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Problem 2.64
[Difficulty: 3]
Given:
Shockfree coupling assembly
Find:
Required viscosity
Solution:
Basic equation
τ
r
θ
μ
du
dr
⋅
=
Shear force
F
τ
A
⋅
=
Torque
TF
R
⋅
=
Power
PT
ω
⋅
=
Assumptions: Newtonian fluid, linear velocity
profile
δ
V
1
=
ω
1
R
V
2
=
2
(
R
+
δ
)
τ
r
θ
μ
du
dr
⋅
=
μ
∆
V
∆
r
⋅
=
μ
ω
1
R
⋅
ω
2
R
δ
+
()
⋅
−
⎣
⎦
δ
⋅
=
τ
r
θ
μ
ω
1
ω
2
−
R
⋅
δ
⋅
=
Because
δ
<< R
Then
ω
2
⋅
=
FR
⋅
ω
2
⋅
=
τ
A
2
⋅
R
⋅
ω
2
⋅
=
μω
1
ω
2
−
⋅
R
⋅
δ
2
⋅
π
⋅
R
⋅
L
⋅
R
⋅
ω
2
⋅
=
P
2
π
⋅
μ
⋅
ω
2
⋅
ω
1
ω
2
−
⋅
R
3
⋅
L
⋅
δ
=
Hence
μ
P
δ
⋅
2
π
⋅
ω
2
⋅
ω
1
ω
2
−
⋅
R
3
⋅
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.
 Fall '07
 Lear
 Fluid Mechanics, Shear

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