In class, Monday, September 28, 2009
Professor Philip S. Marcus
ME 106
Midterm Exam I
The large tank in the Figure is filled with a static fluid with a density
ρ
(
z
) that is linear
in the vertical direction
z
:
ρ
(
z
) =
a
+
b z
, where
a
and
b
are constants. Gravity
g
points
in the downward (

ˆ
z
) direction. The unit vector ˆ
y
points into the paper. Attached to the
interior of the left wall is a suction cup, inside of which there is a vacuum, so the pressure
inside the suction cup is zero. The shape of the suction cup is quite irregular, and I have
lost the equation used to generate it! However, I do know that the volume of the vacuum
inside the suction cup has a value of
V
. I also remember that the suction cup is symmetric
with respect to the
x
–
y
plane at
z
= 0. (That is, if we put a mirror in the
x
–
y
plane at
z
= 0, the image of the top of the suction cup in the mirror looks exactly like the bottom of
the suction cup.) The crosssectional area of the vacuum inside the suction cup in the
x
–
y
plane at
z
= 0 is
AA
. The total surface area of the suction cup is
AAA
. I also remember the
values of
A
0
≡
integraltext
S
dy dz
,
A
2
≡
integraltext
S
z
2
dy dz
, and
A
3
≡
integraltext
S
z
3
dy dz
, where
S
is that portion of
the area of the leftedge wall that is exposed to the vacuum (i.e., covered by the suction cup).
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 Fall '08
 Morris
 Buoyancy, Fundamental physics concepts, Professor Philip S. Marcus

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