Download Lecture 13 - Fluids

Goal: To understand liquids
and gasses
Objectives:
1) To understand Pressure
2) To understand Buoyancy
3) To learn about Hydraulics
4) To learn about Surface Tension
5) To understand Phase Transitions
6) To apply this to The atmosphere
7) To learn about Adiabatic tendencies and Boyle’s Law
8) To learn about Bernoulli’s moving air Principle
9) To explore Plasma
Pressure
• When understanding fluids one of the keys
is Pressure.
• Pressure is a measure of the force a fluid
exerts per area.
• Pressure = Force / Area
• Or, Force = Pressure * Area
Earth example
• On the surface of the earth the
atmosphere exerts a pressure of 16
pounds per square inch.
• Why aren’t we crushed by this pressure?
What causes pressure?
• Pressure in reality is the weight of the stuff
above you pressing down on you.
• So, if you weighed a segment of air 1 inch
by 1 inch which went to the top of the
atmosphere that air would weigh 16
pounds.
Off the Deep End
• You dive into the bottom of the deep end
of a swimming pool.
• What happens and why?
Pressure underwater
• Liquid Pressure = the pressure on the surface of
the liquid + weight density * depth
• What about for water?
• The surface has about 1 bar of pressure (the air
pressure at sea level).
• Every 10 meters is about 1 more bar of
pressure.
• So, Pressure = 1.0 * 105 Pascal + Density * Depth * g *1 m2
Pressure Blow out.
• You are probably familiar with the fact that
winds go from high pressure areas to low.
• However, do you understand why?
• Why does this happen?
Water under the dam
• Imagine a dam which is 100 m high.
• What will the pressure on the bottom of
the dam be on the water side?
• How about on the air side?
• What will the pressure halfway up the dam
be?
• Suppose you poked holes in the dam at
those two positions. What would the result
be and why would the two holes react
differently?
Net force
• As we see, the forces in difference places
(well different depths) are different.
• So, what about the NET force?
• Suppose we have a crate which is 1 cubic
meter and is a perfect cube.
• What is the net force in the sideways
direction (hint how will the forces on each
side compare)?
Buoyancy
• What is the force on the bottom if the crate
is set up so that the top is on the exact
surface of the water? What direction is
this force?
• What is the force on the top of the crate?
What direction is the force.
• Now, find the net force on the crate.
• This force is called Buoyancy.
What are the only things that the
Buoyancy force depends on?
• No I have not given some exact equation,
but look at what you have done here and
think about how that would affect it.
Depends on
• Volume of object
• Density of medium you are in
• NOTICE: the mass of the object is NOT a
dependency.
• So, a cubic meter of ice and rock have the
same Buoyancy force!
Um, wait a minute
• hold the phones – stop the presses!
• How can a rock and ice for the same volume have the
same buoyancy force?
• Clearly they have different masses and therefore
different weights.
• How can this be?
• Well, look at the net force of everything (add the gravity
force and the buoyancy force).
• The mass of a cubic meter of ice is about 700 kg.
• For rock it is about 3000 kg.
• What direction will this net force be for ice vs. rock?
Sink like a rock?
• If the force of buoyancy is less than the
gravitational force, the object will sink.
• However, it won’t fall as fast as if you
dropped it. Its acceleration will be slowed.
• If the force of buoyancy is exactly the
SAME, you will just float where you are at.
• At what density do you think this will be
the case?
Floatation Device
• If buoyancy exceeds gravity you go UP!
• However, what happens when part of the
crate exits the water.
• That is, how does the upwards and
downwards pressure forces change (if at
all) as the crate pushes up?
Some change ends change
• The force on the top stays the same – pretty
much.
• It is moving into air, which is far less dense than
water, so the pressure barely changes.
• The bottom pressure decreases, so that force
decreases.
• So, your buoyancy decreases.
• When will the buoyancy stop decreasing – and
when does that occur?
Archimedes’ Principle
• The buoyancy stabilizes once the buoyancy
force equals the weight of the object.
• At this point, it is good to note that the buoyancy
force is the weight of the liquid you are
displacing (i.e. the weight of the water for the
volume that the object takes up of the water).
• So, the amount of water displaced is equal to the
weight of the crate.
• Why is that useful?
Float vs sink
• If you float, you move water equal to your
weight.
• If the object sinks, it moves water equal to
its volume.
• How can we use this to find the mass and
density of an object?
You ship is in a lock.
• Your ship has an iron anchor.
• You toss the anchor into the water.
• Will the level of water in the lock rise or
fall?
Hydraulics
• Image from wikipedia
• The pressures for each
side are the same.
• F1 / A1 = F2 / A2
• So, a force over a big
area can be held up by
a small force over a
small area.
• Note though that the
works are the same.
Surface tension
• In an infinite liquid at every point you have
liquid pushing against you from every
direction.
• However, when you have a surface, you
press the liquid against that surface, but
nothing pushes back, or liquid doesn’t.
• This causes the surface to become more
adhesive or film like.
Atmosphere
• Air is like a fluid – but one that is not very
dense.
• As you get higher, the air gets thinner (less
dense).
• For every 5.6 km you go up, the
atmospheric pressure decreases by half
(meaning that half of the air is below you).
Buoyancy
• Works the same way, but now it is based
off of the density of local air instead of
water.
• If you are less dense than air, your
buoyancy is greater than weight, so you
fly!
• This is how hot air balloons work.
Tire pressure
• If you have a closed surface, you can add
a lot more of a gas.
• This makes it have a higher pressure
(pressure is stuff running into you, so if
you have more of it, then you have more
pressure).
Boyle’s Law
• P1V1 = P2V2
• Meaning that if you have air inside a
closed object and you make it bigger, the
pressure inside that object decreases.
• If you shrink it, the pressure increases.
Pressure of moving fluids
• This applies to either air or water.
• If it moves, the pressure decreases.
• So, the pressure of the water in a moving
river is less than the pressure of water that
is not moving.
• Note this leads to a problem for
swimmers…
Don’t swim in moving water…
• Imagine the typical river.
• Lets say the water is flowing at 5 m/s in the
center. What is the velocity of water at the
edge?
• Because of this, imagine you were trying to swim
to shore from the center of the river. Since
things get pulled to the region of lowest
pressure, how will this affect you getting to
shore?
• If there were 2 boats 5 meters from each side of
the center of the river that were unanchored
what would happen to those two boats?
Airplanes!
• Airplanes are set up such that the air velocity on
the top of the wing is much higher than the
bottom.
• How do the pressures of air on the top wing and
bottom wing compare?
• What is the direction of the resulting force?
• Why would the magnitude of this force depend
on the aircraft’s velocity?
Curve ball
• The velocity is relative to the surface.
• When you spin a ball, one side of the ball has
lower pressure than the other.
• This creates a force which moves the ball
perpendicular to the direction of motion.
• The direction of the force just depends on the
direction of spin (so you can get it to curve either
direction, down, up, or even at some weird angle
as is the case of a knuckleball).
Plasma
• Plasma is the 4th form of matter (solid,
liquid, gas, plasma).
• Plasma is a super heated gas in which
electrons are stripped from every atom.
• Stars are made of 100% plasma.
Conclusion
• Today we have seem how fluids (liquids
and gasses) affect the world around us.
• We have examined Buoyancy and
pressure.