Problem *3.128
[Difficulty: 4]
x
r
o
θ
r
i
y
Given:
A steel liner is to be formed in a spinning horizontal mold. To insure uniform thickness
the minimum angular velocity should be at least 300 rpm.
For steel, SG = 7.8
Find:
(a) The resulting radial acceleration on the inside surface of the liner
(b) the maximum and minimum pressures on the surface of the mold
(gravity is
downward in
this diagram)
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)
θ
a
g
p
r
=
+
∂
∂
−
1
(Hydrostatic equation transeverse component)
z
z
a
g
z
p
=
+
∂
∂
−
(Hydrostatic equation z component)
Assumptions:
(1) Incompressible fluid
(2) Rigid body motion
a
r
V
2
r
−
=
r
ω
⋅
()
2
r
−
=
r
−
ω
2
⋅
=
a
θ
0
=
a
z
0
=
g
r
g
−
cos
θ
⋅
=
g
θ
g sin
θ
⋅
=
g
z
0
=
Hence:
a
r
4in
⋅
300
rev
min
×
2
π
⋅
rad
⋅
rev
×
min
60 s
⋅
×
⎛
⎝
⎞
⎠
2
×
ft
12 in
⋅
×
=
a
r
329
ft
s
2
⋅
=
a
r
10.23 g
⋅
=
ω
cos
2
g
r
a
g
r
p
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 Fall '07
 Lear
 Fluid Mechanics

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