At resting, can you breath sufficient air through a tube of 100 cm length and 2 cm radius?
normal resting respiration rate: 10 - 20 breaths per minute (3 - 6 seconds per breath)
normal resting respiration volume: 0.5 L
normal pressure difference in respiration = 1 mmHg = approximately 133.322 Pa
viscosity of air is apparently 0.0018 Pa s
Poiseuille's Law for volumetric air flow: Fv = ((P1-P2)pi(r^4)) / 8 eta L
The Attempt at a Solution
Fv = (133.322 Pa * pi * .02 m^4) / (8 * .0018 Pa s * 1 m) = 0.00465 m^3/s = 4650 cm^3/s = 4.65 L/s inhalation
So the conclusion would be that you'd have no problem breathing through the tube.
This seems like an awfully fast rate of inhalation, which makes me wonder if I am doing something wrong. I have never taken a physics class, I am taking a class in which physics is not supposed to be a requirement and we have never discussed or read about air flow in class, but we have been given this problem as a homework assignment. Which is all a way of saying that I know nothing about physics and would greatly appreciate it if somebody could show me where I went wrong and why. Do I have a problem with my units or something?
The other possibility is that this just looks like a really fast rate because it's oversimplified and doesn't include the rate of air flow through the trachea.