I agree Terry and
Joe. It seems to me that the way you state the problem Don, it becomes
almost a circular argument. Another large issue in looking at these issues are the assumptions
that we make in dealing with Bernoulli and Poiseuille for that matter, that are not consistent
with what happens in a patient. Such as: 1. The conduit is a rigid tube with a smooth
surface and no irregularities. 2. The
fluid is Newtonian and
incompressible. 3. No energy loss due to heat. 4. there is steady flow.
While Reynolds > 2000 usually results in turbulence, we can find many
examples of turbulence with much lower numbers and vice versa. My go to book has
become Frank Miele for good models of how this stuff works.

Bill

William B Schroedter, BS, RVT, RPhS,
FSVU

Technical Director, Quality Vascular
Imaging, Inc

4120 Woodmere Park Blvd

Suite 8B

Venice, Florida 34293

(941) 408-8855 office

Cross
sectional area is pi * r2 . If the radius is doubled then the area quadruples
and so velocity would decrease by about 75% to accommodate the same volume
flow. More apropos of what we see in disease if the radius decreases by
50% then the velocity roughly quadruples to accommodate the same volume flow. We
are used to thinking of turbulence occurring in stenoses so if the radius
decreases velocity must increase much more to accommodate the same volume flow
and you can see that this will increase the Reynolds
number.

All
the best

Joe

**From:** UVM Flownet
[mailto:[log in to unmask]] **On Behalf Of **Terry
Zwakenberg**Sent:** Wednesday, October 31, 2012 5:36 AM**To:**
[log in to unmask]**Subject:** Re:
Reynolds

Don, The answer for your student is in the question. The Reynolds
equation is determining the point at which flow becomes turbulent in a
tube. You can solve that riddle for any diameter tube but once you choose
the diameter of the tube you are solving for it is no longer a variable but
rather a fixed constant in the formula. I guess if you were questioning
the diameter required to keep a certain fluid of known viscosity and volume from
becoming turbulent as you deliver it from point a to b than yes your student
question would have some application, but you would first have to determine a
starting diameter and it's associated Reynolds number for that specific fluid to
be able to apply it. I think.

On Oct 31, 2012 12:05 AM, "Don Ridgway" <[log in to unmask]>
wrote:

I got asked an awkward question by a student today, regarding
the Reynolds equation:

Re = V p 2r

n

My primitive school email access won't allow me to make that
lower-case p into a rho for density, nor that lower-case n into an eta for
viscosity, but you get the idea.

The question was this: since we know
from another equation—Q = V x CSA—that a reduction of cross-sectional area means
an increase of mean velocity, then why don''t those two balance out in the
Reynolds equation?

For example, if the radius is doubled, won't that
bring about a decrease to 1/2 of the velocity, leaving Re unchanged?

My
clever response: life is complicated. And I'll get back to you.

I'm
obviously angling for a bit of perspective from Dr. Beach from up there in
Seattle (whence I'm flying Friday, as it happens).

Thanks in advance to
anyone with help on this.

Don Ridgway

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