Biomedical Engineering Reference
In-Depth Information
Pressure at coronary artery:
9
1 mmHg
133
1050
kg
m
3
81
m
s
2
1m
100 cm
p
2
5
120 mmHg
1
:
ð
5cm
Þ
5
123
:
86 mmHg
:
32 Pa
Volume of catheter from femoral artery to aortic arch:
2
2mm
2
57 cm
3
V
5
π
ð
50 cm
Þ
5
1
:
Volume of catheter from aortic arch to coronary artery:
2
2mm
2
157 cm
3
V
5
π
ð
5cm
Þ
5
0
:
Buoyancy force on catheter:
9
9
1050
kg
m
3
81
m
s
2
1050
kg
m
3
81
m
s
2
57 cm
3
157 cm
3
F
:
ð
1
:
Þ
1
:
ð
0
:
Þ
5
0
:
0178 N
5
Note that the force acting on the catheter was not affected by the absolute pressure in the
system because these values cancel when adding the pressure terms (see
Equation 3.14
).
3.3 CONSERVATION OF MASS
The previous two sections described the pressure distribution in static fluids. However,
in most biofluid mechanics problems, the fluid that we are interested in will be in motion
(with an acceleration component), and therefore, the previous analysis may not be applica-
ble or may not be the most accurate. In the following four sections, we will develop rela-
tionships that govern the general fluid movement. Our analysis for each of these four
sections will use a volume of interest (sometimes called a control volume) formulation,
because it is normally quite difficult to identify the same mass of fluid throughout time.
Remember that fluids under motion will deform, and therefore, some identifiable volume
must be defined so that the laws of motion can be applied (
Figure 3.7
illustrates different
ways a fluid volume may be defined at different instances in time). The laws that govern a
system should be familiar from earlier courses in mechanics/thermodynamics. We will
extend these principles to a volume in the following formulations.
FIGURE 3.7
Two possible arrangements for a
fluid element after the fluid experienced some
motion. It is easier to maintain the control volume
square of time 1 to analyze the fluid, instead of
changing the volume of interest with time. This
image shows that there are multiple possible
arrangements for fluid elements after deforma-
tion, depending on the boundary conditions. It is
critical during the analysis of biofluid mechanics
problems to simplify these issues of deformability
by choosing control volumes wisely.
Fluid
element at
time 2
Fluid
element at
time 1
or
Fluid
element at
time 2
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