed. If this were the case, my calcs would be true. In retrospect, I had perahaps oversimplified the problem.

    But you’re right….the volume collapse compensates for some of the pressures difference. Kind of the equivlent if this was a balloon.

    After I opened up the bottle, it went back to it’s original shape. I tried to squeeze it with my hand to see what force was required to squish it the way it was.

    It felt quite significant…perhaps a bit more than a daschund standing on the open bottle.

    So the “REAL” answer is probably between 15 bls and 187 lbs. (though closer to 15, I’d say).

    Of course, this starts to becomes problem in the mechanics of deformable solids, which is beyond my level of expertise.

    (Dammit Jim, I’m a CHEMCIAL ENGINEER, not MECHANICAL!

    @Steph
    Oh, I know who Peter is. This is so TYPICAL of him…he loves to debate shit like this.

    And dammit, he’s almost ALWAYS right!

    (…keeps me on my toes!) 😉

  10. Friar Says:

    @Wendi

    Ooops..you snuck in there, while I was answering other comments.

    It’s a bit of a commute from the Mid-West to Splat Creek Ontario.

    Are you SURE you’re up to being my personal coach?

    (Actually, though, I AM working with a personal coach, as we speak). A good friend of mine…she’s doing her “Training” and she’s been practicing on me for the past year….I’ve been getting a lot out of it, and she kicks my butt if I slack off on my Basil Book!)


  11. Zzzzzzzzzzzzzzzzzz, wake me up when you are funny again.

    Just kidding. I love science. Which is why I went into computers… huh? Long story, but I actually went to the Splat Creek Science Academy. The first class actually (now you know how old I am) and that convinced me that while I love science, it is a lot of really boring work. So I went and did somehting else.

    I still think you should write a science book for the common man. Judging from what I see here, it would be a best seller.

    Francis

  12. Friar Says:

    @Francis

    Well, if you find this ZZZZZzzzzzzzz that probably means you’re not a true science geek.

    Otherwise you’d be all bright eyed and bushy-tailed…like Allison…she’s the STAR PUPIL! 😉

    I agree…Science is 90% boredom and routine…but it’s the other 10% that makes up for it.

  13. Karen JL Says:

    GEEK.
    (you too Peter)
    😉

  14. Friar Says:

    @Karen

    Ooooh…that’s TWICE in one week!

    (At least Peter got it too,this time!)

  15. sushiday Says:

    @Friar – Yay, I’m a star pupil! Do I get a pretty gold star sticker? 😛

    PV = nrT was basic physics for me, but it’s still fun to read your thought processes about it. 🙂

  16. davinahaisell Says:

    Hi Friar. Yayyy hiking, boooo geometry! You had me right up until, “You with me so far?” This was amazing though. Does this mean that it would be harder to loose weight at higher elevations? No, really… does it?

  17. Friar Says:

    @Allison

    You get a gold star (or a bonus helping of sashmi!

    Hmmm….I can get into all kinds of discussions about ideal gases, and non-ideal gases, equations of state.

    (But I think I’d lose and/or scare away all my readers except you)

  18. Friar Says:

    @Davina

    The basic metabolism of the human body is

    (Food) + (Oxygen) = (Energy) + (Carbon Dioxide + Water + Poo + Pee).

    If there’s less oxygen available, theoretically, your body wont’ be able to burn as much food per minute. That suggests you might not lose weight as easily.

    But there are other factors. The lower pressure means water evaporates sooner and you get dehyrdated easily. Which affects your muscles ability to work and their efficiency. Plus the cold.

    Plus, with less air, you get tired faster, and it will take you twice as long to hike 1 mile at altitude, than you would at sea level. So you’re on your feet longer, and you’ll end up burning up more food.

    Seeing how most mountaineers are very skinny, I’d say the weight loss potential is pretty good (but this could just be the intense workout they impose on themelves to get there, regardless of how much food or oxygen they consume).

    Sorry I dont’ have a straight forward answer…that’s was a very GOOD question (the ones you can’t answer easily!)


  19. Friar- hehehe. during the hurricane, the oils in my pack that I use to help with my asthma released into the air without the bottles being opened…talk about a change in pressure. Cool ,perfesser.

    (Hey this is from a fellow NOLA Artist, had to send to you:

    http://www.alangerson.com/web/groupings.asp?id=habeascircus&WorksId=IrreconcilableDifferences

    Thought you’d like this page. )

  20. Friar Says:

    @Janice

    Hey…that’s pretty COOL. I didn’t know that the pressure drop in hurricanes was so extreme! I’ve never experienced one…just the tail end of the storm as they finally make their way up north.

    By the way…those watercolors ROCK. Especially the Viking/Lawyer one! 😀


  21. I KNEW you would like those! Hope Brett takes a look too. And did you see the GREY MEN on his projects page? Those are kneaded erasers!! Widget Factory serreptious arts activity……

    Yeah, it’s quite the phenomenon…at least it was eucalyptus and lavender oils.


  22. This is a bit technical for me, but it sure looks like you live a fun life by the looks of your squished oxygen bottle and other photos.

    I went to Cuzco Peru 11,600 feet… Had 3 naps in one day and it felt like a week. Really weird feeling. What’s the pressure there?

  23. Friar Says:

    @jaden
    11,600 feet is pretty high.

    That’s about the same altitude airplane pilots (in little Cesna airplanes) are required to breathe oxygen.

    According to the charts, it’s about 65% of an atmosphere. Almost down to half of what you’d breathe at sea level.


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