Question
Obtain the dimensional formula for coefficient of viscosity.
✓
Answer
As
$\text{F}=\eta\text{A}\frac{\text{dv}}{\text{dx}}$
Hence, $\eta=\frac{\text{F dx}}{\text{A dv}}$
$\therefore[\eta]=\frac{[\text{F}][\text{dx}]}{[\text{A}][\text{dv}]}$
$=\frac{[\text{MLT}^{-2}.\text{L}]}{[\text{L}^2.\text{LT}^{-1}]}=[\text{M}^1\text{L}^{-1}\text{T}^{-1}]$
$\text{F}=\eta\text{A}\frac{\text{dv}}{\text{dx}}$
Hence, $\eta=\frac{\text{F dx}}{\text{A dv}}$
$\therefore[\eta]=\frac{[\text{F}][\text{dx}]}{[\text{A}][\text{dv}]}$
$=\frac{[\text{MLT}^{-2}.\text{L}]}{[\text{L}^2.\text{LT}^{-1}]}=[\text{M}^1\text{L}^{-1}\text{T}^{-1}]$
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