Biomedical Engineering Reference
In-Depth Information
Interpret the stated results: why
D
=
0
is obtained for the given flow field
2
and what is the physical meaning of
q
=−
α
r
?
13.6 An incompressible Newtonian fluid (density
) is located in a
cavity (rectangular) with a cross section as given in the figure:
ρ
, viscosity
η
−
a
≤
x
≤
a
,
−
b
≤
y
≤
b
. Because the top wall closing the cavity is translating in the
V
y
z
2
b
x
2
a
x
-direction with velocity
V
, a stationary (two-dimensional) fluid flow (in
the shape of a vortex) will develop in the cavity:
v
x
=
v
x
(
x
,
y
),
v
y
=
v
y
(
x
,
y
),
v
z
=
0. No slip conditions hold at all walls of the cavity (moving
as well as stationary).
Which inconsistency ('something leading to contradiction') can be
observed in the above given problem definition?
13.7 A compressible medium (for example a gas) is forced in the
x
-direction
through a contraction (see figure). With respect to the components of the
x
velocity field
∼
of the medium, defined in the Cartesian
xyz
-coordinate sys-
tem, it is assumed that
v
x
only depends on
x
, thus
v
x
=
v
x
(
x
), completed
with
v
y
=
0.
Why is it impossible that this assumption is correct?
v
z
=
13.8
In the neighbourhood of the origin of a Cartesian
xyz
-coordinate system
the stationary (two-dimensional) flow field in an incompressible Newtonian
fluid (with density
ρ
) can be described as
v
=
α
(
−
y
e
x
+
x
e
y
) with
α
a constant.
