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 inhalingexhaling

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 inhalingexhaling

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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