Help With Reynold's Number and Diameter

[SBMDStudent]

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.

 

[jack action]

From Wikipedia:

Flow in pipe

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

where:

• 
  is the hydraulic diameter of the pipe; its characteristic traveled length,
  
  , (m).
• 
  is the volumetric flow rate (m3/s).
• 
  is the pipe cross-sectional area (m²).
• 
  is the mean velocity of the fluid (SI units: m/s).
• 
  is the dynamic viscosity of the fluid (Pa·s = N·s/m² = kg/(m·s)).
• 
  is the kinematic viscosity (
  
  (m²/s).
• 
  is the density of the fluid (kg/m³).

Since the cross-sectional area is proportional to the pipe's diameter squared, the diameter goes to the denominator.

 

[256bits]

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 therefore 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,

, and

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

, and

remain constant ( going from flow Q1 to Q2. )
One can use a different fluid through the pipe. Here, both

, and

may change, and perhaps Q ( subsequentially v ).