When a human takes a breath, the inhaled air flows through the nostrils and trachea before splitting into two primary bronchial tubes. The primary tubes further split to form smaller tubes, and eventually, the air passages end in sacs, called alveoli. In the alveoli, oxygen and carbon dioxide are exchanged with the blood. The typical trachea is 2 cm in diameter; the right primary bronchial tube has a diameter of 12 mm and the left has a diameter of 10 mm. The average adult takes 12 breaths per minute, with each breath, taking in about 0.5 L of air at ambient conditions, which may be taken to be 1.0 atm and 25 degrees Celsius. The velocities of the air in the bronchial tubes are related by the approximation:
(u_L/u_R)=(D_R/D_L)^0.5
The temperature of the air inside the body is 37 degrees Celsius. Recognizing that half of a breathing cycle is exhaling, estimate the mass flow rates and the velocities of air flowing through the trachea and each of the primary bronchial tubes.
Wher u_L and u_R are the velocities in the left and right bronchial tubes, and D_L and D_R are the diameters of the left and right tubes, respectively.
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(Fastest)
