Two liquids of densities $d_1$ and $d_2$ are flowing in identical capillary tubes uder the same pressure difference. Ift $t_1$ and $t_2$ are time taken for the flow of equal quantities (mass) of liquids, then the ratio of coefficient of viscosity of liquids must be
Medium
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(a)
According to poiseuille's equation, Volume of liquid flowing per second in a capillary tube is given by
$Q =\frac{ V }{ t }=\frac{\pi r ^4 \Delta P }{8 \eta L }$
So mass of liquid flowing in a capillary tube is given by
$Q _{ m }=\frac{ m }{ t }=\frac{\pi r ^4 \Delta P }{8 \eta L } d$
$\Rightarrow \frac{ m _1}{ t _1}=\frac{\pi r ^4 \Delta P }{8 \eta_1 L } d _1 \ldots(I)$
$\Rightarrow \frac{ m _2}{ t _2}=\frac{\pi r ^4 \Delta P }{8 \eta_2 L } d _2 \ldots(II)$
Dividing $(I)$ by $(II)$, we have
$\frac{ t _2}{ t _1}=\frac{ d _1}{ d _2} \times \frac{\eta_2}{\eta_1}$
$\Rightarrow \frac{\eta_1}{\eta_2}=\frac{ d _1 t _1}{ d _2 t _2}$
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