HarvardMIT 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 HarvardMIT 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
Crosssectional
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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 Fall '06
 MatthewLang
 Fluid Dynamics, Physiology, Breathing gas

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