Final answer:
To find the average air speed, use the formula v = Q/A after determining the flow rate Q. Calculate the Reynolds number with Re = ρvd/μ to determine if airflow is laminar or turbulent. Without specific values for Q, the average speed and Reynolds number cannot be calculated. Therefore the correct answer is a) 10⁻2 m/s.
Step-by-step explanation:
In the Take-Home Experiment: Inhalation, we need to calculate the average air speed in meters per second through the trachea during each inhalation. Given that the radius of the trachea in adult humans is approximately 10-2 m, and the average volume flow rate of air (Q) is required for this calculation, we would typically use the formula Q = vA where v is the average air speed and A is the cross-sectional area of the trachea.
To find the average speed, we rearrange the formula to v = Q/A, where A is πr2 using the given radius of the trachea. However, without a specific value for Q, we cannot provide an exact number for the average speed.
Once v is determined, the Reynolds number can be calculated using the formula Re = ρvd/μ, where ρ is the density of the fluid (air), v is the speed of the fluid, d is the diameter of the trachea, and μ is the dynamic viscosity of the fluid.
The Reynolds number indicates whether the flow is laminar or turbulent; a low Reynolds number suggests laminar flow, while a higher number suggests turbulence.