What is Viscosity & Viscous Force ?

When a fluid flows through channel the fluid layer in the bottom is in contact with the channel remains at rest.

The upper most fluid layer moves with maximum velocity. Thus there is a velocity gradient existing among different layers of fluid. The faster moving layer intends the slower layer in contact to accelerate and simultaneously the slower moving layer intends the faster moving layer to retard.This property of liquids is called viscosity.

The force existing between the two consecutive layers of fluids due to their velocity gradient is called viscous force.

Let us consider two layers of fluid each of surface area A. The viscous force (F) between them is

$\large F \propto A$

$\large F \propto \frac{dv}{dx}$

On combining ,

$\large F = – \eta A \frac{dv}{dx}$

Where η is the coefficient of viscosity of the fluids.

Thus, the coefficient of viscosity of a liquid is viscous force acting tangentially per unit area of liquid layer having unit velocity gradient in a direction perpendicular to the direction of flow of liquid.

Unit of coefficient of viscosity is poise.

Strokes Law:

When a body falls through a viscous medium (liquid or gas), it drags the layer of the fluid immediately in contact with it. This produces a relative motion between the different layers of the fluid.

As a result of this, the falling body experiences a viscous force. This force tends to retard the motion of the body.

Stokes performed many experiments on the motion of small spherical bodies in different fluids.
He concluded that the viscous forces F acting on a small sphere of radius r depends upon :

(i) coefficient of viscosity (η) of the fluid,

(ii) velocity (v) of the spherical body and

$\large F = 6 \pi \eta r v$