Compressible Fluid Mechanics - Introduction (Under Construction)
Compressibility starts to become significant for Mach Numbers greater than 0.3 - all supersonic flows are compressible
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Governing equationsFor inviscid, compressible flow we only need two equations for two unknowns p and V, 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.
Momentum Equations, which for viscous flows are the Navier Stokes Equations. Energy Equation Equation of State Internal Energy Note : Bernoullis Equation does not hold for compressible flow.
ThermodynamicsFor thermodynamic theory, go here
Total (or Stagnation) ConditionsFrom the theory of a pitot tube, we know that there are two different concepts of pressure - static pressure and total pressure, where
- Static pressure is the pressure you would sense if you were moving with the flow
- Total pressure is the pressure at a point in the flow where the velocity is zero.
We can extend this idea to other quantities, like
- Mach number
Another defined quantityThe 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.