(IV) FLUIDS IN MOTION
Fluid motions manifest themselves in many different ways. Some can be described very easily, while
others require a thorough understanding of physical laws. In engineering applications, it is important
to describe the fluid motions as simply as can be justified. It is the engineer's responsibility to know
which simplifying assumptions (e.g., onedimensional, steadystate, inviscid, incompressible, etc)
can be made.
A. Classification of Fluid Flows
1) Uniform flow; steady flow
If we look at a fluid flowing under normal circumstances  a river for example  the conditions (e.g.
velocity, pressure) at one point will vary from those at another point, then we have nonuniform
flow.
If the conditions at one point vary as time passes, then we have unsteady
flow.
Under some circumstances the flow will not be as changeable as this. The following terms describe
the states which are used to classify fluid flow:
Uniform flow
: If the flow velocity is the same magnitude and direction at every point in the flow it is
said to be uniform. That is, the flow conditions DO NOT change with
position
.
Nonuniform
: If at a given instant, the velocity is not the same at every point the flow is nonuniform.
Steady
: A steady flow is one in which the conditions (velocity, pressure and crosssection) may
differ from point to point but DO NOT change with
time
.
Unsteady
: If at any point in the fluid, the conditions change with time, the flow is described as
unsteady.
Combining the above we can classify any flow in to one of four types:
•
Steady uniform flow
. Conditions do not change with position in the stream or with time. An
example is the flow of water in a pipe of constant diameter at constant velocity.
•
Steady nonuniform flow
. Conditions change from point to point in the stream but do not
change with time. An example is flow in a tapering pipe with constant velocity at the inlet 
velocity will change as you move along the length of the pipe toward the exit.
•
Unsteady uniform flow
. At a given instant in time the conditions at every point are the same,
but will change with time. An example is a pipe of constant diameter connected to a pump
pumping at a constant rate which is then switched off.
•
Unsteady nonuniform flow
. Every condition of the flow may change from point to point and
with time at every point. An example is surface waves in an open channel.
You may imagine that one class is more complex than another –
steady uniform
flow is by far the
most simple of the four.
2) One, two, and threedimensional flows
A fluid flow is in general a threedimensional, spatial and time dependent phenomenon:
(,)
rt
urt
vrt
wrt
==
+
+
G
GG
G
G
VV
i
j
k
39
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)
where
is the position vector,
(
,,
rx
y
z
=
G
( )
i
j k
GGG
are the unit vectors in the Cartesian coordinates,
and
(
are the velocity components in these directions.
As defined above, the flow will be
uniform if the velocity components are independent of spatial position
)
uvw
( )
xyz
, and will be steady if
the velocity components are independent of time
t
.
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 Spring '11
 wong
 Fluid Dynamics, fluid flows, Venturi meter, Bernoulli equation

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