# Unit of Coefficient of Viscosity

## Unit of Coefficient of Viscosity

What is Coefficient of Viscosity?

Coefficient of viscosity is defined for two parallel layers of liquid as the tangential force required to maintain a unit velocity gradients between these layers and also we can say that it is the ratio of shear stress to the velocity gradient of the fluid.

Mathematical representation is:

$$Co-efficient\,\,of\,\,Vis\cos ity(\eta )=\frac{Fr}{Av}$$,

Where,

$$\eta$$ = Co – efficient of Viscosity,

$$F$$ = Tangential Force,

$$A$$ = Area,

$$v$$ = Velocity,

$$r$$ = Distance between the layers.

Unit of Coefficient of Viscosity?

Following is the unit of coefficient of viscosity in different systems:

SI Unit: $$Ns/{{m}^{2}}$$.

Dimensional formula of Coefficient of Viscosity:

$$Co-efficient\,\,of\,\,Vis\cos ity(\eta )=\frac{Fr}{Av}$$.

Now, the dimensional formula of force (F): $${{M}^{1}}{{L}^{1}}{{T}^{-2}}$$.

Dimensional formula of velocity (v): $${{M}^{0}}{{L}^{1}}{{T}^{-1}}$$.

Dimensional formula of distance(r): $${{M}^{0}}{{L}^{1}}{{T}^{0}}$$.

Dimensional formula of area (A): $${{M}^{0}}{{L}^{2}}{{T}^{0}}$$.

Now,

$$Co-efficient\,\,of\,\,Vis\cos ity(\eta )=\frac{Fr}{Av}=\frac{\left( {{M}^{1}}{{L}^{1}}{{T}^{-2}} \right)\left( {{M}^{0}}{{L}^{1}}{{T}^{0}} \right)}{\left( {{M}^{0}}{{L}^{2}}{{T}^{0}} \right)\left( {{M}^{0}}{{L}^{1}}{{T}^{-1}} \right)}=\left[ {{M}^{1}}{{L}^{-1}}{{T}^{-1}} \right]$$.

Therefore, the dimensional formula of Co – efficient of Viscosity is $$\left[ {{M}^{1}}{{L}^{-1}}{{T}^{-1}} \right]$$.