Fundamental Equations

The mathematical models, which simulate the physics involved, are the essential tools for the theoretical analysis of aerodynamical flows. These mathematical models are usually based on the equations which are nothing but the fundamental conservation laws of mechanics. The conservation equations are usually satisfied locally as differential equations; therefore, their unique solution requires initial and boundary conditions which are described with the farfield conditions and the time dependent motion of the body. Let us follow the historical development of the aerodynamics, and start our analysis with potential flow theory. The potential theory will help us to determine the aerodynamic lifting force which is in the direction normal to the flight and necessary to balance the weight of the body in flight. Since the viscous forces are neglected in potential theory, the drag force which is in the direction of flight cannot be calculated. On the other hand, the potential theory can deter­mine the lift induced drag for three dimensional flows past finite wings. Now, in order to perform our aerodynamical analysis let us introduce further defi­nitions and the simplification of the equations for first, (A) The Potential Theory with its assumptions and limitations, and then for the (B) Real Gas Flow which covers all sorts of viscous effects and the effect of composition changes in the gas because of high altitude flows with high speeds.