Question: you are interested in modeling the air flow in the...
You are interested in modeling the air flow in the lungs. The trachea is represented as Generation 0. The diameter of the trachea (D0) is 1.8 cm. The volumetric flow rate in the trachea is 200 mL/sec. The density of air is 0.0012 g/cm^3. and the viscosity of air is 0.00018 g/(cm*s).
The trachea splits into two vessels, represented as Generation 1. These two vessels have the same diameter, each 75% of the diameter of the trachea. Each of the Generation 1 vessels split into two vessels represented as Generation 2. The four vessels in G2 have the same diameter each 75% of the diameter of G1. This pattern continues with each generation.
Write an equation for the linear air velocity, Vn, for Generation n, in terms of m0, n, D0, and p. Calculate the linear air velocity at Generations 6 and 12.
Write an equation for the Reynolds number, Ren, for Generation n, in terms of m0, n, D0, and u. Calculate Reynolds number at Generations 6 and 12.