Hi to all,
I construct a plant including a way for passing of air. I can measure pressure at the start and end of tube and flow rate and maybe temperature. I add an extra artificial orifice as resistance Intentionally. How can i calculate airway resistance of this combination with these measures ?
As you know, the relation between Pressure, flow and airway resistance are obtained as below : R = (P_end - P_start) / (Flow_av) where Flow_av=(Flow_end + Flow_start)/2.
1- I have done numerous experiments with different flow rate. In every flow rate, resistance is different but i expect the airway resistance (based on electrical analogous) is constant ! isn't it ?!
2- Also i have done numerous experiments with constant flow rate and different artificial orifice. When i add a orifice with R=5 cmH2O/lit/s, the airway resistance (obtained from above eq.) was 6 cmH2O/lit/s. Then I add another orifice with R=5 cmH2O/lit/s and repeated the experiment again, but this time the value of airway resistance was 7 cmH2O/lit/s. What is wrong ?!!
Compressible flow in presence of friction with the flow-channel walls is called Fanno flow. You might find answer to your question in compressible flow text books such as Fundamentals of Gas Dynamics by Zucker and Biblarz (2nd edition, chapter 9)
What is your length scale? And is the flow laminar? If so, I would suggest you check your pressure drop using the Hagen-Poiseuille equation: delta P = (8uLQ)/(pi*r^4) . This would be how air flow in the lungs can be modeled. Similarly you can modify the equation to estimate the resistance directly: R = (8uL)/(pi*r^4) . This may be a good check during a control experiment without the additional orifices to see if your pressure meters give an accurate answer. Also to address your first point, I don't think your resistance will necessarily be constant, as by changing your flowrate you could be moving into different flow regimes where wall effects play a greater or lesser role. For your second point, I think doing a control experiment as I mentioned above would help determine what the problem is, for instance, whether it is a meter problem, or the orifice resistances are not correct.
There are three phases of flow - laminar, transitional & turbulent. As the flow leaves the laminar zone the resistance to flow increases non-linearly. A continuous equation for Re has been developed by Nikuradse - you might find this attached preprint useful.
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