Kajal Work: Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or tensile stress.
In everyday terms (and for fluids only), viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. Put simply, the less viscous the fluid is, the greater its ease of movement .

Any real fluids (liquids and gases included) moving along solid boundary will incur a shear stress on that boundary.
The speed of the fluid at the boundary (relative to the boundary) is zero, but at some height from the boundary the flow speed must equal that of the fluid.
The region between these two points is aptly named the boundary layer. For all Newtonian fluids in laminar flow the shear stress is proportional to the strain rate in the fluid where the viscosity is the constant of proportionality.
However for Non Newtonian fluids, this is no longer the case as for these fluids the viscosity is not constant.
The shear stress is imparted onto the boundary as a result of this loss of velocity. The shear stress, for a Newtonian fluid, at a surface element parallel to a flat plate, at the point y, is given by:

$\tau (y) = \mu \frac{\partial u}{\partial y}~~,$

where

μ

is the dynamic viscosity of the fluid;

u

is the velocity of the fluid along the boundary;

y

is the height above the boundary.

A shear stress, $\tau\,$ is applied to the top of the square while the bottom is held in place. This stress results in a strain, or deformation, changing the square into a parallelogram.

Specifically, the wall shear stress is defined as:

$\tau_\mathrm{w} \equiv \tau(y=0)= \mu \left.\frac{\partial u}{\partial y}\right|_{y = 0}~~.$

In case of wind, the shear stress at the boundary is called wind stress.

Viscosity:

Laminar shear of fluid between two plates. Friction between the fluid and the moving boundaries causes the fluid to shear. The force required for this action is a measure of the fluid's viscosity. This type of flow is known as a Couette flow.
In general, in any flow, layers move at different velocities and the fluid's viscosity arises from the shear stress between the layers that ultimately opposes any applied force.
The relationship between the shear stress and the velocity gradient can be obtained by considering two plates closely spaced at a distance y, and separated by a homogeneous substance.
Assuming that the plates are very large, with a large area A, such that edge effects may be ignored, and that the lower plate is fixed, let a force F be applied to the upper plate. If this force causes the substance between the plates to undergo shear flow with a velocity gradient u(as opposed to just shearing elastically until the shear stress in the substance balances the applied force), the substance is called a fluid.
The applied force is proportional to the area and velocity gradient in the fluid and inversely proportional to the distance between the plates. Combining these three relations results in the equation:

$F=\mu A \frac{u}{y}$ ,

where μ is the proportionality factor called viscosity.

$\tau=\frac{F}{A}$ .

Thus as expressed in differential form by Isaac Newton for straight, parallel and uniform flow, the shear stress between layers is proportional to the velocity gradient in the direction perpendicular to the layers:

$\tau=\mu \frac{\partial u}{\partial y}$

Hence, through this method, the relation between the shear stress and the velocity gradient can be obtained.
Note that the rate of shear deformation is $\frac{u} {y}$ which can be also written as a shear velocity, $\frac{du} {dy}$ .
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.

Kajal Work