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Laminar , Turbulent, HeOx

For a fluid, the transition from laminar to turbulent flow is a function of the fluid’s speed, direction, applied pressure, pipe length, pipe radius, fluid viscosity, and fluid density. For human breathing, all of these parameters are generally beyond control, except for the fluid\'s density and viscosity. If the human has trouble breathing, laminar flow is preferred since the person does less work for each breath. In our analysis, the pipe is the airway (or breathing tube) from lips to bifurcation; the throat/pipe radius is known or can be determined; the differential pressure is the excess pressure above or below atmospheric pressure; fluid flow rate is the person’s tidal lung volume divided by the breathing rate. We analyze 13 widely different humans (with differing values for throat length, radius, etc.) to see the effect of breathing two different fluids: air (20% oxygen, 80% nitrogen) and HeOx (20% oxygen, 80% helium). The onset of turbulent flow occurs for the critical radius, and this is calculated for each patient. For 12 patients, the critical radius is much smaller than the throat/tube radius, if HeOx is used--the flow is laminar. For all patients breathing air, the critical radius is larger than the throat/tube radius--the flow is turbulent. Thus, HeOx is shown to be superior in treating patients with breathing problems.