How does the introduction of a non-Newtonian fluid (e.g., water with high clay content) into an irrigation system alter the friction loss calculations compared to using clean water?

The introduction of a non-Newtonian fluid, such as water with high clay content, into an irrigation system significantly alters friction loss calculations compared to using clean water because non-Newtonian fluids do not exhibit a linear relationship between shear stress and shear rate, unlike Newtonian fluids such as clean water. In simpler terms, the viscosity, which is the fluid's resistance to flow, of a non-Newtonian fluid changes with the applied force or flow conditions, whereas a Newtonian fluid's viscosity remains constant at a given temperature. For clean water, which is Newtonian, friction loss calculations typically rely on formulas like Darcy-Weisbach or Hazen-Williams, which assume a constant viscosity. These formulas use a friction factor that depends on the Reynolds number, a dimens....