Biomedical Engineering Reference
In-Depth Information
4.7
An approach to minimizing space in flow systems is to use MEMS-based min-
iature pulsatile pumps. A group of researchers are interested in testing the
influence of viscous forces and inertial forces under pulsatile flow for which
they have developed a 50-mm-deep and 100-mm-wide rectangular channel.
The effect of frequency on these channels is calculated using phosphate buffer
saline solutions, which have a density and viscosity similar to water. Calcu-
late the effect of 1-Hz and 1-kHz frequency on the Strouhal number and the
Womersely parameter for a mean volumetric flow rate of 50 mL/min. Which
factors are dominating? Is the flow laminar or turbulent?
4.8
Consider a 100-mm radius arteriole that has a Poiseuille parabolic flow
profile.
(a) What percentage of the total flow rate
Q
total
is within the center of a
10-mm radius?
(b) What percentage of the total cross-sectional area is within the center of a
10-mm radius of the same vessel?
(c) Make a graph with radius as the
x
-axis in 10-mm increments up to 100
mm. Plot both [
Q
(0
→
r
)/
Q
total
]
×
100% and [
S
(0
→
r
) /
S
total
]
×
100% on
the
y
-axis of the same graph.
4.9
A Lilly-type pneumotachometer is a device that measures lung volumes from
flow measurements. It contains a fine wire mesh screen that introduces resis-
tance to flow. For a patient, the nursing staff was measuring the lung volume
so that they can provide an appropriate amount of anesthetic.
(a) If the pressure drop is measured to be 50 Pa and the flow resistance is 0.2
kPa.s/L for air at 25
°
C and 1 atm, then what is the flow rate?
(b) When they wanted to give an anesthetic whose viscosity is twice that of
air, they used the same pneumotachometer to measure the flow rate. What
is the error introduced in the flow rate?
(c) If another peumotachometer is used to measure the outflow, what is the
error introduced due to the change in temperature from 25
°
C to 37
°
C?
Viscosity of the gas at 37
°
C is 1.3 times that at 25
°
C.
4.10
In humans, the right lung is divided in three lobes perfused by different pul-
monary arteries. Assume that the right upper lobe receives a blood flow (
Q
UL
)
of 1.4 L/min, the middle lobe a blood flow (
Q
ML
) of 0.6 L/min, and the lower
lobe a blood flow (
Q
LL
) of 0.9 L/min. The pressures (
P
PA
) at the entrance of
the three lobes are 15 mmHg and the pressures (
P
PV
) at the exit of the three
lobes are 5 mmHg.
