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# ECUACIONES DIFERENCIALES EN COORDENADAS CILINDRICAS

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```Appendix D ​Equations ​of Motion ​in
Cylindrical Coordinates
The ​equations ​of ​motion ​of ​an ​incompressible ​newtonian ​fluid ​with ​constant u​, ​k​,
a​nd ​C​, ​are ​given ​here ​in ​cylindrical ​coordinates ​(r​ ,​ 0
​ ​, ​2​)​, ​which ​are ​related
to ​cartesian ​coordinates ​(​x​, ​y​, z​ ​) ​as ​in ​Fig​. ​4​.​2​:
(​D​.1
​ ​)
The ​velocity ​components ​are ​v​, Vy​, ​and ​v​.​.
Here ​are the ​equations​: ​Continuity​:
-​-​(​ru​) ​+
-​(​1​)
+
(​V​_​)
= ​0
(​D​.​2
)
Convective ​time ​derivative​:
V​. V
​ ​=
+​-​Vo
Laplacian ​operator​:
(​D​.
3​)
-​+ ​TT
(​D​.​4
)
The ​r​-​momentum
equation​:
The ​6​-momentum
equation​:
se ​pot ​v ​= ​v​) ​=​= v
​ ​ă ​este ​gat ​got ​ofvir​, ​ ​&gt;​=
2 ​(​.​5) ​heyat (​ ​v • ​Povo ​+ ​twins ​- + o
​ ​fv​*​,
- ​(​0.​9​)
+ ​(​VV​)​, ​-​UV
1 ​op ​+ ​?
+ ​8 ​+ ​viv
—
+
The ​z​-​momentum
equation​:
p​r
do
​
+ ​go ​+
vyʻu​.
(​D​.
7​)
The ​energy
equation​:
+ ​m2​(​+
+
+
+
+ ​€​]
(0​.​8)
where
eu
vou
(​D​.
9​)
Viscous ​stress ​components​:
T​o​y ​=
2ue
​ r
Tr​e ​=
LE
​ NO ​Angular
components​:
​velocity
T​oo =
​
2u​en ​To
Tx ​= ​2​u​e​: ​T ​E ​= ​pl​e​,
= ​PLEA
(​D​.1
​ 0
)
(​D​.​1
1​)
```