Viscosity is defined as the ratio of force require to shear a liquid to the velocity of shear (Shear means when adjacent layers of liquid are made to slide over each other ).
Coefficient of viscosity is defined as tangential force required to maintain a unit velocity gradient between two parallel layers of liquid of unit area.
Mathematically,
Coefficient of viscosity (η)= Fr/Av ——- F= tangential Force, Area, r= distance between the layers, v= velocity.
Dimensional Formula of Force = M1L1T-2.
Dimensional Formula of Area= M0L2T0.
Dimensional Formula of distance= M0L1T0.
Dimensional Formula of velocity= M0L1T-1.
Putting these values in above equation we get,
[η]= [M1L1T-2][M0L1T0] / [M0L2T0] [M0L1T-1] = [M1L-1T-1]
Dimensional Formula of Coefficient of viscosity (η)=[M1L-1T-1]
SI unit of Coefficient of viscosity (η) is Pascal-second