Comment

Analogue Traffic

There are a few parallels between highway traffic and supersonic fluid flow.  In the case of subsonic fluid flow, the fluid's velocity decreases as the channel it flows through becomes more narrow.  The opposite is true for supersonic flow.  The speed of information [about disturbances in the fluid] is the same as the speed of sound, which is given by the Newton-Laplace equation:

$$a = { \sqrt{K \over p}}.$$

In supersonic flow, the speeds of information about a disturbance and of the disturbance itself are the same [or the speed of the information is slower].  This means is why particles cannot move out of the way of a disturbance in time, and therefore is why flow slows down with constricting channel diameter.  A normal shock wave forms at the tip of the supersonic flow.  Thermodynamics forces the flow to become subsonic as you traverse the shock wave in the direction of flow.  There is also a discontinuous density/pressure function across the normal shock wave.  

This is very similar to traffic patterns.  How can we increase the speed of information in traffic?  Will this cause traffic to speed up with constricting channel diameter?  

Comment