GAS DYNAMICS

INTRODUCTION

In this course, we learn about flows where the flow speed is comparable to, or greater than, the speed of sound.
To understand why this is important, we must consider the structure of a gas.  Air, the medium of greatest interest to us,  is a mixture of gases. It is roughly 79% nitrogen, a gas composed of diatomic molecules, 20% Oxygen, another diatomic gas, and 1% of other  gases such as  Argon, Carbon di-oxide etc. which do not significantly alter the properties of air.

At any temperature above absolute zero, the molecules of a gas are in constant motion. The speed of this "random thermal motion" varies from molecule to molecule, and instant to instant. The variation occurs through collisions between molecules. At any given instant, one expects to find molecules traveling at many different speeds and in all directions. If one finds the mean velocity of all these molecules, one comes up with the mean velocity of the gas as a whole: if it is flowing, there is a finite mean velocity. If it is just contained in a stagnant chamber, the mean may be close to zero. However, if one finds the mean speed, i.e., ignore the directions, and just see how fast things are moving, one gets a value which is proportional to the temperature. In fact, what we call "temperature" is a measure of the kinetic energy of the molecules. Thus, the greater the temperature, the greater the speed of random thermal motion of molecules.

Pressure is the force, per unit area, felt on a surface due to the "momentum flux" through the surface. If our surface is an imaginary one in a gas, then the "momentum flux" is the rate at which molecules are carrying "momentum", i.e., their own mass times their velocity, across the surface. If it is a solid surface where we feel the pressure, this is due to the momentum transferred to the surface, when the molecules collide with the surface and change direction. Thus pressure is related to how fast the molecules are moving (the temperature), how massive the molecules are (the molecular weight), and how many molecules there are,  per unit volume (number density, related to density).

The temperature and the type of gas determine the "speed of sound". The speed of sound is the speed at which the smallest imaginable disturbances in pressure, travel through an undisturbed medium. It is a property of the medium. For disturbances to propagate, molecules must collide with each other, transferring momentum and kinetic energy. Thus, the speed of sound is roughly equal to the mean speed of the molecules!   In fact, the relation is:  Speed of Sound = square root of ( gRT) where g called the "ratio of specific heats" of the gas, and R is the "gas constant" of the gas. The gas constant is obtained by dividing the Universal Gas Constant (8314 in SI units) by the molecular weight in kilograms per kilogram-mole. Typically, in air at 0 deg. Celsius (273.2 deg. K), the speed of sound is roughly 340 meters per second.

Let us see, below, some of the effects of motion above the speed of sound. For this, we go to the introduction to high speed aerodynamics, contained in the Design-Centered Introduction.