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Real gases
Typical interactional potential between molecules
of real gases. Attractive Van der Waals forces have a very
complex character at distances about 10^-7 cm. They decrease
with distance as ~1/(r^7). At long distance, molecules
attract each other. This attraction is also a response
for the condensation of gases into liquids at low temperatures.
At a short distance, molecules repel each other. This repulsion
is a response for the definite volumes of liquids and solids,
not to collapse to a point.
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From the ideal gas equation:
• For 1 mol of an ideal gas, PV/RT = 1 for all pressures.
• In a real gas, PV/RT varies from 1 significantly.
• The higher the pressure - the bigger deviation from
the ideal behavior.
• For 1 mol of ideal gas, PV/RT = 1 for all temperatures.
• As temperature increases, the gases behave in a more
ideal way.
The assumptions of the kinetic-molecular theory
show where ideal gas behavior breaks down:
• The molecules of gas have finite volume.
• Molecules of gas do attract each other.
• As the pressure on gas increases, the molecules are
forced closer together.
• As the molecules get closer together, the volume of
the container gets smaller.
• The smaller the container, the more of the total space
the gas molecules occupy.
• Therefore, the higher the pressure, the less the gas
resembles the ideal gas.
• As gas molecules get closer together, the intermolecular
distances decrease.
• The smaller the distance between the gas molecules,
the more likely that attractive forces will
develop between the molecules.
• Therefore, the less probability the gas resembles
the ideal gas.
• As temperature increases, the gas molecules move faster
and further apart.
• Also, higher temperatures mean more energy available
to break intermolecular forces.
• As temperature increases, the negative departure from
ideal gas behavior disappears.
Although the ideal gas model is very useful, it is only
an approximation of the real nature of gases, and the equations derived
from its assumptions are not entirely dependable. As a consequence,
the measured properties of a real gas will very often differ from the
properties predicted by calculations. Ref.
Real gases sometimes don't obey the ideal gas laws because
the ideal gas model is based on some assumptions that aren't completely
true. The main flaw in the ideal gas model is the assumption that
gas molecules do not attract or repel each other. Attractions and
repulsions are negligible when the distance between molecules is large,
but they do become larger as the molecules become closer together.
If you can contrive conditions that force the molecules into close
contact, so that attractions and repulsions can't be neglected, you
will likely see deviations from ideal behavior. Ref.
Viscosity of air
It seems natural to see the origin of viscosity in terms
of the attractive and repulsive forces between molecules. However, gases
have substantial viscosity even though their inter-molecular forces
are weak, suggesting some other mechanism. Viscosity in gases arises
principally from the molecular diffusion that transports momentum between
layers of flow. A lot of fluid dynamics is concerned with inviscid flow,
but the role of viscosity is crucial to understanding some of the most
important fluid phenomena, such as lift produced by a wing. (Author:
Fred Senese senese@antoine.frostburg.edu). Ref.
Touch a lift force in water
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Inner surface
The water "reflects" from spoon surface. According
to the third Newton's law ("For every action there is
an equal and opposite reaction") spoon moves to the opposite
direction. The motion is shown by arrows.
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Outer surface
The water follows the surface of the spoon. According
to the third Newton's law the spoon moves to the opposite
direction.
Why water sticks to the surface of spoon?
You can replace the surface tension's attractive
force by a repulsive one. Just put oil or fat film on spoon
surface. See that static forces (as capillarity) make no
changes to water stream. It still attracts the spoon. The
effect has a dynamic origin. It is explained by Coanda effect.
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Does Coanda effect also "work" in free streams?
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See interaction of oil and water
streams. The streams are centered. They pull each other below
a point of convergence. The pull turns into push when speed
of both streams becomes equal. Then oil begins to collapse
into drops, and the two phase system becomes unstable. Second
picture shows oil drops, which split from water. Note, that
static surface tension force is repulsive for water - oil interface.
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The streams are directed in the
way, that oil stream just touches surface of water stream. Above
the convergence point water stream is more slow than oil one.
An attractive force of water and oil streams is explained by
Coanda effect.
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Touch a lift force in air
Take a shield of paper (A4 format). Cut it into 2 pieces.
Take hair dryer and one of the paper strips. Make an experiment.
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Inner surface
Direct air blow to inner surface. Lift force pushes
the strip up.
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Outer surface
Air is blowed at small angle to a curved surface.
Lift force pushes the strip up.
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Outer surface
Almost no lift? You can push the strip down, but
how to pull it up?
Note1: Lift force appears as the result of surface
and air flow interaction. It seems that some special conditions
should be met to get a lift.
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Peculiarities of dynamic ant static pressure
Dynamic pressure is the component of fluid pressure that
represents fluid kinetic energy (i.e., motion), while static pressure
represents hydrostatic effects.
Static
pressure is isotropic - the same in all x,y,x directions.
In air it equals the atmospheric pressure and does not depend
on the wing speed.
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Dynamic pressure of a fluid stream with density and speed u is given by
Dynamic pressure represents the fluid stream motion at
a certain direction. Air speed u is evaluated as a relative
speed of the wing.
Note1. Pillow phenomenon may explain why air flow
speed near the curved upper surface is accelerated and is higher if
compared to the air flow near the lower surface.
Note2: Air stream "sticks" to surface and bends
down the near upper surface of the wing not due to Pillow phenomenon
but due to Coanda effect.
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Note3: Do not confuse Dynamic pressure with a pressure
near airfoil surfaces. Air stream interaction with both
airfoil surfaces has a complex dependence and gives some
relative pressure, which may be applied to the normal of
surface.
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Ref: |
Static pressure in a free air stream.
Static pressure is the pressure inside the stream measured
by a manometer moving with the flow. At the same time, the static
pressure is the pressure which is excerted on a plane parallel
to the flow. Thus the static pressure within an air stream has to
be measured carefully using a special probe. A thin disk must cover
the probe except for the opening. The disk must be positioned parallel
to the streaming flow, so that the flow is not interfered with.
If the static pressure is measured in the way outlined
above within a free air stream generated by a fan or a hair dryer
it can be shown that the static pressure is the same as in the
surrounding atmosphere. Bernoulli's law cannot be applied to a
free air stream because friction plays an important role. It may
be noted that the situation is similar to the laminar flow of a
liquid with viscosity inside a tube. The different velocity of the
stream layers is caused by viscosity. The static pressure is the same
throughout the whole cross-section. A free air stream in the atmosphere
is exclusively decelerated by friction. If static pressure in a
free air stream is equal to atmospheric pressure, some of the striking
lecture demonstrations are interpreted incorrectly since the effects
observed are not caused by Bernoulli's law.
Measurement of static pressure
within a free stream
A sufficiently sensitive manometer can be produced easily
if not available in the lab. A fine pipe of glass is bent at one side
to dip in a cup and to be fixed according to figure 7. The meniscus
must be positioned in the middle of the pipe. The suitable inclination
should be 1:15 - 1:30. A rubber tube connects the glass pipe with a
probe. As has been pointed out before a flat disk must be glued on top
of the probe leaving the opening free. The disk has to be held parallel
to the streaming. If the static pressure is measured in such a way it
can be shown that it is equal to the pressure in the environmental atmosphere.
