Answer to Question #189733 in Classical Mechanics for Abraham emmanuel

Question

how do you derive the dimensional formular of absolute viscosity

Answer 1

We know that,

Force $(F)=\eta A\frac{dV}{dx}$

Dimensional formula of force $(F)=[MLT^{-2}]$

Dimensional formula of area of contact $(A) = [L^2]$

$dV=[LT^{-1}]$

$dt= [T]$

Now, substituting the values,

$[MLT^{-2}]=\eta [L^2][LT^{-1}][T^{-1}]$

$\Rightarrow [MLT^{-2}]=\eta [L^3 T^{-2}]$

$\Rightarrow \eta = \frac{[MLT^{-2}]}{ [L^3 T^{-2}]}$

$\Rightarrow \eta = [ML^{-2}]$