I got asked an awkward question by a student today, regarding the Reynolds equation:
Re = V p 2r
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.
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