-
=
主D × V
像变形
旋天
=
栽 列
+
=
变形 →τ= )M( 8)
Equation sheet
1. Cartesian coordinates: ωu = u î + v ĵ + w k̂
• Continuity equation:
εϑ εϑu εϑv εϑw
+
+
+
=0
εt
εx
εy
εz
(1)
• x→momentum:
!
"
! 2
"
εu
εu
εu
εu
εp
ε u ε2u ε2u
ϑ
+u
+v
+w
=→
+ ϑgx + µ
+ 2 + 2
εt
εx
εy
εz
εx
εx2
εy
εz
• y→momentum:
!
"
! 2
"
εv
εv
εv
εp
ε v
ε2v ε2v
εv
ϑ
+u
+v
+w
=→
+ ϑgy + µ
+
+
εt
εx
εy
εz
εy
εx2 εy 2 εz 2
• z→momentum:
!
"
! 2
"
εw
εw
εw
εw
εp
ε w ε2w ε2w
ϑ
+u
+v
+w
=→
+ ϑgz + µ
+
+
εt
εx
εy
εz
εz
εx2
εy 2
εz 2
(2)
(3)
(4)
2. Cylindrical coordinates: ωu = ur eˆr + uω eˆω + uz eˆz
• Continuity equation:
εϑ 1 εϑrur
1 εϑuω
εϑuz
+
+
+
=0
εt
r εr
r εϖ
εz
(5)
• r→momentum:
ϑ
!
ϑ
!
u2
εur
εur
uω εur
εur
+ ur
+
→ ω + uz
εt
εr
r εϖ
r
εz
"
#
!
"
$
εp
1 ε
εur
ur
1 ε 2 ur
2 εuω
ε 2 ur
= → +ϑgr +µ
r
→ 2 + 2
→ 2
+
εr
r εr
εr
r
r εϖ2
r εϖ
εz 2
(6)
• ϖ→momentum:
εuω
εuω
uω εuω
ur uω
εuω
+ ur
+
→
+ uz
εt
εr
r εϖ
r
εz
"
#
!
"
$
1 εp
1 ε
εuω
uω
1 ε 2 uω
2 εur
ε 2 uω
=→
+ϑgω +µ
r
→ 2 + 2
+ 2
+
r εϖ
r εr
εr
r
r εϖ2
r εϖ
εz 2
(7)
• z→momentum:
ϑ
!
εuz
εuz
uω εuz
εuz
+ ur
+
+ uz
εt
εr
r εϖ
εz
労が +
"
#
!
"
$
εp
1 ε
εuz
1 ε 2 uz
ε 2 uz
=→
+ ϑgz + µ
r
+ 2
+
εz
r εr
εr
r εϖ2
εz 2
等 たに + + w
崎
功量 程 : を=
職
Jos
9 Vdf
steady >werdt
9 ( ) rdA
-
[FztD
=
J
=
0
9 (vn)udA
1
=
m( Vont
(
=
Vin
u
)}
s= (f 뉴
Hminor
-
(8)
崎 006 Re 法 ) た
些 4 . 4ke ÷ ( 法)
=
-
方
自
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DV
=
( Kl) 让
g