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ME 521
Fall 2007
Professor John M. Cimbala
Lecture 09
09/17/2007
Today, we will
:
•
Derive the constitutive equation for a Newtonian fluid
•
Discuss the NavierStokes equation
•
If time, begin some example problems
Recall
Cauchy’s equation of motion
:
ij
i
i
j
ii
j
j
Du
g
Dt
x
uu
u
tx
ρρ
τ
∂∂
∂
=+
+
∂
∂
=
∂
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: The integral and differential equations of mass conservation and linear momentum
Conservation of Mass:
Integral form
:
CV
CS
0
ii
du
d
A
t
ρ
∂
=+
∂
∫∫
v
V
Differential form
:
()
0
i
i
u
tx
∂∂
+=
The Linear Momentum Equation:
Integral form
:
i
ij
j
i
i
j
j
u
u
d
A
g
d
d
A
t
ρρ
τ
∂
+
∂
∫
∫
vv
VV
Differential form
:
j
i
i
j
jj
uu
u
g
x
∂
+
∂
(conservative)
i
j
j
Du
g
Dt
x
ρτ
∂
∂
(nonconservative)
The Constitutive Equation for a Newtonian Fluid:
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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 Pennsylvania State University, University Park.
 Fall '07
 CIMBALA

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