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Re: [Phys-l] question about Bernoulli



On 11/18/2010 11:34 PM, John Mallinckrodt wrote:
On Nov 18, 2010, at 6:41 PM, brian whatcott wrote:

On 11/18/2010 7:15 PM, John Mallinckrodt wrote:
Another question about Bernoulli:

The Bernoulli equation (for incompressible fluids) says that the sum of the kinetic energy density, the gravitational potential energy density, and the pressure is constant along a streamline so that if the speed DECREASES from point A to point B along a horizontal streamline, the pressure must be HIGHER at point B than at point A.

But in the rest frame of the fluid at point A, the speed is zero at point A and, thus, necessarily is higher at point B so that, in THAT frame, the pressure must be LOWER at point B than at point A.

What's up with that?

John Mallinckrodt
Cal Poly Pomona
I expect John noticed that in the rest frame of the fluid at point A,
the fluid speed is lower, ( even negative!)
at point B where the pressure in the sub-sonic divergent section is rising?
Speed is never negative (and even if it were it wouldn't matter for Bernoulli's eqn. I don't understand the "pressure in the sub-sonic divergent section is rising" thing.

Anyway the explanation is much simpler, but I dare say nicely subtle.

John Mallinckrodt
Cal Poly Pomona


Where pressure recovers in a duct, it is natural to look for a diverging section.
In a diverging duct, speed is reduced. From the point of view of a particle in the faster section, downstream particles are approaching.

Brian W