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Problem *3.119
[Difficulty: 2]
R
c
ω
d
Given:
Centrifugal manometer consists of pair of parallel disks that rotate to develop a
radial pressure difference. There is no flow between the disks.
Find:
(a) an expression for the pressure difference,
∆
p, as a function of
ω
, R, and
ρ
.
(b) find
ω
if
∆
p = 8 μm H2O and R = 50 mm
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 in radial direction)
Assumptions:
(1) Incompressible fluid
(2) Standard air between disks
(3) Rigid body motion
(4) Radial direction is horizontal
For rigid body motion:
a
r
V
2
r
−
=
r
ω
⋅
()
2
r
−
=
r
−
ω
2
⋅
=
In addition, since r is horizontal:
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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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