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Problem *3.124
[Difficulty: 3]
r
2
V
max
=
ω
r
2
Given:
Gas centrifuge, with maximum peripheral speed Vmax = 950 ft/s contains
uranium hexafluoride gas (M = 352 lb/lbmol) at 620 deg F.
Find:
(a) Ratio of maximum pressure to pressure at the centrifuge axis
(b) Evaluate pressure ratio at 620 deg F.
Solution:
We will apply the hydrostatics equations to this system.
a
g
p
G
G
ρ
=
+
∇
−
Governing Equations:
(Hydrostatic equation)
r
r
a
g
r
p
=
+
∂
∂
−
(Hydrostatic equation radial component)
Assumptions:
(1) Incompressible fluid
(2) Rigid body motion
(3) Ideal gas behavior, constant temperature
2
r
T
R
p
a
r
p
g
r
=
−
=
∂
∂
For rigid body motion:
a
r
V
2
r
−
=
r
ω
⋅
()
2
r
−
=
r
−
ω
2
⋅
=
Thus:
Separating variables and integrating:
p
1
p
2
p
1
p
⌠
⎮
⎮
⌡
d
ω
2
R
g
T
⋅
0
r
2
r
r
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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

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