L-14 Fluids [3]

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L-14 Fluids 3

• Why things float
• Fluids in Motion ? Fluid Dynamics
• Hydrodynamics
• Aerodynamics

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Buoyancy why things float
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.

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Buoyant Force
Pressure increases with depth
submerged object that has a mass density
?O The density of the water is ?W
PTopA
F P ? A
h
W
PBottomA
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Archimedes Principle

• PBottomA gt PTopA
• 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

FB
W
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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 ? 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 objects 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 match 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

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Floating objects
lighter object
heavier object
too heavy
The weight of displaced water is less than
the weight of the object
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example problem

• 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? If
  it floats, what fraction of its volume will be
  submerged?
• If the object were completely submerged, the
  buoyant force would beBmax 10N/liter x 6
  liters 60 N
• thus, the object will float with half of its
  volume submerged, so that B W 30 N

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Oil Tankers
empty tanker
full tanker
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Floating in a cup of water
Only a thin layer of water around the hull is
needed for the ship to float!
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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!

• When the ice cube melts will
• the water spill out, or
• the water level stay the same, or
• the level go down ????????

ice cube
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!
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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.

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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.
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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 ? volume flow rate

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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)
• To measure u just see how long it takes to fill a
  gallon jug from a hose and measure the diameter
  of the hose.

m3/s
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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 ? coming out
  of a hose of cross sectional area A with speed v
  the mass flow rate is
• mass flow rate ? ? 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

Stanton, IA Montgomery Co.
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Pressure differences
P2
P1
a pressure difference must be established across
the ends of the pipe to push the water along. ?
P2 must be greater than P1 This pressure
difference can be set up by a water pump.
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Water does not disappear!

• 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!

This applies to pipes that have constrictions
also.
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Continuity of flow

• 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.

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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.

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An amazing thing about moving fluids

• The pressure in a moving fluid is less than the
  pressure in a fluid at rest! ? 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
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roof
Bernoulli applies to household plumbing too!
wind
air vent
When the wind is really blowing, watch the water
level in the toilet go up and down
sewer
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Prairie dogs know how to useBernoulli's principle
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atomizers

• fine droplets of liquid (not atoms) are sprayed
  from this device using the Bernoulli effect

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END HERE
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Hot air balloon

• The ideal gas law tells is that when a gas is
  heated, its density goes down
• so the air density inside the balloon is less
  than the density of cold air on the outside.
• The cold air exerts an upward buoyant force on
  the balloon.