Biomedical Engineering Reference
In-Depth Information
carbonic acid, which accounts for nearly 70% of all of the carbon dioxide transported
through the blood. This reaction proceeds through the action of an enzyme, carbonic anhy-
drase, which is stored within red blood cells. Carbonic acid immediately dissociates into a
hydrogen ion and a bicarbonate ion. This kinetic reaction can be described by
+
−
+
+
CO
H O
Carbonic Anhydrase
H
HCO
2
2
3
Most of the hydrogen ions formed in this way bind to hemoglobin to maintain the pH of
the plasma (e.g., if the hydrogen ion was transported into the plasma the pH would
decrease). Most of the bicarbonate ions are transported into the plasma through a mem-
brane bound transport protein. For every bicarbonate ion that enters the plasma, one chlo-
ride ion is transported into the red blood cell using the same transport protein. No energy
is required for this transport, and it results in a large movement of chloride ions into the
red blood cells, which is known as the chloride shift. The second possible outcome for car-
bon dioxide is adhesion to hemoglobin. Close to 25% of carbon dioxide follows this path.
Carbon dioxide binds to the hemoglobin protein and not the iron ions like oxygen.
Specifically, carbon dioxide binds to free amino groups (NH
2
), forming carbaminohemo-
globin (HbCO
2
) in the following reaction:
Hb
1
CO
2
2
HbCO
2
The remaining portion of carbon dioxide (approximately 5% to 7%) is transported as
dissolved carbon dioxide in blood. Recall that the solubility of carbon dioxide is approxi-
mately 20 times greater than that of oxygen, and therefore, we would anticipate that blood
can carry some carbon dioxide as compared with oxygen.
9.6 COMPRESSIBLE FLUID FLOW
One of the most critical differences in compressible fluid flow, as compared with incom-
pressible fluid flow, is that the physical properties of the fluid are dependent on changes
in container area, frictional forces along the walls and heat transfer. We will begin our dis-
cussion of compressible fluid flow with isentropic flows. For this type of flow, friction and
heat transfer are neglected and the only independent variable is the change in the cross-
sectional area of the conducting vessel. The equations for isentropic flows are derived
from the basic equations developed in Chapter 3 of this textbook, for a fixed volume of
interest with steady one-dimensional flow. The properties of interest for an isentropic flow
are generally the fluid's temperature, the pressure, the density, the cross-sectional area,
and the velocity at any location within the flow field (
Figure 9.9
).
For a steady isentropic flow, the continuity equation simplifies to
ρ
1
v
1
A
1
5
ρ
2
v
2
A
2
5
m
ð
9
:
12
Þ
With the same assumptions, the Conservation of Momentum equation will simplify to
R
x
1
p
1
A
1
2
p
2
A
2
5
mv
2
2
mv
1
ð
9
:
13
Þ
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