The interesting thing about our three equations (1-3) is that if they are satisfied for states 1 and 2, they are still satisfied if you flip around the velocity vectors, i.e. if you replace u_{1} by -u_{1} and u_{2} by -u_{2}. (Check this.) So for any shock that looks like this:
there is also a shock that looks like this:
In one case the fluid density changes from to when the fluid moves across the shock, while in the other case it changes from into . So, the fluid will change from low density to high density in one of the two flows above, and from high to low density in the other. The one in which the fluid density increases is called the ``compression shock'' since the fluid is being compressed, and the other the ``expansion shock'', since the fluid expands. So we have learned:
Note however that while all conservation laws are satisfied, there is still a problem with the second law of thermodynamics. Depending on which side, 1 or 2, has the higher entropy, the fluid in one case increases in entropy while going through the shock, and in the other decreases in entropy. Since the shock is adiabatic, entropy cannot decrease according to the second law. It follows that:
It turns out (from results obtained later) that it is the compression shock that has an entropy that is correctly increasing, so
From continuity, (1), is constant, so if density increases, the velocity decreases:
So far for what can be seen immediately. Let's now start solving the three equations to see what more we can learn there.