MEDE3005 – TRANSPORT PHENOMENA IN
BIOLOGICAL SYSTEMS
2008 – 2009 Academic Year
Part I (11 hours, Dr. K. W. Chow) – Governing Equations of Fluid
Dynamics
(A) Elementary concepts of fluid flows
Dependence on space and time
(1) Conditions in a body of fluid can vary from point to point and, at any given
point, can vary from one moment of time to the next. A flow is
uniform
if the
velocity at a given instant is the same in magnitude and direction at every point
in the fluid. If at any instant in time, the velocity changes from point to point,
the flow is
non–uniform
.
(2) A flow is
steady
if the fluid properties, e.g. velocity and pressure, at any
given point do not change with time. A flow which is not steady, i.e. with time
dependent properties, is termed
unsteady
.
(3) Note that all these combinations are possible:
(a) Steady uniform flows – flow properties independent on position and time;
(b) Steady non–uniform flows – flow properties independent of time but
depending on position;
(c) Unsteady uniform flows – flow properties independent of position but
depending on time;
(d) Unsteady non–uniform flows – flow properties depending on both position
and time.
Real and ideal fluids
(4) When a real fluid flows past a boundary, the fluid immediately in contact
with the boundary will have the same velocity as the boundary (the
no slip
boundary condition
, or friction will not permit a relative motion along the
boundary). In most problems encountered in practice, this boundary is taken to
be at rest.
(5) A frictionless fluid which permits sliding along the boundary will be termed
an
ideal fluid
.
1
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(6) In practice, the no slip condition must be enforced. A thin portion of fluid
around the boundary, termed the boundary layer, will be the region where
viscous effects are the largest. This is also the region where drag force,
momentum transfer and energy loss are important considerations. Tremendous
efforts have been spent over the years to understand this dynamics, and we shall
attempt a brief introduction later this course.
Compressible and incompressible flows
(7) If the density of a fluid does not change in the flow, the fluid is
incompressible
(otherwise,
compressible
). In practice, a liquid can be taken as
incompressible. The dynamics of a gas will usually require compressible effects
to be taken into account. However, as a working rule, a gas can still be treated
as almost incompressible if the Mach number is small (about 0.1 or 0.2). The
Mach number is the ratio of flow speed to the local sound speed. Given sound
speed in air as roughly 340 m s
–1
, it is remarkable that a gas is still roughly
incompressible for a speed as fast as say 40 m s
–1
. Compressibility must be
considered when the Mach number reaches say 0.4 or 0.5.
One, two and three
(1D, 2D, 3D)
dimensional flows
(8) A flow is termed 1D, 2D or 3D if the flow depends on one, two or three
spatial coordinates respectively.
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 Spring '12
 Fluid Dynamics, Velocity, Incompressible Flow

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