# Newton's Law of Viscosity and Equation

## Newton’s law of viscosity

Newton’s law of viscosity states that the stress on fluid layers is directly proportional to the rate of shear strain.

Mathematically,

Mathematically,

## Dynamic Viscosity (μ)

Viscosity is defined as the measure of fluid resistance to the flow of one layer of fluid over adjacent layer. Fig shows two fluid layers at distance y and y+dy from the surface. They move with different velocities u and u+du as shown in fig. The top layer causes a shear stress on lower while lower layer causes shear stress on the top layer. The shear stress τ is proportional to the rate of change of velocity with respect y.

Mathematically, Here constant of proportionality μ is known as the coefficient of dynamic viscosity known as the velocity gradient.

From the above equation,

**Unit of dynamic viscosity**

In SI: Newton-Sec/m

^{2}= NS/m

^{2}

In CGS: dyne-Sec/cm

^{2}

1 dyne-Sec/cm

^{2}called one poise.

One poise = 0.1 NS/m

^{2}

## Kinematic viscosity (ν)

It is defined as the ratio between dynamic viscosity and density of the fluid.

In SI system: m

In CGS: cm

One cm

One stoke = 10-4 m

**Units of Kinematic viscosity**In SI system: m

^{2}/sIn CGS: cm

^{2}/s,One cm

^{2}/s known as StokeOne stoke = 10-4 m

^{2}/s
Remember

- For a Newtonian fluid, the coefficient of viscosity remains constant.
- The viscosity of a liquid decreases with increase in temperature.
- The viscosity of gases increases with increase in temperature.
- Material in the increasing order of their viscosity: gasoline < water < crude oil < castor oil

**-**What is meant by viscosity**-**What Does Surface Tension Mean**-**Properties of Fluids