BAKER HUGHES - Drilling Fluids Reference Manual

Hydraulics
Newtonian Fluid Model
The Newtonian Fluid Model is the basis from which other fluid models are developed. The flow
behavior of Newtonian fluids has been discussed and it can be seen from this equation that the shear
stress-shear rate relationship is given by:
where,
τ
=
( μ) ( γ)
τ = shear stress
μ = viscosity
γ = shear rate
At a constant temperature, the shear stress and shear rate are directly proportional. The
proportionality constant is the viscosity (μ).
Figure 1-7 illustrates the flow curve of a Newtonian fluid. Note that the flow curve is a straight line
which passes through the origin (0, 0) and the slope of the line is the viscosity (μ).
Figure 1-7
Bingham Plastic Model
Flow Curve for a Newtonian Fluid
In the early 1900s, E.C. Bingham first recognized that some fluids exhibited a plastic behavior,
distinguished from Newtonian fluids, in that they require a yield stress to initiate flow. No bulk
movement of the fluid occurs until the applied force exceeds the yield stress. The yield stress is
commonly referred to as the Yield Point. The shear stress / shear rate relationship for the Bingham
Plastic Model is given by:
where,
τ = τ o
+ ( μ
∞ )γ) (
τ = shear stress
τ o = yield point
μ ∞ = Plastic viscosity
γ = shear rate.
Reference Manual
Baker Hughes Drilling Fluids
1-12 Revised 2006