Transcript Lecture 12 - WebPhysics

Goal: To understand liquids
and gasses
Objectives:
1) To understand Pressure
2) To understand Buoyancy
3) To understand Archimedes Principal
4) To learn about Hydraulics
5) To learn about Surface Tension
6) To learn about how pressure is affected
when a fluid moves
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 14
pounds per square inch.
• Why aren’t we crushed by this pressure?
What causes pressure?
• Atmospheric 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 14
pounds.
Summer door
• In the summer the outside pressure on a door
with an area of 2 square meters is 1.01 * 105
Pascals
• On the inside of the air conditioned house the
force is 1.00 * 105 Pascals
• A) What is the air pressure force pushing out?
• B) What is the air pressure force pushing in?
• C) What is the net force on the door and would
you be able to open this door?
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
Deep sea dive
• You dive to a depth of 240 m.
• A) What is the pressure at this depth?
• B) If a mini submarine with a surface area
of 0.4 square meters were at this depth
then what would be the inwards crushing
force on the sub due to the water
pressure?
Buoyancy
• Each side of the object will have a force on
it.
• However, the pressure on the bottom of an
object will be higher than the pressure on
the top.
• This means more force pushing up than
down.
• This creates a net pressure force.
• This force is called Buoyancy.
Depends on
• Volume of object
• Density of medium you are in
• F = density * Volume * g
(i.e. the weight that is displaced)
• NOTICE: the mass of the object is NOT a dependency.
• So, a cubic meter of ice and rock have the same Buoyancy
force!
• What is the buoyancy force on an object with a volume of 1
cubic meter in water with a density of 1000 kg/cubic meter?
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.
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?
Float vs sink
• If you float, you move water equal to your
weight.
• If the object sinks, it moves water equal to
its volume.
Archimedes's Principal
• The buoyancy force is equal to the weight
of fluid you displace (and note that air is
considered fluid for this)
• F = density * Volume * g
(i.e. the weight that is displaced)
STOP!
• Dear Dr. Rhoads, please do not advance
past this point until Monday.
• Your students have a test tomorrow and so
you need to let them review…
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…
Bernoulli’s Equation
• Pmoving = Prest – ½ density * v2
• Also, if the area of a tube or pipe changes:
• A1V1 = A2V2
• So, smaller area means faster moving
fluid.
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?
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?
Tale of two pipes
• A pipe was an initial radius of 0.15 m.
• The fluid flows through this pipe with a velocity of 0.4
m/s.
• The pipe then goes down and shrinks to a radius of 0.05
m
• A) What is the velocity of water in the shrunk down
section of pipe?
• B) If the water pressure in shrunk section of pipe was 2.3
* 105 Pascals and the density of fluid in the pipe was
1100 kg/m3 then what would the pressure be in the pipe
if the fluid was not moving?
• C) If the larger pipe was 5 m above the shrunken pipe
then what would the pressure of the fluid be if the fluid
was not moving?
• D) What is the pressure in the larger pipe when the fluid
is moving at 0.4 m/s?
Conclusion
• Today we have seem how fluids (liquids
and gasses) affect the world around us.
• We have examined Buoyancy and
pressure.