**1. n. [Drilling Fluids]**

A fluid described by a three-parameter rheological model. A Herschel–Bulkley fluid can be described mathematically as follows:

τ = τ_{0} + *k*(γ)^{n},

where

τ = shear stress

τ_{0} = yield stress

*k* = consistency factor

γ = shear rate

*n* = flow index, a power law exponent.

The Herschel–Bulkley equation is preferred to power law or Bingham relationships because it results in more accurate models of rheological behavior when adequate experimental data are available. The yield stress is normally taken as the 3 rpm reading, with the *n* and *k* values then calculated from the 600 or 300 rpm values or graphically.

Reference: Hemphill T, Campos W, and Pilehvari A: "Yield-Power Law Model More Accurately Predicts Mud Rheology," *Oil & Gas Journal* 91, no. 34 (August 23, 1993): 45–50.

**See:**
Bingham plastic model,
direct-indicating viscometer,
gel strength,
Newtonian fluid,
non-Newtonian fluid,
plastic fluid,
power-law fluid,
pseudoplastic,
rheological property,
rheology,
shear rate,
shear stress,
viscosity,
yield stress

X-Y plots of rheological models.