Biomedical Engineering Reference
In-Depth Information
the reaction force in the x-direction must now include frictional forces (F
x
), so that the
Conservation of Momentum will become
R
x
1
F
x
1
p
1
A
1
2
p
2
A
2
5
mv
2
2
mv
1
ð
9
:
20
Þ
The fluid flow is no longer reversible since energy is lost to friction. Therefore, the sec-
ond law of thermodynamics becomes
2
Rln
T
2
T
1
p
2
p
1
s
2
2
s
1
5
c
p
ln
ð
9
:
21
Þ
If the fluid can be assumed to be an ideal gas, we can also make use of the ideal gas laws,
described in
Equations 9.16 through 9.18
.
If there is heat being transferred during the flow conditions but there is no friction, then
the equations to describe the flow field will take the following form. Continuity and
Conservation of Momentum take the same form as
Equations 9.12 and 9.13
, respectively
(although there may be no surface forces acting on the flow). The first law of thermody-
namics will simplify to
v
2
v
1
2
Q
5
_
mh
2
1
2
2
h
1
2
ð
9
:
22
Þ
The second law of thermodynamics is the same as
Equation 9.21
.
In general, the equations just provided are all applicable to the diffusion of gas across
the respiratory boundary. Under these conditions, it is possible that there is some exchange
of energy during gas flow and potentially friction losses. Because the respiratory boundary
is so thin, it is possible to use the more general formula for steady isentropic flows.
9.7 DISEASE CONDITIONS
9.7.1 Emphysema
Emphysema is a chronic disease that is associated with shortness of breath which pre-
vents the patient from participating in strenuous activities. One of the most common
causes of this disease is exposure to cigarette smoke, both from mainstream smoke (i.e.,
the smoker) and from sidestream smoke (i.e., secondhand smoke). This biological problem
is associated with the destruction of the alveolar space. This effectively reduces the surface
area for oxygen/carbon dioxide exchange to occur, which reduces the diffusion rate of
each molecule. In severe cases of emphysema, alveoli merge, forming large sacs covered
with fibrous tissue that ineffectively participate in gas exchange. These sacs are fairly rigid
and also decrease the lung elasticity, making it more difficult to experience volume
changes with the small pressure changes (i.e., Boyle's Law) during inspiration and exhala-
tion. Without the proper surface area for gas exchange, the body does not get enough oxy-
gen and not enough carbon dioxide leaves the body.
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