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Motion of Fluid Particles
Author: John M. Cimbala, Penn State University
Latest revision: 20 September 2007
A fluid particle can undergo four different types of motion, which we express as rates:
rate of translation
,
rate of
dilatation
,
rate of shear strain
, and
rate of rotation
. The diagram below illustrates all four of these simultaneously
for motion in the 2D
x
1

x
2
plane. The concepts can easily be extended to three dimensions. Let point P be the fluid
particle, with neighbor particles A and B initially at infinitesimal distances
δ
x
1
to the right, and
x
2
to the top of
point P, respectively. The velocity components are shown. The locations of particles P, A, and B are shown both at
time
t
and at some infinitesimal time later,
t
+
dt
, where they are denoted by primes.
x
1
x
2
P
A
B
u
1
u
2
P
′
A
′
B
′
time t
time t + dt
u
1
dt
x
1
x
2
u
2
+
u
2,2
x
2
u
1
+
u
1,2
x
2
u
2
+
u
2,1
x
1
(
u
2
+
u
2,1
x
1
)
dt
u
1
+
u
1,1
x
1
(
u
1
+
u
1,1
x
1
)
dt
u
2
dt
(
u
2
+
u
2,2
x
2
)
dt
(
u
1
+
u
1,2
x
2
)
dt
Rate of translation
The rate of translation of point P is simply the change in location divided by the time period. In the
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This note was uploaded on 07/23/2008 for the course ME 521 taught by Professor Cimbala during the Fall '07 term at Penn State.
 Fall '07
 CIMBALA

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