Kinematic Viscosity Formula

Viscosity is the important property of fluid while analyzing the liquid behavior and fluid motion near solid boundaries. Clearly, the viscosity of a fluid is the measurement of the resistance for gradual deformation due to shear stress or tensile stress. As we know that the shear resistance in a fluid is due to its inter-molecular friction exerted. It happens when layers of fluids attempt to slide by one another. Thus, we may say that viscosity is the measure of a fluid’s resistance to flow. In this article, the student will learn about the kinematic viscosity formula in particular. Let us learn it!

Definition of Kinematic Viscosity

Viscosity is a concept where fluid shows struggle against a flowing, which is being distorted due to extensional stress forces or shear stress. There are two related measures of fluid viscosity: Dynamic and Kinematic.

Absolute viscosity i.e. dynamic viscosity coefficient is a measure of internal resistance. It is at a unit velocity while maintaining a unit distance apart in the fluid. The shearing stress between the layers of a no turbulent fluid which is moving in straight parallel lines may be defined for a Newtonian fluid.

Whereas Kinematic viscosity is the sort of viscosity that is computed by calculating the ratio of the fluid mass density to the dynamic fluid, viscosity or absolute fluid viscosity. It is from time to time also known as momentum diffusivity. The units of kinematic viscosity are established on time and area of fluid.

Source:en.wikipedia.org

Therefore, Kinematic viscosity is the measurement of the inherent resistance of a fluid to flow when no external force is imparted except gravity. This is the ratio of the dynamic viscosity to its density, i.e. a force independent quantity. Kinematic viscosity can be computed by dividing the absolute viscosity of a fluid with the fluid mass density.

Formula for Kinematic Viscosity

As we know that it is the ratio of dynamic viscosity to fluid mass density. Thus,

Kinematic viscosity = \(\frac {Dynamic viscosity} {Fluid mass density}\)

Mathematically, \(v = \frac { \mu } {\ rho }\)

v	kinematic viscosity (square m per second)
\(\mu\)	absolute or dynamic viscosity ( unit is N s \(m^{- 2 })\)
\(\rho\)	density (unit is kg per cubic m)

Solved Examples for Kinematic Viscosity Formula

Q.1: The absolute viscosity of a flowing fluid is given as 0.67 N s per square m. If the density is known to be 10 kg per cubic m, calculate its kinematic viscosity coefficient using Kinematic Viscosity Formula.

Solution: Known parameters are as,

Absolute viscosity \(\mu  0.67 N\) s per square m

Density, \(\rho = 10\) kg per cubic m.

The kinematic viscosity in formula is:

\(v = \frac { \mu } {\ rho } \\\)

\(= \frac { 0.67 N s per square m } {10 kg per cubic m} \\\)

\(= 0.067 m^{2} s^ {-1 }\)

Therefore the kinetic viscosity is \(0.067 m^{2} s^ {-1 }\)

Q.2: Calculate the density of the fluid having an absolute viscosity of 0.89 N s per square m and kinematic viscosity of \(2 m^{2} s^ {-1 }\)

Solution: Known parameters are as,

Absolute viscosity \(\mu = 0.89\) N s per square m

Kinematic viscosity,\( v = 2 m^{2} s^ {-1 }\)

The density is: \(v = \frac { \mu } {\ rho }\)

i.e. \(\rho = \frac {v} {\mu}\)

\(= \frac {0.89}{2}\)

= 0.445 kg per cubic m

Therefore, the density of fluid is 0.445 kg per cubic m.