Newton's Law of Viscosity and Equation


Newton’s law of viscosity

It states that the stress on fluid layers is directly proportional to the rate of shear strain.

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

From the above equation, viscosity_equation

Unit of dynamic viscosity
In SI: Newton-Sec/m2 = NS/m2
In CGS: dyne-Sec/cm2
1 dyne-Sec/cm2 called one poise.
One poise = 0.1 NS/m2

Kinematic viscosity (ν)

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

Units of Kinematic viscosity
In SI system: m2/s
In CGS: cm2/s,
One cm2/s known as Stoke
One stoke = 10-4 m2/s

  • 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

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