Question

Dimensions of coefficient of viscosity is?

Answer 1

1. The coefficient of Viscosity is the ratio of shearing stress of fluid to the velocity gradient between parallel layers of that fluid
2. The SI unit of coefficient of viscosity is $Newtonsecmete{r}^{-2}$
3. The formula for viscosity is $F=\mu A\frac{u}{y}$ Here $A$ is the area of the plate,$F$ is the force on the plate, $\frac{u}{y}$is the rate of shear deformation, and $\mu$ is the viscosity
4. Dimension of $\frac{u}{y}=\left[T^{-1}\right]$
5. Dimension of $F=\left[m\frac{dv}{dt}\right]=\left[M^1{L}^1{T}^{-2}\right]$
6. Dimension of $A=\left[M^0{L}^2{T}^0\right]$
7. Hence the dimension of viscosity is $\left[\mu \right]=\frac{\left[F\right]}{\left[A\right]\left[{\displaystyle \frac{u}{y}}\right]}=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]\left[T^{-1}\right]}=\left[M^1{L}^{-1}{T}^{-1}{K}^0\right]$
8. Therefore the dimension of the coefficient of viscosity is $\left[M^1{L}^{-1}{T}^{-1}{K}^0\right]$, Where M refers to mass, L refers to the length, T refers to time, and K refers to the temperature