Dynamic Viscosity Formula

At first glance, viscosity seems like a very simple concept. It helps to describe how thick a product is or how well it can flow. In reality, there are different terms that come under this concept of viscosity. These terms can be derived from how the viscosity is measured. When we talk about the viscosity, then we are talking about one of two things i.e kinematic viscosity or dynamic viscosity. In this topic, we will discuss the dynamic viscosity formula with examples. Let us begin the interesting learning!

Source:en.wikipedia.org

Dynamic Viscosity Formula

What is Dynamic Viscosity?

It is not easy to find a lot of information on the differences between dynamic and kinematic viscosity. One way is to measure a fluid’s resistance to flow when an external force is applied and is the dynamic viscosity.

Viscosity is an important property of the fluid material and is useful to understand the fluid’s behavior. Also, the way it will move when it comes in contact with solid boundaries.

A fluid’s viscosity is the measure of the resistance to its gradual deformation by tensile or shear stress. Shear stress in the fluid is possible due to the intermolecular friction exerted when layers of fluids attempt to slide over each other.

Dynamic Viscosity Formula for the fluid will define its internal resistance to flow due to some shearing force. This is a kind of tangential force that acts when one horizontal plane moves with another one. The viscosity acts as an important fluid property during the analysis of liquid behavior and fluid motion near solid boundaries.

Therefore, the dynamic viscosity is the force needed by a fluid to overcome its own internal molecular friction so that the fluid can flow.

Thus dynamic viscosity can be expressed as the tangential force per unit area required to move the fluid in one horizontal plane with respect to another plane, with a velocity of unit value while the fluid’s molecules maintain a unit distance apart.

The rotational viscometer is a popular instrument, used to measure the dynamic viscosity. These instruments will rotate a probe in the liquid sample. Viscosity is determined by measuring the force i.e. torque required to turn the probe.

The formula for Dynamic Viscosity

Since dynamic viscosity is the tangential force required to move one horizontal plane of a fluid with respect to another. Thus, we can express it as:

Dynamic viscosity = \(\frac {shearing stress} { shearing rate change}\)

In the form of the equation, we can write it as:

\(\eta = \frac {T}{\gamma }\)

Where,

\(\eta\)	Dynamic viscosity
T	Shearing stress
\(\gamma\)	Shear rate

We measure Dynamic viscosity in the unit of Pascal second or  \(Pa\; s\)

Solved Examples

Q.1: A fluid with a shear rate of 0.5 per second, and the shearing stress 0.76 N per m². According to its dynamic viscosity, to which one of these fluids corresponds?

Water with dynamic viscosity 1 \(Pa\; s\)

Air with dynamic viscosity 0.018 \(Pa\; s\)

Mercury with dynamic viscosity 1.526 \(Pa\; s\)

Solution: First calculate the dynamic viscosity using the following formula, using the given values,

T= 0.76 N per m² and

\(\gamma\) = 0.5 per second

\(\eta = \frac {T}{\gamma }\)

= \(\frac { 0.76 }{ 0.5 }\)

= 1.52 Pa\(\; s\)

Therefore it is clear that Mercury fluid will correspond with this fluid.