Biomedical Engineering Reference
In-Depth Information
where h is the separation distance between the two flat plates and the origin is located half-
way between the plates. Consider the flow of blood at 37
C(
3.5cP) with maximum
velocity of 25 cm/s and a separation distance of 10 mm. Calculate the force on a 0.25 m
2
section of the lower plate.
2.11
A biofluid is flowing down an inclined plane. The velocity profile of this fluid can be
described by
μ5
sin
y
2
2
5
ρ
g
μ
u
hy
2
θ
if the coordinate axis is aligned with the inclined plant. Determine a function for the shear
stress along this fluid. Plot the velocity profile and shear stress profile, if the fluid density
is 900 kg/m
3
and viscosity is 2.8 cP. The fluid thickness h is equal to 10 mm and the plane
is inclined at an angle of 40
.
2.12
*A block with mass M
1
is in contact with a thin fluid layer of thickness h. The block is con-
nected to a second mass M
2
via a cable that goes over an ideal pulley. Determine a relation-
ship for the velocity of the block when the second mass is released from rest.
FIGURE 2.23
Figure
for Homework
Viscosity,
μ
Thickness, h
M
1
Problem 2.12.
M
2
2.13
For the following velocity field
-
-
-
xt
2
z
2
v
5 ð
1
2y
2
Þ
1 ð
xt
2
2yt
Þ
1 ð
3xt
1
z
Þ
calculate the shear rate tensor, the vorticity, the hydrostatic pressure (use a viscosity of
μ
)
and the acceleration of the fluid.
2.14
A velocity field is given by
2s
2
1
x
-
Þ
2
1
y
2
-
v
5
0
:
2
0
:
35
ð
mms
where x and y are given in millimeters. Determine the velocity of a particle at point (2,4)
and the position of the particle at t
0s.
2.15
A fluid is placed in the area between two parallel plates. The upper plate is movable and
connected to a weight by a cable. Calculate the velocity of the plate for (a) the fluid between
the plates is water; (b) the fluid between the plates is blood (assumed to have no yield
stress); and (c) the fluid between the plates is blood with a yield stress of 50 mPa. For all
cases take the mass to be 10 g, the height between the plates to be 10 mm and the contact
area to be 0.5 m
2
.
5
6s of the particle that is located at (2,4) at t
5
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