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 equations

For inviscid, compressible flow we only need two equations for two unknowns p and V, i.e.

• continuity equation
• momentum equation

(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.

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

• Continuity Equation

• 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.

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Thermodynamics

For thermodynamic theory, go here

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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 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

• temperature
• density
• Mach number
• enthalpy

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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.

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Shock Waves

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