BAKER HUGHES - Drilling Fluids Reference Manual

Hydraulics
Determination of Flow Regime
The experiments conducted by Reynolds, besides naming the behavior of fluid flow, made the most
celebrated application of dimensional analysis in the history of fluid mechanics by introducing the
Reynolds Number (Re).
Reynolds number takes into consideration the basic factors of pipe flow – pipe diameter, average fluid
= V D ρ
μ
velocity, fluid density, and fluid viscosity. Reynolds number is defined as
Re ( )( )( )
where,
V = average fluid velocity
D = pipe diameter
ρ = fluid density
μ= fluid viscosity
Reynolds showed that for smooth, circular pipes, for all Newtonian fluids, and for all pipe, the
transition from laminar to turbulent flow occurs when the Reynolds number has a value of
approximately 2000. However, turbulent flow throughout the fluid occurs when the Reynolds number
is more than 4000.
Therefore, for Newtonian fluids, laminar flow is defined as a Reynolds number of 2000 or less.
Turbulent flow is defined as a Reynolds number of 4000 or greater. Transitional flow is defined when
the Reynolds number is between 2000 and 4000.
As previously shown, the viscosity of non-Newtonian fluids depends upon the relationship between
shear stress and shear rate. Likewise, the value of the Reynolds number at which the transition from
laminar to turbulent flow occurs depends upon the shear stress/shear rate relationship.
The relationship between shear stress and shear rate for non-Newtonian fluids is developed in the
subsection, Mathematical Fluid Models .
Reference Manual
Baker Hughes Drilling Fluids
1-10 Revised 2006