An important property of any gas
is its pressure. We have some experience with gas
pressure that we don't have with properties like
and compressibility. Every day we hear the TV meteorologist give
value of the barometric pressure of the atmosphere (29.8 inches of
mercury, for example). And most of us have blown up a balloon or used
a pump to inflate a bicycle tire or a basketball.
Because understanding what pressure is and how it works is so
fundamental to the understanding of aerodynamics, we are including
several slides on gas pressure in the Beginner's Guide. An
interactive atmosphere simulator
allows you to study
how static air pressure changes with altitude. The
shows you how the pressure varies around a lifting wing, and the
shows how the pressure changes through a turbine engine.
Another simulator helps you study how pressure changes across
shock waves that occur at high speeds.
There are two ways to look at pressure: (1) the small scale action
of individual air molecules or (2) the large scale action of a large
number of molecules.
Molecular Definition of Pressure
kinetic theory of gases, a gas is composed
of a large number of molecules that are very small relative to the
distance between molecules. The molecules of a
are in constant, random
motion and frequently collide with each other and with the walls of
any container. The molecules possess the physical properties of mass,
momentum, and energy.
The momentum of a single molecule is the
product of its mass and velocity, while the kinetic energy is one
half the mass times the square of the velocity.
As the gas molecules collide with the walls of
a container, as shown on the left of the figure, the molecules impart
momentum to the walls, producing a force perpendicular to the wall.
The sum of the forces of all the molecules striking the wall divided by the area of the
wall is defined to be the pressure. The pressure of a gas is
then a measure of the average linear momentum
of the moving molecules of a gas.
The pressure acts perpendicular (normal) to the wall; the tangential (shear)
component of the force is related to the
of the gas.
Let us look at a static gas; one that does not appear to move or flow.
While the gas as a whole does not appear to move, the individual
molecules of the gas, which we cannot see, are in constant random
motion. Because we are dealing with a nearly infinite number of molecules
and because the motion of the individual molecules
is random in every direction, we do not detect any motion. If we
enclose the gas within a container, we detect a pressure in the
gas from the molecules colliding with the walls of our container. We
can put the walls of our container anywhere inside the gas, and the
force per area (the pressure) is the same.
We can shrink the size of our "container" down to
an infinitely small point, and the pressure has a single value
at that point. Therefore, pressure is a
quantity, not a
vector quantity. It has a magnitude but no direction associated with
it. Pressure acts in all directions at a point inside a gas. At the
surface of a gas, the pressure force acts perpendicular to the
If the gas as a whole is moving,
the measured pressure is different in the
direction of the motion. The ordered motion of the gas
produces an ordered component of the momentum in the
direction of the motion.
We associate an additional pressure
dynamic pressure, with this fluid momentum.
The pressure measured in the direction of the motion is called the
total pressure and is equal to the sum of the static and dynamic pressureas described by Bernoulli's equation.
Macro Scale Definition of Pressure
Turning to the larger scale, the pressure is a
of a gas, like the
temperature and the
The change in pressure during any process is
governed by the laws of
You can explore the effects of pressure on other gas variables
at the animated gas lab.
Although pressure itself is a scalar, we can define a
to be equal to the pressure (force/area) times the surface
in a direction perpendicular to the surface.
The pressure force is a vector quantity.
Pressure forces have some unique qualities as compared to gravitational
or mechanical forces.
In the figure shown above on the right, we have a red gas
that is confined in a box. A mechanical force is applied to the top of the
box. The pressure force within the box opposes the applied force
according to Newton's
third law of motion.
The scalar pressure equals the external force divided by the area of the top
of the box. Inside the gas, the pressure acts in all directions. So
the pressure pushes on the bottom of the box and on the
sides. This is different from simple solid mechanics. If the
red gas were a solid, there would be no forces applied to the sides
of the box; the applied force would be simply transmitted to the
bottom. But in a gas, because the molecules are free to move about
and collide with one another, a force applied in the vertical
direction causes forces in the horizontal direction.
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