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Problem *3.120
[Difficulty: 2]
ω
= 1000 s
1
r
2
r
1
= 50 mm
r
1
r
2
= 130 mm
ρ
Given:
Test tube with water
Find:
(a) Radial acceleration
(b) Radial pressure gradient
(c) Rotational speed needed to generate 250 MPa pressure at the bottom of the tube
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) Rigid body motion
(3) Radial direction is horizontal
For rigid body motion:
a
r
V
2
r
−
=
r
ω
⋅
()
2
r
−
=
r
−
ω
2
⋅
=
a
r
r
−
ω
2
⋅
=
2
ω
r
r
p
=
∂
∂
In addition, since r is horizontal:
g
r
0
=
Thus, the hydrostatic equation becomes:
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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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