Biomedical Engineering Reference
In-Depth Information
that there is no change in area within this distance. Determine the amount of work per-
formed by the heart during systole and the power that the heart generates.
3.14
Air at standard atmosphere conditions (1 atm and 25
C) enters the lungs at 50 cm/s and
leaves at a pressure of 1.1 atm, 37
C, and a velocity of 60 cm/s (with a constant mass flow
rate of 1.2 g/s). The body removes heat from the lungs at a rate of 15 J/g. Calculate the
power required by the lungs.
3.15
The left common coronary artery has an axisymmetric constriction because of a plaque
buildup (see
Figure 3.30
). Given the upstream conditions of a velocity of 20 cm/s (systole)
and 12 cm/s (diastole), calculate the velocity at the stenosis throat and the pressure differ-
ence between the stenosis throat and the inlet.
FIGURE 3.30
Figure for homework problem 3.15.
d
=
6 mm
d
=
15 mm
3.16
Blood flows through a 25% restricting (diameter reduces by 25%) blood vessel that experi-
ences a 5 cm vertical drop (see
Figure 3.31
). The blood pressure at the inlet is 65 mmHg,
and the blood velocity is 50 cm/s. Calculate the blood velocity the pressure at the outlet.
FIGURE 3.31
Figure for homework problem 3.16.
5 cm
3.17
The cross-sectional area of a diverging vein may be expressed as
A
A
1
e
ax
, where
A
1
is the
cross-sectional area of that inlet. Develop a relationship for the velocity profile within the
vein (in terms of
x
,
v
1
). Also, develop a relationship for the pressure (if the inlet pressure is
p
1
) in terms of
x
. Assume that there is no variation in height.
5
10
-4
m/s
2
by gravity
only (see
Figure 3.32
). Solve the appropriate Navier-Stokes equations to find the velocity
distribution
v
Z
(
r
) and compute the average velocity.
3.18
Blood flows through a vertical tube with a kinematic viscosity of 3
3
FIGURE 3.32
Figure for homework problem 3.18.
r
g
z
3.19
Solve problem 3.18 assuming that the blood is flowing within a vertical parallel plate (i.e.,
calculate with the Cartesian Navier-Stokes equations), where the coordinate system is
aligned with the wall and channel width is
h
(see
Figure 3.33
).
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