Depending on the relationship between shear stress and the rate of strain and its derivatives, fluids can be characterized as one of the following:
*Newtonian fluids: where stress is directly proportional to rate of strain
*Non-Newtonian fluids: where stress is not proportional to rate of strain, its higher powers and derivatives.
Newtonian fluids follow Newton's law of viscosity and may be called viscous fluids.
Fluids may be classified by their compressibility:
*Compressible fluid: A fluid that causes volume reduction or density change when pressure is applied to the fluid or when the fluid becomes supersonic.
*Incompressible fluid: A fluid that does not vary in volume with changes in pressure or flow velocity (i.e., ρ=constant) such as water or oil.
Newtonian and incompressible fluids do not actually exist, but are assumed to be for theoretical settlement. Virtual fluids that completely ignore the effects of viscosity and compressibility are called perfect fluids.