Re: [Phys-l] question about Bernoulli

[John Mallinckrodt <ajm@csupomona.edu>]

> If the flow is adiabatic, then pressure and density have to change in the same direction - so it's kind of chicken and egg.

True enough.

> On the microsopic level, why does the density lower?

Dare I say, because the pressure is lower?  I didn't think so!  ;-)

> Mass continuity requires rho*A*v to be constant in equilibrium flow, so small A will require higher v - but why a rho change?

Seriously, though.  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.  Now, see the answer to the previous question!

> - it's not needed with a liquid obviously - so why with gas molecules with lots of space between them?

A density change *is* needed (or perhaps, it's better to say "*is* produced" (but then again, perhaps not!)) with a liquid, it's just very small.  It wouldn't be needed (or produced) for the gas if you could arrange for the temperature to be sufficiently reduced, but that would violate the second law of thermodynamics.  The process is adiabatic, not isopycnic.

> If the gas molecules speed up, they must have suffered more collisions from the direction of the wider pipe and fewer from the direction of the narrower pipe - so we're back around the circle again.

That's not wrong!

John Mallinckrodt
Cal Poly Pomona