Normal-shock relations: Difference between revisions

Now, one question remains. How come that we by analyzing the control volume using the upstream and downstream states get the normal shock relations. There is no way that the governing equations could have known about the fact that we assumed that there would be a shock inside of the control volume, or is it? The answer is that we have assumed that there will be a change in flow properties from upstream to downstream. We have further assumed that the flow is  adiabatic (we are using the adiabatic energy equation) so there is no heat exchange. We are, however, allowing for irreversibilities in the flow. The only way to accomplish a change in flow properties under those constraints is a formation of a normal shock (a discontinuity in flow properties - a sudden flow compression) between station 1 and station 2.

\noindent The Hugoniot equation is an alternative normal shock relation based on thermodynamic quantities only. It is derived from the governing equations and relates the change in energy to the change in pressure and specific volume. The starting point of the derivation of the Hugoniot equation is the governing equations (Eqns~\ref{eq:governing:cont} - \ref{eq:governing:energy}).