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ps7 (1) - Harvard-MIT Division of Health Sciences and...

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Harvard-MIT Division of Health Sciences and Technology HST.542J: Quantitative Physiology: Organ Transport Systems Instructors: Roger Mark and Jose Venegas MASSACHUSETTS INSTITUTE OF TECHNOLOGY Departments of Electrical Engineering, Mechanical Engineering, and the Harvard-MIT Division of Health Sciences and Technology 6.022J/2.792J/BEH.371J/HST542J: Quantitative Physiology: Organ Transport Systems PROBLEM SET 7 Assigned: April 1, 2004 Due: April 9, 2004
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Problem 1 In this problem, consider the different factors which, in combination, give rise to the pressure dif- ferences encountered in the lung during breathing. For this purpose, use a simple model comprised of five generations with the geometry described below. Number of Generation Airways Total Cross-sectional Area (cm 2 ) Length (cm) 1 1 2 10 2 4 3 2 3 16 5 1.5 4 128 10 1.0 5 2000 50 0.5 In the following questions, consider inspiration at a normal breathing rate of 0.5 L/sec. Assume the flow to be steady and the fluid to be ν = 0 . 15 cm 2 /sec and ρ = 2 × 10 3 gm/cm 3 . (Remember ν = µ/ρ , the kinematic viscosity.) A. Compute the mean flow velocity in each generation assuming a uniform distribution of ven- tilation. B. Assume the flow to be inviscid and calculate the total pressure difference between the first and fifth generations. This represents the pressure difference necessary to decelerate a fluid
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