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:

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


\(\eta \) = 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): \({{M}^{0}}{{L}^{2}}{{T}^{0}}\).


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

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