Physics 5B
L
Lecture
22, JJanuary11,
11 2011
Chapter
13, Fl
Fluids
Ch t 13
id
Pressure
Which container has the largest pressure at the bottom? Assume
that each container holds the same volume of water.
2
Two Dams
A
B
Two dams of equal height and area prevent
water from entering the basin. Compare the
magnitudes of the net forces due to the water
on the two dams.
B) FA=FB
C) FA< FB
A) FA > FB
33
Three glass jars have equal weight but different shapes.
shapes. They
are filled to equal depth with water.
water. Which filled jar weighs
the most? (The jars’ bases are of equal size.
size.)
A. Filled jar A
B. Filled jar B
C. Filled jar C
D The
D.
Th three
h
jars
j weigh
i h the
h same.
4
Three glass jars have equal weight and equallyequally-sized bases but
diff
t shapes.
h
Th are filled
fill d to
t equall depth
d th with
ith water.
t . Which
Whi h
different
shapes
. They
water
filled jar has the greatest force exerted by the fluid on the base?
A. Filled jar A
B. Filled jar B
C. Filled jar C
D The
D.
Th three
h
jars
j have
h
equall forces
f
exerted
d on their
h i bbases.
5
Note that for Jars A and B there are vertical forces exerted by the
fluid on the walls as well as on the base
base.. The total vertical force
exerted by the fluid will be equal to the weight of the fluid, but you
have to include the vertical components of the forces on the walls
when calculating that total
total..
6
Pascal’ss Principle
Pascal
If an external
t
l pressure iis applied
li d tto a confined
fi d
fluid, the pressure at every point within the
fluid increases by that amount.
amount
This occurs because a difference in pressure will cause
fluid to flow from high pressure regions to low
pressure regions (unless another force, such as gravity,
maintains the
h pressure difference).
d ff
) When
Wh
the
h fluid
fl d
reaches equilibrium the pressure will be constant
g
the fluid ((at a ggiven height,
g in case ggravityy is
throughout
present).
Pascal’ss Principle
Pascal
Pin  Pout
What is the work
required to lift the car
a height h?
d
=M g
M
h
Pascal’ss principle demo
Pascal
Hydraulic Jack
Example
In working out his principle, Pascal showed dramatically how force can
be multiplied with fluid pressure. He placed a long, thin tube of radius
rr=0.003
0.003 m vertically into a wine barrel of radius R
R=0.21
0.21 m. He found
that when the barrel was filled with water and the tube filled to a
height of 12 m, the barrel burst. Calculate (a) the mass of water in the
tube, and ((b)) the net force exerted byy the water in the barrel on the lid
just before rupture.
Archimedes’
Archimedes Principle
FB is the “buoyant force” = the net force
of the water pressure on the rock.
water
water
rock
Imaginary
g
y surface
identical to the
rock’s surface
Archimedes’
Archimedes Principle
FB is the “buoyant force” = the net force
of the water pressure on the rock.
The buoyant force on an object
immersed in a fluid (or floating in
a liquid) is equal in magnitude to
the weight
g of the fluid “displaced”
p
by the object.
Archimedes’
Archimedes Principle Demo
Example problem
While vacationingg at the Outer Banks of North
Carolina, you find an old coin that looks like it is made
of gold. You know there were many shipwrecks there,
so you take the coin home to check the possibility of it
being gold. You suspend the coin from a spring scale
and find that it has a weight in air of 49.7 g. You then let
the
h coin hang
h
submerged
b
d in a glass
l
off water and
d find
f d
that the scale reads 47.1 g. Should you get excited
about the ppossibilityy that this coin might
g reallyy be ggold?
Density of Au= 19,300 kg/m3
(s g of Au=19.3)
(s.g.
Au=19 3)
Which weighs
g more?
Since the shipp is
floating, its buoyant
force must be exactly
equal and opposite to
its weight.
A. A large bathtub filled to the
brim with water.
B A large bathtub filled to the
B.
brim with water with a battleship floating in it.
Tub of water + ship
C. They will weigh the same.
D. It is impossible to know
without knowingg what is inside
the battleship.
Tub of water
Overflowed water
(Don’t include the weight of the overflowed water.)
Ice cube riddle
A cube of fresh
fresh--water ice is floating in a glass of fresh water
that is filled upp exactlyy to the rim. As the ice melts,
Volume of
water
displaced
Just as for the battleship, the ice
cube weighs exactly as much as
the water displaced
displaced, so when it
melts into water, it will fill exactly
the volume of the water
displaced.
wate overflows
water
ove ows the
t e rim..
B. no water overflows, and the water level
doesn’tt change
doesn
change.
C. the water level drops.
A..
Ice cube riddle
Volume of
water
displaced
Here is a longer explanation:
• The ice cube is floating, so it’s buoyant force exactly counteracts its weight.
• From Archimedes'
Archimedes principle the buoyant force is also equal to the weight of the
water displaced, i.e. the volume enclosed by the red box above.
• Therefore, from the two points above we conclude that the weight of the ice
cube is exactly equal to the weight of water displaced.
• Now, when the ice melts it turns into an equal weight of water (no mass is lost
during the melting). So the ice cube melts into water of weight exactly equal
to the weight of water displaced.
• The melted ice is pure water
water, and two equal masses of pure water will have
equal volumes, so the melted ice will fill with water the red volume, exactly.
The water level does not change, and no water overflows.