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The NavierStokes Equation
The Taxonomy of Fluid Dynamics
•
Valid for any fluid
•
( )
()
ij
V
VV
g
t
ρ
ρσ
∂
+∇⋅
=
∂
r
rr
r
r
r
The Cauchy Equation
Inviscid Flow
•
Nonlinear
•
Viscous terms drop out
•
Bernoulli equation valid
along streamlines
•
Euler equation
•
DV
P
g
Dt
=−∇ +
r
r
r
•
Valid for
Newtonian
fluid only
•
2
DV
P
gV
Dt
ρρ
µ
= −∇
+
+
∇
r
r
r
r
Irrotational Flow
•
Linear
•
Viscous terms drop out
•
Bernoulli equation valid
everywhere
•
Superposition valid
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This note was uploaded on 07/23/2008 for the course ME 33 taught by Professor Cimbala during the Fall '05 term at Pennsylvania State University, University Park.
 Fall '05
 CIMBALA
 Fluid Dynamics

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