Question

What are the SI unit and dimensional formula of the coefficient of viscosity?

Answer 1

The SI unit of viscosity is the dyne-second per square centimetre [dyne s/${cm}^2$ ], which is given the name poise [P] after the French physiologist Jean Poiseuille.
Its dimensional formula is given by,
Coefficient of viscosity $\left(\eta \right)=\frac{Fr}{Av}$ - - - - - F = tangential Force, Area, r = distance between the layers, v = velocity.
Dimensional formula of force $=M^1{L}^1{T}^{-2}$
Dimensional formula of area $=M^0{L}^2{T}^0$
Dimensional formula of distance $=M^0{L}^1{T}^0$
Dimensional formula of velocity $=M^0{L}^1{T}^{-1}$
Putting these values in the above equation we get,
$\eta =\frac{\left[M^1{L}^1{T}^{-2}\right]\left[M^0{L}^1{T}^0\right]}{\left[M^0{L}^1{T}^0\right]\left[M^0{L}^1{T}^{-1}\right]}=\left[M^1{L}^{-1}{T}^{-1}\right]$
Dimensional formula of coefficient of viscosity, $\eta =\left[M^1{L}^{-1}{T}^{-1}\right]$