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Problem 2.43
[Difficulty: 2]
Given:
Velocity profile
Find:
Plot of velocity profile; shear stress on surface
Solution:
The velocity profile is
u
ρ
g
⋅
μ
hy
⋅
y
2
2
−
⎛
⎜
⎝
⎞
⎠
⋅
sin
θ
()
⋅
=
so the maximum velocity is at y = h
u
max
ρ
g
⋅
μ
h
2
2
⋅
sin
θ
⋅
=
Hence we can plot
u
u
max
2
y
h
1
2
y
h
⎛
⎝
⎞
⎠
2
⋅
−
⎡
⎢
⎣
⎤
⎥
⎦
⋅
=
0
0.25
0.5
0.75
1
0.25
0.5
0.75
1
u/umax
y/h
This graph can be plotted in
Excel
The given data is
h
0.1 in
⋅
=
μ
2.15
10
3
−
×
lbf s
⋅
ft
2
⋅
=
θ
45 deg
⋅
=
Basic equation
τ
yx
μ
du
dy
⋅
=
τ
yx
μ
du
dy
⋅
=
μ
d
dy
⋅
ρ
g
⋅
μ
⋅
y
2
2
−
⎛
⎜
⎝
⎞
⎠
⋅
sin
θ
⋅

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