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Fluid Mechanics - Reynolds Number

Viscous flow is when friction forces dominate the behavior of a moving fluid, typically in cases where viscosity (internal fluid friction) is great. Inviscid flow, by contrast, is where friction within a moving fluid is negligible. The Reynolds number of a fluid is a dimensionless quantity expressing the ratio between a moving fluid’s momentum and its viscosity.

A couple of formulae for calculating Reynolds number of a flow are shown here:

 

Where,

  Re = Reynolds number (unitless)

  D = Diameter of pipe, (meters)

 
  = Average velocity of fluid (meters per second)

  ρ = Mass density of fluid (kilograms per cubic meter)

  μ = Absolute viscosity of fluid (Pascal-seconds)

 

 

Where,

  Re = Reynolds number (unitless)

  Gf = Specific gravity of liquid (unitless)

  Q = Flow rate (gallons per minute)

  D = Diameter of pipe (inches)

  μ = Absolute viscosity of fluid (centipoise)

 

The Reynolds number of a fluid stream may be used to qualitatively predict whether the flow regime will be laminar or turbulent. Low Reynolds number values predict laminar flow, where fluid molecules move in straight “stream-line” paths, and fluid velocity near the center of the pipe is substantially greater than near the pipe walls:

 

 

High Reynolds number values predict turbulent flow, where individual molecule motion is chaotic on a microscopic scale, and fluid velocities across the face of the flow profile are similar:

 

 

A generally accepted rule-of-thumb is that Reynolds number values less than 2,000 will probably be laminar, while values in excess of 10,000 will probably be turbulent. There is no definite threshold value for all fluids and piping configurations, though. To illustrate, I will share with you some examples of Reynolds number thresholds for laminar versus turbulent flows are given by various technical sources:

 

Chapter 2.8: Laminar Flowmeters of the Instrument Engineer’s Handbook, Process Measurement and Analysis, Third Edition (pg. 105 – authors: R. Siev, J.B. Arant, B.G. Lipt´ak) define Re < 2,000 as “laminar” flow, Re > 10,000 as “fully developed turbulent” flow, and any Reynolds number values between 2,000 and 10,000 as “transitional” flow.

Chapter 2: Fluid Properties – Part II of the ISA Industrial Measurement Series – Flow (pg. 11) define “laminar” flow as Re < 2,000, “turbulent” flow as Re > 4,000, and any Reynolds values in between 2,000 and 4,000 as “transitional” flow.

The Laminar Flow in a Pipe section in the Standard Handbook of Engineering Calculations (pg. 1- 202) defines “laminar” flow as Re < 2,100, and “turbulent” flow as Re > 3,000. In a later section of that same book (Piping and Fluid Flow – page 3-384), “laminar” flow is defined as Re < 1,200 and “turbulent” flow as Re > 2,500.

Douglas Giancoli, in his physics textbook Physics (third edition, pg. 11), defines “turbulent” flow as Re < 2,000 and “turbulent” flow as Re > 2,000.

 

Finally, a source on the internet (http://flow.netfirms.com/reynolds/theory.htm) attempts to define the threshold separating laminar from turbulent flow to an unprecedented degree of precision: Re < 2,320 is supposedly the defining point of “laminar” flow, while Re > 2,320 is supposedly marks the onset of “turbulent” flow.

Clearly, Reynolds number alone is insufficient for consistent prediction of laminar or turbulent flow, otherwise we would find far greater consistency in the reported Reynolds number values for each regime. Pipe roughness, swirl, and other factors influence flow regime, making Reynolds number an approximate indicator only. It should be noted that laminar flow may be sustained at Reynolds numbers significantly in excess of 10,000 under very special circumstances. For example, in certain coiled capillary tubes, laminar flow may be sustained all the way up to Re = 15,000, due to something known as the Dean effect!

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written by Zikri, December 13, 2017
How temperature, viscocity, density, and pipe diameter will change the reynolds number and type of flow

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