Buoyancy – why things float
L-14 Fluids [3]
•ReviewÆ fluid statics
–Pascal’s Principle
–Why things float
•Fluids in Motion Æ Fluid Dynamics
–Hydrodynamics
–Aerodynamics
TITANIC
• The trick is to keep the water on the outside of
the ship, and
• to avoid hitting icebergs (which also float), and
• are easy to miss since 90 % of it is submerged.
Buoyant Force FB
The area of the hole in the Titanic’s bow
was just over a square meter.
It sank in 160 minutes.
Pressure increases with depth
submerged object
that has a mass
density ρO
PTopA
F=P⋅A
h
PBottomA
Archimedes’ Principle
• PBottomA > PTopA
FB
W
• A buoyant force FB equal to the
weight of displaced water is
exerted on a submerged object.
• The object sinks to the level
where FB = W
• every liter of water displaced
provides a buoyant force of 10 N
W
The density of the
water is ρW
Archimedes principle
The buoyant force on an object in
a fluid equals the weight of the
fluid which it displaces.
– this works for objects in water
– helium balloons (density of He = 0.18 kg/m3,
about 7 times less dense than air)
– hot air balloons Æ the density of
hot air is lower than the density of cool
air so the weight of the cool air that is
displaced is higher than the weight
of the balloon
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Will it float?
• The buoyant force is always there whether the
object floats or not
• The object will float if the buoyant force is
enough to support the object’s weight
• The object will displace just enough water so
that the buoyant force = its weight
• If it displaces as much water as possible and this
does not equal its weight, it will sink.
• Objects that have a density less than water will
always float- when fully submerged, they weigh
less than the water, so the water supports them
• water weighs about 10 N per liter
Floating objects
lighter object
Oil Tankers
• An object having a volume of 6 liters and weighing
W = 30 N is placed in a tank of water. What will
happen? Will it sink? Will it float? What fraction of
its volume will be submerged if it floats?
• If the object were completely submerged, the
buoyant force would be
FB, max = 10N/liter x 6 liters = 60 N
W
too heavy
The weight of displaced
water is less than the
weight of the object
example problem
• thus, the object will float with half of its volume
submerged, so that FB = W = 30 N
heavier object
empty
tanker
full
tanker
FB
Floating in a
cup of water
Only a thin layer of
water around the hull
is needed for the ship
to float!
Why does ice float?
• Water, the most plentiful substance on
earth is also one of the most unusual in its
behavior in that it expands when it freezes.
• Since it expands the density of ice is
slightly less than the density of water (917
kg/ m3 as compared to 1000 kg/ m3 for
water). So the part of the iceberg above
the surface is less than 10% of the total
volume.
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Place your bets!
ice cube
When the ice cube melts will:
1)the water spill out, or
2)the water level stay the same, or
3)the level go down ????????
Answer: The level stays the same.
Ice is less dense than water, so that
the volume occupied by the ice is
exactly big enough to hold the
volume of melted water that was
not submerged!
fluid flow example – leaky cup
Pressure increases
with depth, so the
speed of water leaking
from the bottom hole is
larger than that from the
higher ones.
Volume flow rate
• If the water comes out of a tube of cross
sectional area A with a flow speed u the
volume flow rate is
• volume flow rate = u × A (m/s ×m2)
m3/s
• To measure u just see how long it takes to
fill a gallon jug from a hose and measure
the diameter of the hose.
Fluid Flow
• The physics of fluid
flow was worked out
by Daniel Bernoulli
• He was born in
Switzerland in 1700
• He was one of 5
brothers and came
from a large family of
mathematicians and
scientists.
How do we measure fluid flow?
• We see how much comes out
in some time interval
• Time how long it takes to fill the
bucket, say 30 seconds
• the flow rate is then 1 bucket
say per 30 seconds
• in other words volume per unit
time
• gallons per min (gpm), liters/s,
cubic feet per min (cfm), gpf,
or m3/s Å volume flow rate
Mass flow rate
• We could also measure how much mass
comes out per unit time – kg/s for example
• if you are using a fluid of density ρ coming
out of a hose of cross sectional area A
with speed v the mass flow rate is
• mass flow rate = ρ × u × A
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What makes water flow?
• gravity
• by placing the water
up high the pressure
at the bottom is high
enough to supply
water to all parts of
town that are lower
than the tower
Pressure differences
P2
P1
a pressure difference must be established
across the ends of the pipe to push the water
along. Æ P2 must be greater than P1
This pressure difference can be set up by
a water pump.
Stanton, IA
Montgomery Co.
Water does not disappear!
Continuity of flow
• If water goes in one end of a pipe it must
come out the other end (if there are no
leaks of course. Sounds obvious, but it has
a number of interesting consequences!
• since whatever goes in must come out we
have that the incoming flow rate –
outgoing flow rate or
• v1 A1 = v2 A2
• thus the fluid in the narrow part of the tube
must flow FASTER that the fluid on the
left.
• Cardiologists use this to determine if
arteries might be clogged.
This applies to pipes that have constrictions also.
v1, A1
v2, A2
Other examples - the nozzle effect
• you use this principle
whenever you hold
your finger over the
end of the hose to
make the water spray
farther.
An amazing thing about
moving fluids
• The pressure in a moving fluid is less
than the pressure in a fluid at rest! Æ
this is Bernoulli's principle.
• Where a fluid moves faster its pressure is
lower, where it moves slower, its pressure
is higher.
• As we will see, this is the principle that
makes airplanes work.
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The Venturi Meter
Bernoulli applies
to household
plumbing too!
wind
roof
air vent
When the wind is
really blowing, watch
the water level in the
toilet go up and down
sewer
Prairie dogs know how to use
Bernoulli's principle
“atomizers”
• fine droplets of liquid (not
atoms) are sprayed from this
device using the Bernoulli
effect
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