Friday, February 12, 2010

Darwin Day Fermi Problem (Darwin Award)

Happy Darwin Day!

200 years ago today Charles Darwin was born.
You may also have heard of the Darwin Awards, an award given (usually) posthumously to commemorate those who improve our gene pool... by accidentally removing themselves from it.

 Here is a nice Fermi problem to determine candidacy for a Darwin Award. This is based on a discussion I had at work.

------- Start Fermi Problem -------

A manager brings a problem to a physicist to design a system to put a pure nitrogen blanket into a small enclosed (but vented) box. However, there is some concern on assuring that the percentage of nitrogen in the box is as close to 100% as possible, and how to measure this.

A first design is to pump pure nitrogen from a gas cylinder into the box, and (relatively) quickly empty the bottle so that there is no diffusion of O2 back into the box through the vent holes. This should purge most of the O2 from the box.

The manager has read about people dying from Nitrogen asphyxiation, and is concerned that he could suffocate if he used too much nitrogen.

The physicist, after glancing at the room where the box is to be located, and the size of the pressurized nitrogen bottle, confidently proclaims that there is no real danger.

Is the physicist a Darwin award candidate?

Note that the dimensions of the room are 15 ft x 30 ft x 8 feet.

As an aside, assuming a standard airgas bottle of compressed nitrogen (250) what is the smallest size room you could safely vent such a bottle in?

You may have to look up (or estimate) what O2% is dangerous to such a candidate. =)

And finally, as a back of the envelope problem:
Say the box is 3 feet by 4 feet by 3 feet.
Design the flow rate of N2 and vent holes such as to assure a 99.99% purity of N2 after 1 hour. ;)

---- End Fermi problem ---

Note, because nitrogen does not trigger a suffocation reflex in the human body, breathing pure nitrogen gas is very dangerous. Just two or three breaths reduces the amount of O2 in the lungs where the O2 diffuses back into the lungs from the blood stream. For this reason, even if you determine the physicist is not a Darwin award candidate, please take precautions in dealing with nitrogen gas, and maintain adequate ventilation of the room. 

A quick rule of thumb to file away for future Fermi problems:

Liquid to gas expansion ratios: Liquid:gas (approximate)

N2.    1:700
O2.    1:860
He2.  1:760
H2.    1:850
Ne.    1:1400

Taking the average expansion of the first 4 gases, a rule of thumb is that if you deal with many liquid cryogens, the expansion ratio is about 1:800.


  1. Let's see. You breath in about 21% O2, and breath out about %15. When breathing in a plastic bag it is CO2 that does you in, not the lack of O2. Lets say 10% is when I would start getting worried.

    %O2 = 100*.21*(Vroom - Vleak)/Vroom

    Volume of the room is 15*30*8 ft^3 = 3600 ft^3.

    Standard tank of nitrogen holds about 220 cubic feet of compressed N2.

    %O2 = 100*.21(3600 - 220)/3600 = 19.5%

    Nothing to worry about. Also, dealing with air exchanges can counter the reduction in O2.

    You would need to crack open nearly 9 cylinders of N2 to get to 10% O2 in the room. Need to pay attention to loud hissing!

  2. Liquid N2 would be more dangerous. Easy to transport, vaporizes and expands 700 times. To reach 10% O2 would require about 2.7 ft^3, or about 75 L, or 76 gallons of LN2.

    As for the second back of envelope, this is setting up as a mixing problem, set up the DfEQ.

  3. Actually, our breathing is regulated by amount of CO2 in our lungs/bloodstream. Our breathing doesn't measure oxygen content directly. So, excess nitrogen won't necessarily be felt, but it'll be impacting our O2 saturation and survivability directly. So the lack of CO2 effect makes it worse, not better, since it can kill you without you feeling it until it's too late. That's what's meant by the lack of suffocation reflex above.