Biomedical Engineering Reference
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in cylindrical coordinates. From either of these sets of equations, the fully developed fluid
velocity profile can be directly solved for as a function of location within the flow field.
3.8
The Bernoulli equation is a useful formula that relates the pressure variation in a fluid to the
height and the speed of the fluid element. However, this formulation is only valid for steady,
incompressible, and invisicid flows. The Bernoulli equation states that
v
2
2
1
p
ρ
1
gz
5
constant
HOMEWORK PROBLEMS
3.1
A two-fluid manometer is used to measure the pressure difference for flowing blood in a
laboratory experiment (see
Figure 3.24
). Calculate the pressure difference between points
A and B in the fluid.
FIGURE 3.24
Water
Figure for homework problem
3.1.
d
2
=
190 mm
d
1
=
500 mm
d
3
=
275 mm
A
B
Blood
3.2
NASA is planning a mission to a newly found planet and will monitor the density of the
new planet's atmosphere. Assume that NASA knows that atmosphere behaves as an ideal
gas and that
7
s
2
the planet's gravitational
force is a function of altitude
g
ð
z
Þ
5
18
:
z
, where z is in m). The temperature of the atmosphere is constant at 250 K,
and the gas constant is 340 Nm/kgK. Assume that the pressure at the planet's surface is
2 atm. Calculate the pressure and density at an altitude of 1 km, 5 km, and 9 km.
1
Þ
2
10
;
000 m
3.3
Calculate the hydrostatic pressure in the cranium and in the feet at the end of systole and
the end of diastole for a hypertensive patient (end systolic pressure is equal to 185 mmHg
and end diastolic pressure is equal to 145 mmHg). Assume that the blood density does not
change significantly with height and that the cranium is 25 cm above the aortic valve and
the feet are 140 cm below the aortic valve. Compare this with a normal patient.
3.4
A balloon catheter has been placed within a femoral artery of a patient, to be passed to the
coronary artery (use the same dimensions stated with
Figure 3.6
). Assume that the catheter
consists of two components: 1) a chamber to hold the balloon, which is 2 mm in diameter
and 1 cm in length (a perfect cylinder) and 2) a tube 0.5 mm in diameter and the total
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