A
graphical
version of this slide is available which gives the standard day
values of all of the flow properties.
Air is a mixture of gases, 78%
nitrogen and 21% oxygen with traces of water vapor, carbon dioxide,
argon, and various other components. We usually model air as a
uniform (no variation or fluctuation) gas with properties that
are averaged from all the individual components.
Any gas has certain properties that we can detect with our senses.
The values and relations of the properties define the state of
the gas. The pressure (p) of a gas equals the
perpendicular (normal)
force exerted by the gas divided by the
surface area on which the force is exerted.
A gas can also exert a tangential (shearing) force on a surface, which
acts like friction between solid surfaces. This "sticky" property of
the gas is called the
viscosity (mu)
and it plays a large role in aerodynamic
drag.
A gas is composed^M
of a large number of molecules which are in constant motion.
The temperature (T)
of a gas is a measure of the kinetic energy of the gas.
The sum of the mass of all the
molecules is equal to the mass of the gas.
A gas occupies some
volume in three dimensional space. For a given pressure and
temperature, the volume depends directly on the amount of gas.
Since the mass and volume are directly related, we can express both
the mass and volume by a single variable.
When working with a static (unmoving) gas, it is convenient
to use specific volume (v), which is the
volume divided by the mass. When a gas is moving, it is more
convenient to use the density (r) of a gas,
which is the mass divided by the volume the gas occupies. Either
variable can be used to define the state of the gas, since they are
reciprocals.
The density (specific volume), pressure, and
temperature of a gas are related to each other through the equation
of state.
There is a universal gas constant which relates these variables
and the molecular weight of any gas. Including the value of the
molecular weight, we can define a particular gas constant (R)
for air.
The state of a gas can be changed by external
processes, and the reaction of the gas can be predicted using the
laws of thermodynamics.
Studies of the
zeroth and
first laws introduce the idea of the
heat capacity of a substance.
The specific heat
of a gas is a measure of the amount of energy necessary to raise
the temperature of the gas by a single degree.
Since the amount depends on the process used to raise the temperature,
there a
specific heat (cv)
coefficient for a constant volume process, and a different valued
coefficient for a constant pressure process (cp). The ratio of these
coefficients is denoted by the greek letter gamma and appears
in many thermodynamic equations.
Typical values of the density,
pressure, and temperature of air at sea level static conditions for a
standard day are:
Density: 1.229 kilogram per cubic meter or .00237 slug per cubic feet
Specific Volume: .814 cubic meters per kilogram or 422 cubic feet per slug
Pressure: 101.3 kilo Newtons per square meter or 14.7 pounds per square inch
Temperature: 15 degrees Celsius or 59 degrees Farenheit
Absolute Temperature: 288 degrees Kelvin or 519 degrees Rankine
Viscosity: 1.73 time 10^-5 Newton-second per square meter or 3.62 times
10^-7 pound-second per square foot.
Gas Constant: .286 Joules per gram per degree Kelvin or
53.5 foot-pounds per pound per degree Rankine.
Specific heat at constant volume: .715 Joules per gram per degree Kelvin or
.17 BTU's per pound per degree Rankine.
Ratio of specific heats: 1.4
We are all aware that pressure and temperature (and
density) of the air depend on your location on the earth and the
season of the year. And while it is hotter in some seasons than
others, pressure and temperature change day to day, hour to hour,
sometimes even minute to minute (during severe weather). The values
presented on the slide are simply average values used by engineers to
design machines. That's why they are called standard values.
We also know that all of the state-of-the-gas variables will change
with altitude, which is why the typical values are given at sea
level, static conditions. Because the gravity of the earth holds the
atmosphere to the surface, as altitude
increases, air density, pressure, and temperature (for lower
altitudes) decrease. In deep space, the density is almost zero. The
variation of the air from the standard can be very important since it
affects the aerodynamic
lift
and
drag.
For the same geometry, the lift and
drag decrease with altitude.
The Wright brothers never had to worry about these variations from standard
conditions because their aircraft seldom flew higher than
100 feet off the ground and they never flew in Denver or any other cities located
at high altitude.
A quick look at the table shows that there are two quoted values for the
temperature. The lower value in each column is the absolute temperature
referenced to absolute zero. There are two different English units for
energy (ft-lbs and BTU's), which is part of the "fun" of working in English
units.
Activities:
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