Jet thrust equation - theory behind how it was derived and how you know its results PDF

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theory behind how it was derived and how you know its results...

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AERO 309 Jett hr ustequat i on In this video we are going to look at the jet thrust equation. Not drive it but look at. Discuss this theory behind how it was derived and how you know its results. So, the picture we have here on the right is for an ideal jet engine. There are no moving parts in it. Air comes in that area. Energies have added through combustion. And here is expelled. So, let us think about the usual explanation of how, how a jet produces thrust. And usually we get this from. People like to use Newton’s law equal and opposite reactions. We have a jet you know pushes air out the back. And because of equal and opposite from its third law the air pushes back and we have thrust. That is, it works. Newton law does explain it and it can be used. But we also know from our discussion of Arrow forces, drives here. A force can be created from a difference some pressures. So, there are is pressure acting all everywhere around this engine front and back some all those up. We see overall there is lower pressure in the front. There's higher pressure in the back and that difference in pressure in the X direction creates a thrust forward. So, we looked at pressures. We could calculate the thrust. Also, and these are all equivalent. This is just different ways of looking at the same thing. Also. A force is just. Time, Rate of change. That is weird way of saying a derivative of momentum. So, looking at the more basic way of right Newton’s second law. Force is derivative of momentum which means you have a change. Mass never change in velocity never have change in both. So, this is the more basic way of writing articles in May which make people laugh at times and see spring for second long. But the basic true form of Newton’s second law is change momentum. So why do we want to know these small. Using these concepts. We cannot drive. Fundamental. Equation. For a jet engine. And this is of course in an ideal jet engine. What do we get? We have thrust. Is equal to. Mass flow rate of the air plus the mass flow rate of fuel. Times X velocity minus the mass flow rate of the air times the free stream velocity plus pressure at the exit minus free stream pressure. times the area of the exit. If we know those values, we can calculate thrust. And so that is the fundamental thrust equation for an ideal jet engine. Now. Right here. Since amount of fuel added is typically, small compared to the amount of air. Or if you write this, is mathematically fuel right mass fuel. The rate of mass flow rate of fuel the ratio of that to mass of the rate of air is less is small uses much less than one. If we do that that means we can basically ignore the fuel rate mass rate mass of fuel, rate of mass flow rate of fuel. If we got rid of that this equation can simplify. To simplify it we end up with thrust is slow rate of error times difference in velocity minus stream velocity plus ex pressure minus extreme pressure times the area the accent. So really, we end up removing this one term here since we only have mass flow rate of the air clean up with the difference velocities and difference and pressure. So that is a very basic explanation of the jet threats jet equation.

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