Question

The rate of flow of a liquid through a capillary tube of length $L$ and radius $r$ under a pressure difference $p$ is given by the poiseuille's formula $V=\pi p{r}^4/8\eta L$. Determine the dimensions of the coefficient of viscosity $\eta$ of the liquid.

Answer 1

It is given that

$V=\frac{\pi {Pr}^4}{8\eta L}$

$\eta =\frac{\pi {Pr}^4}{8VL}$

Where V is volume rate $\left[L^3{T}^{-1}\right]$

P is pressure $\left[M{L}^{-1}{T}^{-2}\right]$

$\eta$ is viscosity

L is length $\left[L\right]$

So the dimensional formula of viscosity is

$\frac{\left[M{L}^{-1}{T}^{-2}\right]\left[L^4\right]}{\left[L^3{T}^{-1}\right]\left[L\right]}$

$\left[M{L}^{-1}{T}^{-1}\right]$