FLUID KINEMATICS
F
luid kinematics
deals with describing the motion of fluids without neces
sarily considering the forces and moments that
cause
the motion. In this
chapter, we introduce several kinematic concepts related to flowing
fluids. We discuss the
material derivative
and its role in transforming the con
servation equations from the
Lagrangian description of fluid flow
(following
a
fluid particle
) to the
Eulerian description of fluid flow
(pertaining to a
flow
field
). We then discuss various ways to visualize flow fields—
streamlines
,
streaklines
,
pathlines
,
timelines
, and various surface flow visualization meth
ods. The concepts of
vorticity
,
rotationality
, and
irrotationality
in fluid flows
are then discussed. Finally, we discuss the
Reynolds transport theorem
(
RTT
),
emphasizing its role in transforming the equations of motion from those fol
lowing a
system
to those pertaining to fluid flow into and out of a
control
volume
.
89
CHAPTER
4
OBJECTIVES
When you finish reading this chapter, you
should be able to
■
Understand the role of the
material derivative in
transforming between
Lagrangian and Eulerian
descriptions
■
Distinguish between various
types of flow visualizations
■
Distinguish between rotational
and irrotational regions of flow
based on the flow property
vorticity
■
Understand the usefulness of
the Reynolds transport theorem
Satellite image of a hurricane near the Florida
coast; water droplets move with the air, enabling us
to visualize the counterclockwise swirling motion.
However, the major portion of the hurricane is
actually
irrotational
, while only the core (the eye
of the storm) is
rotational
.
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4–1
■
LAGRANGIAN AND EULERIAN DESCRIPTIONS
The subject called
kinematics
concerns the study of
motion
. In fluid dynam
ics,
fluid kinematics
is the study of how fluids flow and how to describe fluid
motion. From a fundamental point of view, there are two distinct ways to de
scribe motion. The first and most familiar method is the one you learned in
high school physics—to follow the path of individual objects. For example,
we have all seen physics experiments in which a ball on a pool table or a
puck on an air hockey table collides with another ball or puck or with the wall
(Fig. 4–1). Newton’s laws are used to describe the motion of such objects,
and we can accurately predict where they go and how momentum and kinetic
energy are exchanged from one object to another. The kinematics of such ex
periments involves keeping track of the
position vector
of each object,
x
→
A
,
x
→
B
, . . . , and the
velocity vector
of each object,
V
→
A
,
V
→
B
, . . . , as functions of
time (Fig. 4–2). When this method is applied to a flowing fluid, we call it
the
Lagrangian description
of fluid motion after the Italian mathematician
Joseph Louis Lagrange (1736–1813). Lagrangian analysis is analogous to
the (closed)
system analysis
that you learned in your thermodynamics class;
namely, we follow a mass of fixed identity. The Lagrangian description re
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 Fall '10
 Dr.Ra’fatAlWaked
 Fluid Dynamics, Derivative, Acceleration, velocity field, fluid particle

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