## Compressible Fluid Mechanics - Introduction (Under Construction)

## Compressibility starts to become significant for Mach Numbers greater than 0.3 - all supersonic flows are compressible

All links to external sites are on External Links

## Governing equations

Forinviscid, compressible flowwe only need two equations for two unknowns p andV, i.e.(these basic equations are combined to form Laplace's and Bernoulli's equations). The energy equation is not required. Incompressible flows require only mechanical laws, with no thermodynamic considerations.

- continuity equation
- momentum equation
For

compressible flow, we have five unknowns, p,V, rho, e and T, so we need five equations.

Continuity EquationMomentum Equations, which for viscous flows are the Navier Stokes Equations.Energy EquationEquation of StateInternal EnergyNote: Bernoullis Equationdoes nothold for compressible flow.

## Thermodynamics

For thermodynamic theory, go here

## Total (or Stagnation) Conditions

From the theory of a pitot tube, we know that there are two different concepts of pressure - static pressure and total pressure, where

Static pressureis the pressure you would sense if you were moving with the flowTotal pressureis the pressure at a point in the flow where the velocity is zero.We can extend this idea to other quantities, like

- temperature
- density
- Mach number
- enthalpy

## Another defined quantity

The values all the above quantities would have at sonic conditions is denoted by an asterisk, for example is the temperature which would exist at a point if sonic conditions prevailed there. Note by analogy with total temperature, this is not, in general, the value actually existing at a particular point in question.

## Shock Waves