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These are all the same arguments we use in our classes - to have an equilibrium flow the fluid has to speed up in the narrower pipe, therefore the pressure must be less, etc. They are entirely reasonable on the macroscopic level. However, these arguments unfortunately all boil down to "the pressure is lower because it has to be".
On the microscopic level, it's not anywhere near as satisfying to say the molecules must speed up at the constriction because the pressure is lower. Molecules don't react to the macroscopic quantity pressure directly, they react to collisions.
To say the molecules speed up because there is a higher number of collisions from the direction where the density is higher, and then follow that up by stating that the density is lower in the narrower pipe because the speed is higher is circular. Unfortunately that appears to be the argument that needs to be made to explain the pressure decrease.
I'm looking for an "Aha" moment here.
John Mallinckrodt wrote:
The situation is not unlike that which happens when a current is set up in a simple circuit. For a very few microseconds, the current may not be the same across every cross section of the wire. But if there is more (conventional) current entering a region than leaving, then (positive) charge is building up in that region. The effect of that (positive) charge build up is to produce an extra push on the (positive) charge leaving and to retard the (positive) charge entering, that is, to move things in the direction of uniform current.
The same thing happens with fluid flowing through a pipe of variable cross section. Suppose the speed in the constriction was a little too slow. Then pressure would build up behind it to make it speed up more. Depending on the size of the pipe and the speed of sound, the process of equilibration may take very little time or quite a long time, but eventually the pressure arranges itself self-consistently in order for the flow to become steady.