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Viscosity - Newton's theory

Viscosity - Newton's theory: Encyclopedia II - Viscosity - Newton's theory

When a shear stress is applied to a solid body, the body deforms until the deformation results in an opposing force to balance that applied, an equilibrium. However, when a shear stress is applied to a fluid, such as a wind blowing over the surface of the ocean, the fluid flows, and continues to flow while the stress is applied. When the stress is removed, in general, the flow decays due to internal dissipation of energy. The "thicker" the fluid, the greater its resistance to shear str ...

Viscosity: Encyclopedia II - Viscosity - Newton's theory

Viscosity - Newton's theory

In general, in any flow, layers move at different velocities and the fluid's "thickness" arises from the shear stress between the layers that ultimately opposes any applied force.

Isaac Newton postulated that, for straight, parallel and uniform flow, the shear stress, τ, between layers is proportional to the velocity gradient, ∂u/∂y, in the direction perpendicular to the layers, in other words, the relative motion of the layers.

Here, the constant μ is known as the coefficient of viscosity, viscosity, or dynamic viscosity. Many fluids, such as water and most gases, satisfy Newton's criterion and are known as Newtonian fluids. Non-Newtonian fluids exhibit a more complicated relationship between shear stress and velocity gradient than simple linearity.

In many situations, we are concerned with the ratio of the viscous force to the inertial force, the latter characterised by the fluid density ρ. This ratio is characterised by the kinematic viscosity, defined as follows:

James Clerk Maxwell called viscosity fugitive elasticity because of the analogy that elastic deformation opposes shear stress in solids, while in viscous fluids, shear stress is opposed by rate of deformation.

Viscosity is the principal means by which energy is dissipated in fluid motion, typically as heat.