Newton's Law of Viscosity

on . Posted in Fluid Dynamics

Newton's law of viscosity states that shear stress between adjacent fluid layers is porportional to the velocity gradients between the two layers.  The ratio of shear stress to shear rate is a constant for a given temperature and pressure.  Stated another way, the law states that the shear stress within a fluid is directly proportional to the dynamic viscosity of the fluid and the rate at which the fluid's velocity changes across its flow.  The dynamic viscosity measures the resistance of a fluid to flow and determines how easily it deforms under an applied force.

According to Newton's law of viscosity, fluids that follow this relationship are called Newtonian fluids.  These fluids have a constant viscosity regardless of the shear stress or shear rate applied.  Common examples of Newtonian fluids include water, air, and many oil-based liquids.  It is important to note that some fluids, known as non-Newtonian fluids, do not follow this simple relationship.  Non-Newtonian fluids exhibit complex behavior, such as changing viscosity with applied stress or exhibiting time dependent responses.

This law is widely applied in various fields, including fluid dynamics, engineering, and industrial processes.  It forms the foundation for studying fluid flow, designing pipelines, understanding lubrication, and analyzing the behavior of many everyday liquids and gases.

Newton's Law of Viscosity formula

$$\tau \;=\; \mu\; ( d \nu \;/\; dy )$$     (Newton's Law of Viscosity)

$$\mu \;=\; \tau \;/\; ( d \nu \;/\; dy )$$

$$d \nu \;/\; dy \;=\; \ \tau \;/\; \mu$$

Symbol English Metric
$$\tau$$  (Greek symbol tau) = shear stress $$lbf\;/\;in^2$$  $$Pa$$
$$\mu$$  (Greek symbol mu) = dynamic viscosity $$lbf-sec\;/\;ft^2$$ $$Pa-s$$
$$\frac {d \nu}{dy}$$ = rate of shear deformation $$ft\;/\;sec$$  $$m\;/\;s$$