Conservation Laws - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 56

which is the volume of the element of interest (in Figure 3.5 this would be the shaded
cylinder). Therefore, the summation of all of the forces that act on the immersed body
would be

ð ð

V ρ

F z dF z gdV

5 ρ

gV

5 5

V

where V is the immersed volume of the element. This pressure force is equal to the force
of gravity on the liquid displaced by the object. For biomedical applications, this is useful
for designing any probe, which would be immersed within a biological fluid. Any cardio-
vascular implantable device would fall within this category as well.

Example
Determine the maximum buoyancy of a catheter that is inserted into the femoral artery of a
patient and is passed through the cardiovascular system to the coronary artery (see Figure 3.6 ).
The location where the catheter is inserted into the femoral artery is 50 cm below the aortic arch.
The coronary artery is 5 cm below the aortic arch. Assume that the maximum buoyancy would
occur at the end of systole on a normal healthy individual (120 mmHg). Also assume that the
catheter is perfectly cylindrical with a diameter of 2 mm.

Solution
Pressure at incision:

9 1 mmHg

133

1050 kg
m 3

81 m
s 2

1m
100 cm

p 1 5 120 mmHg 1 : ð 50 cm Þ 5 158 : 63 mmHg

: 32 Pa

FIGURE 3.6 Catheter inserted at the femoral artery which is passed

to the coronary artery. These catheters are commonly used during sur-
geries to remedy atherosclerotic lesions.

Aorta

Catheter

Femoral
artery