Problem 8.14
[3]
Given:
Hydrostatic bearing
Find:
Required pad width; Pressure gradient; Gap height
Solution:
For a laminar flow (we will verify this assumption later), the pressure gradient is constant
p x
( )
p
i
1
2 x
⋅
W
−
⎛
⎜
⎝
⎞
⎟
⎠
⋅
=
where p
i
= 700 kPa is the inlet pressure (gage)
Hence the total force in the y direction due to pressure is
F
b
x
p
⌠
⎮
⎮
⌡
d
⋅
=
where b is the pad width into the paper
F
b
W
2
−
W
2
x
p
i
1
2 x
⋅
W
−
⎛
⎜
⎝
⎞
⎟
⎠
⋅
⌠
⎮
⎮
⎮
⌡
d
⋅
=
F
p
i
b W
⋅
2
⋅
=
This must be equal to the applied load F.
Hence
W
2
p
i
F
b
⋅
=
W
2
m
2
700
10
3
×
N
⋅
×
50000 N
⋅
m
×
=
W
0.143m
=
The pressure gradient is then
dp
dx
Δ
p
W
2
−
=
2
Δ
p
⋅
W
−
=
2
−
700
10
3
×
N
⋅
m
2
×
1
0.143 m
⋅
×
=
9.79
−
MPa
m
⋅
=
The flow rate is given
Q
l
h
3
12
μ
⋅
−
dp
dx
⎛
⎜
⎝
⎞
⎟
⎠
⋅
=
(Eq. 8.6c)
Hence, for h we have
h
12
μ
⋅
Q
l
⋅
dp
dx
−
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 Fall '08
 ZOHAR
 Fluid Dynamics, Fig, Pressure gradient

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