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MEEN 344: Section 502
HW Problem Set #2 Solutions
1
A hollow metal cube with sides 100 mm floats at the interface between a layer of water
and a layer of SAE 10W oil such that 20% of the cube is exposed to the oil.
What is the
pressure difference between the upper and the lower horizontal surfaces?
What is the
average density of the cube?
Solution
The pressure difference is obtained by applying the equation
)
(
1
2
1
2
h
h
g
P
P
−
=
−
ρ
Suppose
P
U
and
P
L
are the upper and lower pressures,
P
o
is the oil free surface pressure,
H
is the depth of the interface, and
d
is the cube size then
)
2
.
0
(
10
d
H
g
P
P
W
SAE
o
U
−
⋅
⋅
=
−
d
g
H
g
P
P
Water
W
SAE
o
L
8
.
0
10
⋅
⋅
+
⋅
⋅
=
−
Pressure difference between upper and lower surfaces =
Δ
P = P
L
P
U
Subtracting equations gives:
d
g
d
g
P
P
Water
W
SAE
U
L
8
.
0
2
.
0
10
⋅
⋅
+
⋅
⋅
=
−
From Table A.2:
SG
SAE10W
= 0.92 and since
ρ
Water
= 999 kg/m
3
Ρ
SAE10W
= (0.92)(999 kg/m
3
) =919.1 kg/m
3
Using d = 100mm = 0.1m and g = 9.81 m/s
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 Fall '08
 SCHOBEIRI

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