If your reading this, your still stuck on planet Earth, the third planet.
In the last chapter, we followed a rocket into space. Now we will follow a molecule from the injector to the nozzle exit of a rocket engine. The injectors job is to rather rudely spray the fuel and oxidizer into the combustion chamber, where they can mix and burn to produce lots of hot high pressure gas. The injector should produce enough pressure loss to isolate the propellant feed system from instabilities in the combustion chamber, and also serves as the primary metering system to determine propellant flow rates. The combustion process that occurs adjacent to the injector face is really quite remarkable. With a flow rate of nearly two pounds per second for every square inch of injector area, the temperatures can range from -423 deg F, to nearly 5000 deg F, within a distance of one inch. Horsepower's can range upwards to 1000 hp per square inch of injector area. It is still a controlled combustion, but just barely below the rate of detonation. The velocity of the gas leaving the injector face is limited by velocity of combustion of the propellants. We now pick up a molecule of carbon dioxide, a typical combustion product, as it leaves the injector face. The molecule is very hot, it has a lot of energy, it exhibits a high thermal velocity. IT IS MOVING! It exists in a crowd of other hot gas molecules and bounces against them with tremendous energy. These energetic collisions are evident as high pressure in the area below the injector which we call the combustion chamber. The energy of the molecule is so high that it is unstable and may split and recombine several time before it reaches the nozzle exit. The gas is so dense that our molecule will travel in the straightest possible line to the nozzle exit, there is very little mixing after the gas leaves the injector face. The nozzle exit of the engine is open to the outside environment and the hot high pressure gas at the injector face pushes the gas in the combustion chamber towards that lower pressure. Daniel Bernoulli and Leonhard Euler, in the 1730's discovered that the energy in a high pressure gas can be converted to kinetic energy. Since the energy remains the same, the formula is; energy = pressure + 1/2*mass*(velocity squared) The term 1/2 M(V)2, represents the kinetic energy of the gas, and that is what we want to maximize. Note that the velocity is much more important than the mass, therefore we want the lightest possible gas for the combustion product. This is the reason that hydrogen is preferred as a propellant and gives the highest exhaust velocity. In addition to the highest energy, we want the most force from the mass we expend. Force = mass * acceleration, to maximize force we want to reach a high velocity in a short amount of time. our nozzle system must be an efficient accelerator of gas, but also as short as possible to reduce weight. In 1880, a steam turbine engineer named Carl Laval, discovered the a convergent-divergent nozzle would efficiently accelerate steam to high velocity. The gasses in the combustion chamber accelerate to pass through the small opening of the throat. Mach the speed of sound, is the velocity at which it becomes difficult to compress a gas, it begins to act like a solid. Because of incompressibility, the gas cannot exceed mach 1 until it has passed the smallest point of the nozzle throat. After the gas passes that point the expansion portion of the nozzle accelerates the gas to very high velocity, mach 4 or 5. With the "action" of the high velocity gas out the back of the engine, the "reaction" (any action causes an equal and opposite reaction) causes the vehicle to be pushed forward. The chemical energy of the propellants has been converted to pressure energy by combustion, and the pressure energy has been converted to kinetic energy by the nozzle. The momentum of the gas is converted to vehicle momentum. To demonstrate these principals I constructed a small plastic rocket engine that runs on compressed air. With a chamber pressure of 40 psi, the pressure at the throat is 30 psi, indicating the higher velocity. At the nozzle exit the pressure is 5 psi below atmospheric. The exhaust velocity is high enough that a slight vacuum exists at the nozzle exit. The strange journey of our molecule does not end, after leaving the nozzle it still has a considerable amount of thermal velocity. As it collides with other gas molecules in the exhaust stream, in the vacuum of space it may bounce off in a forward direction, traveling with enough velocity to overtake and pass the rocket! The measure of the efficiency of the whole process is called "specific impulse" or ISP and is measured in seconds. ISP = engine thrust / propellant consumption / second. Our nitrous oxide / propane engine has an ISP of 230 at sea level, and 290 at high altitude where there is no atmospheric back pressure on the engine. The F1 liquid oxygen / kerosene engines that powered the Saturn 5, produced an ISP of 260 at sea level and 310 at altitude. The Space Shuttle Main Engine burning liquid oxygen and liquid hydrogen produces 363 at sea level and 455 at altitude. The record for specific impulse in a chemical engine was set by an engine that burned fluorine and lithium, with hydrogen added as a coolant and to lighten the exhaust. The flame was intensely hot and produced an altitude ISP of 528! However good the performance of the engine was, the chemicals were just too difficult to handle to be practical.The rules for gas flow. For Subsonic flow; converging sections = faster, diverging sections = slower. For Supersonic flow; converging sections = slower, diverging sections = faster. This has to do with the fact that at supersonic velocities, air begins to act like a solid, it just won't compress very well.