Calculating something wrong with Poiseuille's Law

[dvora]

Homework Statement

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

Homework Equations

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.

Thanks!

 

[haruspex]

I'm not sure what you are expected to take into account, but it seems to me that in the real world there are two significant aspects your calculation ovelooks:
1. The drag in the tube is in addition to the drag that is already present in drawing the air through the nostrils etc.
2. To breathe successfully through the tube, enough fresh air must be drawn in each time. If the expelled air goes through the tube also then the total tube volume may be too great.

 

[dvora]

Thank you! I had just looked up the tracheal air flow when you replied and it's slower than air flow through the tube, so I can base my calculations on the rate of tracheal air flow instead. Maximal inspiration/expiration volume is greater than resting inspiration volume + dead space in the tube, so I think the person should be able to get enough fresh air even breathing out through the tube.

 

[dvora]

We weren't told what to take into account; we were just told to decide whether or not people can breathe with a 100 cm length, 2 cm radius tube. We've also never discussed solving problems like this, so I'm just guessing about what to take into account.

 

[haruspex]

We weren't told what to take into account; we were just told to decide whether or not people can breathe with a 100 cm length, 2 cm radius tube. We've also never discussed solving problems like this, so I'm just guessing about what to take into account.

Ok, sounds good.

 

[dvora]

Thank you! I had just looked up the tracheal air flow when you replied and it's slower than air flow through the tube, so I can base my calculations on the rate of tracheal air flow instead. Maximal inspiration/expiration volume is greater than resting inspiration volume + dead space in the tube, so I think the person should be able to get enough fresh air even breathing out through the tube.

That, of course, is assuming that I've correctly calculated the air flow through the breathing tube.

 

[haruspex]

That, of course, is assuming that I've correctly calculated the air flow through the breathing tube.

I could not see an error, and it does seem reasonable. That is quite a large radius, so I'm not surprised it yields a greater flow rate that the respiratory tract, particularly if the normal pressure diffence you quote is for breathing through the nose.

 

[dvora]

Thank you for all of your help!