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physics 2211
MP15: Chapter 15
Due at 5:30pm on Sunday, November 25, 2007
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Floating Cream
In the 1950s, fresh unhomogenized milk in glass bottles was delivered to suburbanites' back doorsteps well before
dawn. When delivered, the milk was thoroughly mixed, so that it appeared homogenized, but anyone rising much after
sunrise would find that the milk had separated, the cream having risen to the top.
Cream and milk are immiscible (like oil and water), and the
total volume of liquid does not change when they separate.
The top part of the bottle was intentionally given a much
smaller diameter than the bottom, so that the cream,
typically 3 percent of the total volume, occupied much more
than 3% of the total vertical height of the milkbottle. For
this problem, assume that the total height of the milk bottle
is
and the depth of the cream layer is
.
Part A
Assume that before separation, the weight of the milk bottle's contents (mixed milk and cream) is
. How does
the combined weight of the milk and cream after separation,
, compare to
?
ANSWER:
Part B
Assume that before separation, the pressure at the bottom of the milk bottle is
. How does the pressure at the
bottom of the milk bottle after separation,
, compare to
?
For simplicity, you may assume that the weight and density of the cream is negligible compared to that of the
milk.
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Part B.1
Pressure when the bottle contents are mixed
For simplicity, assume that the density of the cream is zero, and the density of the rest of the milk is
(in
general, cream is less dense than the rest of the milk). If the cream represents 3 percent of the total volume of the
milk bottle, what is the gauge pressure
at the bottom of the milk bottle when the milk and cream are
homogeneously mixed?
Hint B.1.a
Formula for gauge pressure (at depth h)
Gauge pressure in a fluid of uniform density
is
. This pressure is independent of the shape of the
crosssection of the container.
Part B.1.b
Density of the milk and cream mixture.
If the density of the cream (3% by volume) is zero, and the density of the rest of the milk is
, what is the
density of the milk and cream mixture,
?
ANSWER:
=
Express your answer in terms of
,
, and any physical constants needed.
ANSWER:
=
Part B.2 What is the pressure after the bottle contents have separated
Now compute
, the gauge pressure on the bottom of the milk bottle after the milk and cream have separated.
Assume that the depth of the layer of cream is 20% of the total height of the milk bottle (
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 Fall '08
 DUNCAN
 Physics, Fluid Mechanics, Buoyancy, Archimedes, Assignment Print View

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