Final answer:
To find the average air speed, use the equation Q = A ⋅ V, where Q is flow rate and A is the cross-sectional area. The Reynolds number is then calculated using density, velocity, characteristic length, and viscosity to predict whether the flow is laminar or turbulent.
Step-by-step explanation:
To calculate the average air speed V in meters per second through the trachea during each inhalation, you would use the equation of flow rate Q = A ⋅ V, where A is the cross-sectional area of the trachea. Given that the radius of the trachea is approximately 10-2 m, the area A = π⋅r2. Using the measured flow rate Q, you can solve for V = Q/A.
Once you have the average air speed, you can then calculate the Reynolds number (Re), which is used to predict the flow regime of the fluid within the tube. The Reynolds number is calculated by Re = (density ⋅ velocity ⋅ characteristic length)/viscosity. In this case, the characteristic length would be the diameter of the trachea, which is twice the radius. Higher values of Re indicate turbulent flow, while lower values suggest laminar flow. If Re exceeds a certain threshold, typically around 2000, the flow is likely to be turbulent.