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.