Did you notice that the time required to inflate a tire or a basketball is shorter than the time…

Did you notice that the time required to inflate a tire or a
basketball is shorter than the time needed by the compressed air to leak out if
the valve is left open? Think about this as you model the inhaling–exhaling
cycle executed by the lungs and try to explain why the exhaling time is longer
than the inhaling time even though the two times are on the same order of
magnitude. A simple one-dimensional model is shown in Fig. P13.12. The lung
volume expands and contracts as its contact surface with the thorax travels the
distance L. The thorax muscles pull this surface with the force F. The
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Did you notice that the time required to inflate a tire or a
basketball is shorter than the time needed by the compressed air to leak out if
the valve is left open? Think about this as you model the inhaling–exhaling
cycle executed by the lungs and try to explain why the exhaling time is longer
than the inhaling time even though the two times are on the same order of
magnitude. A simple one-dimensional model is shown in Fig. P13.12. The lung
volume expands and contracts as its contact surface with the thorax travels the
distance L. The thorax muscles pull this surface with the force F. The pressure
inside the lung is P, and outside the pressure is Patm. The flow of
air into and out of the lung is impeded by the flow resistance r such that Patm
_ P = r__n in during inhaling and P _ Patm
= r__ n out during exhaling. The exponent n is a
number between n _
2 (turbulent flow) and n = 1 (laminar flow). For simplicity, assume that the
density of air is constant and that the volume expression rate during inhaling
(dx_dt) is constant. The lung tissue is elastic and can be modeled as a
linear spring that places the restraining force kx on surface A. Detemine
analytically the inhaling time (t1) and the exhaling time (t2)
and show that t2_t1 _ 2.

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