The viscosity of drilling mud will change with a change in the shear rate because in some degree drilling fluids are shear-thinning. Because of its nature of drilling mud, people create the new term of viscosity called “Effective Viscosity” to compensate the change in shear rate of viscosity. By definition, the effective viscosity means the viscosity of Newtonian fluid that gives the same shear stress at the same shear rate.
The following equation is the effective viscosity equation.
µea = effective viscosity in the annulus, centi-poise
Ka = consistency factor in the annulus, poise
Dh = hole diameter, inch
Do = Outside diameter of pipe, inch
na = power law constant of drilling mud in the annulus
Va = annular velocity in the annulus, ft/sec
Please see the following example for more understanding.
Ka = 6.63 poise
Dh = 8.5 inch
Do = 5 inch
na = 0.514
Va = 7 ft/sec
µea = 42.53 centi-poise
Reference: Drilling Hydraulic Books