**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 \(\left[ {{M}^{1}}{{L}^{-1}}{{T}^{-1}} \right]\).