Help With Reynold's Number and Diameter

  • #1
Hey guys,
I am looking at the concept of Reynold's number applying to anesthesia circuits. I understand that one formulation for Reynold's number as it relates to a fluid flowing through a tube of constant dimensions is:
R# = (Velocity x Diameter x Density)/Viscocity
I know that a high R# is characteristic of turbulent flow. I also understand that increasing the diameter of a tube should promote laminar flow through it, how do I reconcile that with the Diameter term being in the numerator (thus increasing the R#, which should promote turbulent flow)?

I did not see this specific questions addressed in other R# threads. If so, sorry for the redundancy.
 

Answers and Replies

  • #2
jack action
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From Wikipedia:
Flow in pipe

For flow in a pipe or tube, the Reynolds number is generally defined as:

813a39bbed6a40500e3c78d6ec2d92e8.png

where:

Since the cross-sectional area is proportional to the pipe's diameter squared, the diameter goes to the denominator.
 
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  • #3
256bits
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I also understand that increasing the diameter of a tube should promote laminar flow through it
That statement is much much too general to adequately describe fluid flow.
Strictly speaking, if a pipe has a change in diameter from one section to the next, each section has a different Reynold's number. Since by continuity, the flow Q in each section is the same, it follows that the velocity will change as an inverse function of area, or of D^2. Increase D, but v will decrease faster, resulting in a lower Re. Conversely, decrease D, and v will increase faster.
That pretty much describes what Jack Action wrote from Wiki, but in different terms.


Reynold's number, as you most likely know, is the ratio of inertial forces to viscous forces.
It is also a dimensionless number, and therfore can be used for comparative analysis of flow when one, or more, of the terms is or needs changing.
One can have flow Q1 through a pipe with sections of a different diameter. In which case Q,
503c8a1cfcdb94c6397f5b81c6437c42.png
, and
de862b1d87605de43d72d6087b71939c.png
remain constant throughout.
One can alter the flow to Q2, through the same pipe. In which case, Re is different from above in the sections, and only
503c8a1cfcdb94c6397f5b81c6437c42.png
, and
de862b1d87605de43d72d6087b71939c.png
remain constant ( going from flow Q1 to Q2. )
One can use a different fluid through the pipe. Here, both
503c8a1cfcdb94c6397f5b81c6437c42.png
, and
de862b1d87605de43d72d6087b71939c.png
may change, and perhaps Q ( subsequentially v ).
 

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