Re: [Phys-l] question about Bernoulli

[John Mallinckrodt <ajm@csupomona.edu>]

I wrote:

> One can at least say that, the only way to get the molecules to speed up in the constriction is to do some work on them while they are entering the constriction, which, in turn, requires a pressure drop on the way into the constriction.

Following up on that thought a bit more.  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.

John Mallinckrodt
Cal Poly Pomona