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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 $\frac{d_{1} t_{1}}{d_{2} t_{2}}$
we know that from the concept of Reylonld's number $R e = \frac{d v t}{μ}$
given that fluid is flowing in identical capillaries under same pressure difference, so ${R e}_{1} = {R e}_{2}$
$\frac{d_{1} \times v \times t_{1}}{μ_{1}} = \frac{d_{2} \times v \times t_{2}}{μ_{2}}$
$\frac{μ_{1}}{μ_{2}} = \frac{d_{1} t_{1}}{d_{2} t_{2}}$

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