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Problem 2.46
[Difficulty: 2]
Given:
Block moving on incline on oil layer
Find:
Speed of block when free, pulled, and pushed
f
θ
N
x
x
U
y
d
W
Solution:
Governing equations:
τ
yx
μ
du
dy
⋅
=
Σ
F
x
Ma
x
⋅
=
Assumptions:
Laminar flow
The given data is
M1
0
k
g
⋅
=
WM
g
⋅
=
W
98.066 N
=
w
250 mm
⋅
=
d
0.025 mm
⋅
=
θ
30 deg
⋅
=
F7
5
N
⋅
=
μ
10
1
−
Ns
⋅
m
2
⋅
=
Fig. A.2 SAE 1039 @30
o
C
Equation of motion
Σ
F
x
x
⋅
=
0
=
so
Ff
−
W sin
θ
()
⋅
−
0
=
The friction force is
f
τ
yx
A
⋅
=
μ
du
dy
⋅
A
⋅
=
μ
U
d
⋅
w
2
⋅
=
Hence for uphill motion
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 Fall '07
 Lear
 Fluid Mechanics

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