# What is Viscosity in Fluid Mechanics?

## What is Viscosity?

Viscosity is a property of a fluid which offers resistance to flow of one layer of a fluid over another adjacent layer of fluid. In simple language it is defined as the property which offers resistance to flow.

### Formula of Viscosity

Considered two layers of fluid which are at a distance dy apart. Let the velocity of the lower layer of fluid is u and the upper adjacent layer is u + du as shown in the figure. Due to the viscosity and relative velocity, shear stress is induced in between the two layers of the fluid.

The top layer induces shear force on the adjacent lower and the lower layer induces shear force on the adjacent top layer. The shear stress caused in between the two layers of fluid is proportional to the rate of change of velocity with respect to y. The shear force is denoted by symbol τ (tau).

Mathematically

Where

τ = Shear stress

du/y = Rate of shear strain or rate of sear deformation or velocity gradient.

Here μ is the constant of proportionality and called as coefficient of dynamic viscosity or only Viscosity.

From the above formula of shear stress, the formula of viscosity is can be written as

Viscosity is also defined as the shear stress required producing a unit rate of shear strain.

### Unit of Viscosity

The unit of Viscosity in MKS, CGS and SI units are given below

Since N/m2 is equals to the Pascal (Pa).

### Numerical Conversion of unit of Viscosity

#### From MKS unit to CGS unit

In numerical problems, if you want to convert viscosity in CGS unit from MKS unit than multiplied it with 98.1. And divide it by 98.1 if you want to convert CGS unit into MKS unit.

#### From MKS to SI and from SI to CGS

To convert MKS unit to SI unit, multiply it by 9.81 and divide it by 9.81 to convert again in MKS unit.

To convert SI unit into CGS unit, multiply it by 10 and divide it by 10 to convert again in SI Unit.

Sometime centipoise (cP) is also used as unit of viscosity.

**Remember this chart for the conversion of unit form one system to another.**

### Explanation of conversion of unit of viscosity

**Question: **

The viscosity of fluid is given as 10 poise. What is the value of viscosity in MKS and CGS unit.

**Answer: **

10 poise = 10/98.1 = 0.1019 kgf-sec/m2 (In MKS)

10 poise = 10/10 = 1 Ns/m2

In this we have learnt about what is Viscosity, unit of viscosity and formula of viscosity. If you find anything missing or incorrect than comment us. And if you find this article informative than don’t forget to like and share.