Newton's Law of Viscosity and Equation
![Newton's_Law_of_Viscosity](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy9NQpT1nArmEvi2TLhJdHeS1Dsh5i-nAx0-Hdp6NoRRxS5kwIgoqnjQtUXMTmRA3jDBwd-3C_2M_4QojYX8SQjgjRIvydm-mqApv8BbWUTFBMlyKoyq58vMNdcrvIQAln6q2Ozb2sHGII/s640/newtons+law+of+viscosity.png)
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,![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8IbM71uIB_xjn51Ofce_xXpUI4xVSHMA0k-0MdLqMCpTBxDVht_E8mGv4gaQSXlhJIiGY2fkLf5HXkqYsZOUi9VYv7s4pWXJwza8yjwyhpsI46mK3u8mLoak5n1CPJW2rH1YPfzKaP4lS/s400/newtons+law+of+viscosity+equation.png)
Mathematically,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8IbM71uIB_xjn51Ofce_xXpUI4xVSHMA0k-0MdLqMCpTBxDVht_E8mGv4gaQSXlhJIiGY2fkLf5HXkqYsZOUi9VYv7s4pWXJwza8yjwyhpsI46mK3u8mLoak5n1CPJW2rH1YPfzKaP4lS/s400/newtons+law+of+viscosity+equation.png)
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](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEik3HMgxoVD1y3wmk3XordSa6eWQkQJHogdRTNCzN74FLlVggUtMhlLsSh3_Xst4mgWWlWhj9ylycMIEleiLUs_OEe7RO0q8Tl4DroqvYaCX_BGh3Jzsd87YHBRakEsIdD-CZYJvk-bw2Uw/s400/newtons+law+of+viscosity+equation.png)
![newtons_law_of_viscosity_equation](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjikWpNC-Tor9G11xWE446_noZ8lHVLO2UmjO5Uw3xIDvo861ejXWvAMRi_2kZNr28xhCQ0k5r54R8Z4HEbTcigY9pac2qMyvgpvgPRNEHtSjtmHuGD_rduKGMX345s-cpHDq5HrlMagL-o/s400/newtons+law+of+viscosity+equation1.png)
Here constant of proportionality μ is known as the coefficient of dynamic viscosity
![velocity_gradient](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2A9X3o1_-rFJK-I7jTimJV5XTwBpnoQE4E-DhbxfgADunvvV0x11T_jyViCvKirL0B3PGlBzRoLrfmw5zblzCtVV4BKbiR-m6a4wkADaVc_PPAWw7AYJld47V0gJOZxJJB5TYtl7qfdIC/s400/velocity+gradient.png)
From the above equation,
![viscosity_equation](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXGBEee9YhnhorcNljCsFCoTI4nXvc4TsLXd5gGlryWItKgQRhl8myBKy8eQEK2DFgzaiT2A4dxkyj8woosZOZNF5-6Yaywiu7ivWoyNjL45hMb4lrMOq22rr44M3wrlGWQC_5YEbaMs9F/s400/from+newtons+law.png)
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
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
![kinematic_viscosity_equation](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZzcPF7NCSjcCiWg_lGAd50XpCh87Xi4O5Ji5jo8zMp2nyQ2YAUSbQEF9Z821_rMTHQZOlPCsEND3xvAgPq0DkDXvM7a102EtkjygQpHn1-8_M0NE3S7svZ5e9orK_oPxxe7PyS8Yz5viV/s400/kinematic+viscosity+equation.png)
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
Remember
- What Does Surface Tension Mean
- Properties of Fluids
- 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 Does Surface Tension Mean
- Properties of Fluids