Navier Stokes1
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Transcript of Navier Stokes1
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The Navier-Stokes equations incylindrical coordinates:
If r, , z denote the radial, azimuthal, and axial coordinates, respectively, of a three-
dimensional system of coordinates, and zr vvv ,, denote the velocity components in the
respective direction (incompressible fluid flow), then the equations become:
+
+
+
+
=
+
+
+
2
2
22
2
222
22 2
z
vv
r
v
rr
v
r
v
rr
v
r
pF
z
vv
r
vv
r
v
r
vv
t
v rrrrrr
r
z
rr
r
r
+
+
+
+
+
=
++
+
+
2
22
2
222
2
2
z
vv
r
v
rr
v
r
v
rr
vp
rF
z
vv
r
vvv
r
v
r
vv
t
vr
z
r
r
+
+
+
+
=
+
+
+
2
2
2
2
22
2
z
vv
rr
v
rr
v
z
pF
z
vv
v
r
v
r
vv
t
vzzzz
z
z
z
zz
r
z
!
=
+
++
z
vv
rr
v
r
vzrr
