Problem 3.5
[Difficulty: 2]
Given:
Data on system
Find:
Force on bottom of cube; tension in tether
Solution:
Basic equation
dp
dy
ρ
−
g
⋅
=
or, for constant
ρ
Δ
p
ρ
g
⋅
h
⋅
=
where h is measured downwards
The absolute pressure at the interface is
p
interface
p
atm
SG
oil
ρ
⋅
g
⋅
h
oil
⋅
+
=
Then the pressure on the lower surface is
p
L
p
interface
ρ
g
⋅
h
L
⋅
+
=
p
atm
ρ
g
⋅
SG
oil
h
oil
⋅
h
L
+
(
)
⋅
+
=
For the cube
V
125 mL
⋅
=
V
1.25
10
4
−
×
m
3
⋅
=
Then the size of the cube is
d
V
1
3
=
d
0.05m
=
and the depth in water to the upper surface is
h
U
0.3 m
⋅
=
Hence
h
L
h
U
d
+
=
h
L
0.35m
=
where h
L
is the depth in water to the lower surface
The force on the lower surface is
F
L
p
L
A
⋅
=
where
A
d
2
=
A
0.0025m
2
=
F
L
p
atm
ρ
g
⋅
SG
oil
h
oil
⋅
h
L
+
(
)
⋅
+
⎡
⎣
⎤
⎦
A
⋅
=
F
L
101
10
3
×
N
m
2
⋅
1000
kg
m
3
⋅
9.81
×
m
s
2
⋅
0.8
0.5
×
m
⋅
0.35 m
⋅
+
(
)
×
N s
2
⋅
kg m
⋅
×
+
⎡
⎢
⎢
⎣
⎤
⎥
⎥
⎦
0.0025
×
m
2
⋅
=
F
L
270.894N
=
Note: Extra decimals needed for computing T later!
For the tension in the tether, an FBD gives
Σ
F
y
0
=
F
L
F
U
−
W
−
T
−
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 Fall '07
 Lear
 Fluid Mechanics, Trigraph, g⋅ SGoil⋅ hoil

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