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