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)
One straightforward and often quite accurate way to find the resistance to the stress created by the internal pressure is to use the cylinder stress assumption. If the tube thickness is less than about one-tenth of the radius, then you may apply the thin-walled assumption. The tangential stress is simply given by the ratio between P R and t where P is the maximum pressure inside the tube, R is the tube mean radius and t is the thickness (here P is the relative pressure).
When your tube has a R / t ratio of less than 10, then you may apply the thick-walled assumption because the thin-walled assumption is no longer valid. In order to calculate the stresses, you may use the equations known as the Lamé equations, and apply the right boundary conditions. Once you have the stress distribution as a function of the radial distance, look to the maximum stress. This maximum stress should not exceed the admissible one specified by the constructor, for a certain security coefficient.
For further reading, see the link below:
http://en.wikipedia.org/wiki/Cylinder_stress
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.
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