You wish to model the air flow in the lungs. The trachea is represented as Gener

Question

You wish to model the air flow in the lungs. The trachea is represented as Generation 0. The diameter of the trachea, d0, is 19 mm, and the volumetric flow rate in the trachea is 12 L/min. The trachea splits into two vessels, represented as Generation 1 (see Figure). These two vessels have the same diameter, and each diameter is 75% of the diameter of the trachea. Each of the Generation 1 vessels splits into two vessels, represented as Generation 2. The four vessels in Generation 2 have the same diameter; and each diameter is 75% of the diameter of a vessel in Generation 1. This pattern continues with each vessel bifurcating (splitting into two) at each new generation, and the diameter of the vessel of the new generation is always 75% of the diameter of the preceding generation. Determine the linear air velocity, v5, for Generation 5.

Explanation / Answer

The diameter of trachea at the zero generation = 19 mm

Diameter of bronchi in the first generation G1 = 14.25 mm

Diameter in G2 = 10.68 mm

Diameter in G3 = 8.015 mm

Diameter in G4 = 6.011 mm

Diameter in G5 = 4.508 mm

Speed of air flow at 19 mm diameter = 12L/ min

Speed at 4.508 mm diameter = 4.508* 12/ 19 = 2.84L/ min.

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