# Turpentine oil is flowing thorough a tube of length l and radius r. the pressure difference between the two ends of the tube is P. the viscocity of oil is given by n=P(r2-v2)/4vl,where vis the velocity of oil at a difference x from the axis of the tube. find the dimensions of eeta

$Thedimensionof\phantom{\rule{0ex}{0ex}}pis[M{L}^{-1}{T}^{-2}]\phantom{\rule{0ex}{0ex}}Thedimensionofris\left[L\right]\phantom{\rule{0ex}{0ex}}Thedimensionofvis\left[L{T}^{-1}\right]\phantom{\rule{0ex}{0ex}}ThedimensionofIis\left[L\right]\phantom{\rule{0ex}{0ex}}Therefore,thedimensionof\eta willbe\phantom{\rule{0ex}{0ex}}\left[\eta \right]=\frac{\left[P\right][{r}^{2}-{x}^{2}]}{\left[4vl\right]}=\frac{[M{L}^{-1}{T}^{-2}]\left[{L}^{2}\right]}{\left[L{T}^{-1}\right]\left[L\right]}\phantom{\rule{0ex}{0ex}}So\left[\eta \right]=[M{L}^{-1}{T}^{-1}]$

Regards

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