Re: Scientific Errors
- From: "Thomas Smid" <thomas.smid@xxxxxxxxx>
- Date: 29 Jun 2006 07:34:48 -0700
blair.houghton@xxxxxxxxx wrote:
At a narrowing of the tube, the flux rate is the same as at any other
cross-section of the tube, but the cross-sectional area is smaller,
therefore the flow is faster.
In order for the flow speed to increase, the average speed of the
molecules must increase - they are accelerated into the narrow space.
What you are addressing here is actually the continuity condition (i.e.
in a steady state the amount of fluid you put into the tube on one side
must be the same that comes out on the other side). This has
essentially nothing to do with Bernoulli's principle but is effectively
just the law of mass conservation.
As an example, consider a gas that has no viscosity whatsoever i.e.
collisions of molecules with each other can be neglected (as well as
any viscous effects due to interactions with the wall of the tube).
Assume the cross section of the tube to narrow down suddenly at a
certain point as shown in my illustration
http://www.physicsmyths.org.uk/imgs/flow.gif . What happens here is
that the molecules in the center of the flow
(i.e. that corresponding to the cross section of the narrow section)
will simply pass through without being affected in any way, whereas the
other molecules will bounce back from the wall representing the
restriction of the tube. So there is actually no acceleration of
molecules taking place here. On the contrary, those molecules that hit
the wall are *decelerated* and according to Newtons's law excert a
force on the tube in the direction of the flow. This force is exactly
the same force that is responsible for the aerodynamic lift and drag
(as explained in more detail on my pages
http://www.physicsmyths.org.uk/bernoulli.htm and
http://www.physicsmyths.org.uk/drag.htm ). These forces have nothing
whatsoever to do with the flow velocity tangential to a surface but
only with the flow normal to a surface. It is obvious from the
illustration that the pressure on the walls before and after the
restriction must be exactly the same as nothing happens at all to the
velocity components perpendicular to the wall.
Pressure changes can thus only occur as a secondary effect due to the
viscosity of the medium. The paradoxical situation is that Bernoulli's
principle is usually introduced for inviscid fluids, which in the light
of the above arguments is physically inconsistent and erroneous.
Thomas
.
- References:
- Scientific Errors
- From: Dennis B
- Re: Scientific Errors
- From: blair . houghton
- Scientific Errors
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