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ME 330 Fluid Mechanics
Spring 2007
Department of Engineering
Western Kentucky University
CHAPTER 3D HW  Homework Solutions
Problem #’s 373, 385, and 388, Due February 16, 2007
373
Solution
A retaining wall against mud slide is to be constructed by rectangular
concrete blocks. The mud height at which the blocks will start sliding, and the blocks will
tip over are to be determined.
Assumptions
Atmospheric pressure acts on both sides of the wall, and thus it can be
ignored in calculations for convenience.
Properties
The density is given to be 1800 kg/m
3
for the mud, and 2700 kg/m
3
for
concrete blocks.
Analysis
(
a
) The weight of the concrete wall per unit length (
L =
1 m) and the friction
force between the wall and the ground are
N
1271
)
N
4238
(
3
.
0
N
4238
m/s
kg
1
N
1
)
m
1
8
.
0
2
.
0
)[
m/s
81
.
9
)(
kg/m
2700
(
block
friction
2
3
2
3
block
=
=
=
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⋅
×
×
=
=
W
F
g
W
μ
ρ
V
The hydrostatic force exerted by the mud to the wall is
( )
()
(
)
avg
32
2
2
2
1 N
1800 kg/m
9 81 m/s
2 (1
)
1 kg m/s
8829
N
Hx
C
FF
P
Ag
h
h
/
A
.h
/
h
h
ρρ
==
=
=
⎛⎞
=×
⎜⎟
⋅
⎝⎠
=
Setting the hydrostatic and friction forces equal to each other gives
m
0.38
=
→
=
→
=
h
h
F
F
H
1271
8829
2
friction
(
b
) The line of action of the hydrostatic force passes through the pressure center, which is
2
h
/3 from the free surface. The line of action of the weight of the wall passes through the
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