Editing Compressible flow (section)

==Introductory concepts==
[[File:Breakdown of Fluid Mechanics Chart.png|thumb|right|Breakdown of fluid mechanics chart]]
There are several important assumptions involved in the underlying theory of compressible flow. All fluids are composed of molecules, but tracking a huge number of individual molecules in a flow (for example at atmospheric pressure) is unnecessary. Instead, the continuum assumption allows us to consider a flowing gas as a continuous substance except at low densities. This assumption provides a huge simplification which is accurate for most gas-dynamic problems. Only in the low-density realm of rarefied gas dynamics does the motion of individual molecules become important.

A related assumption is the [[no-slip condition]] where the flow velocity at a solid surface is presumed equal to the velocity of the surface itself, which is a direct consequence of assuming continuum flow. The no-slip condition implies that the flow is viscous, and as a result a [[boundary layer]] forms on bodies traveling through the air at high speeds, much as it does in low-speed flow.

Most problems in [[incompressible flow]] involve only two unknowns: pressure and velocity, which are typically found by solving the two equations that describe conservation of mass and of linear momentum, with the fluid density presumed constant. In compressible flow, however, the gas density and temperature also become variables. This requires two more equations in order to solve compressible-flow problems: an [[equation of state]] for the gas and a [[conservation of energy]] equation.  For the majority of gas-dynamic problems, the simple [[ideal gas law]] is the appropriate state equation. Otherwise, more complex equations of state must be considered and the so-called [[Non ideal compressible fluid dynamics|non ideal compressible fluids dynamics]] (NICFD) establishes.

Fluid dynamics problems have two overall types of references frames, called Lagrangian and Eulerian (see [[Joseph-Louis Lagrange]] and [[Leonhard Euler]]). The Lagrangian approach follows a fluid mass of fixed identity as it moves through a flowfield. The Eulerian reference frame, in contrast,  does not move with the fluid. Rather it is a fixed frame or control volume that fluid flows through. The Eulerian frame is most useful in a majority of compressible flow problems, but requires that the equations of motion be written in a compatible format.

Finally, although space is known to have 3 dimensions, an important simplification can be had in describing gas dynamics mathematically if only one spatial dimension is of primary importance, hence 1-dimensional flow is assumed.  This works well in duct, nozzle, and diffuser flows where the flow properties change mainly in the flow direction rather than perpendicular to the flow.  However, an important class of compressible flows, including the external flow over bodies traveling at high speed, requires at least a 2-dimensional treatment.  When all 3 spatial dimensions and perhaps the time dimension as well are important, we often resort to computerized solutions of the governing equations.