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Coefficient of Viscosity

Two liquids o...

Question

Two liquids of densities $d_{1}$ and $d_{2}$ are flowing in identical capillaries under same pressure difference. If $t_{1}$ and $t_{2}$ are the time taken for the flow of equal quantities of liquids, then the ratio of coefficients of viscosities of liquids must be

A

\frac{d_{1} d_{2}}{t_{1} t_{2}}

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B

\frac{d_{1} t_{1}}{d_{2} t_{2}}

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C

\frac{d_{1} t_{2}}{d_{2} t_{1}}

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D

\sqrt{(\frac{d_{1} t_{1}}{d_{2} t_{2}})}

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Solution

The correct option is B $\frac{d_{1} t_{1}}{d_{2} t_{2}}$
According to Poiseuille's law, the rate of flow of liquid through a capillary tube having viscosity coefficient, can be expressed as
$η = \frac{π \cdot r^{4} t P}{8 vl}$
For, identical capillary, $η α P t$ and $P α ρ g h t$
$P$ is hydrostatic pressure, $t$ is time, $g$ is gravity, $d$ is density, $h$ is height and $η$ is viscosity.$
$η_{1} \propto d_{1} gh t_{1} and η_{2} \propto d_{2} gh t_{2}$

$\frac{η_{1}}{η_{2}} = \frac{d_{1} t_{1}}{d_{2} t_{2}}$

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