Question

If ${{\eta }_{1}}$ and ${{\eta }_{2}}$ are the coefficients of viscosity of two liquids ${{d}_{1}}$ and ${{d}_{2}}$ their densities and ${{t}_{1}}$ and ${{t}_{2}}$ the flow times in Ostwald viscometer, then:
A. $\dfrac{{{\eta }_{1}}}{{{\eta }_{2}}}=\dfrac{{{d}_{1}}{{t}_{2}}}{{{d}_{2}}{{t}_{1}}}$
B. $\dfrac{{{\eta }_{1}}}{{{\eta }_{2}}}=\dfrac{{{d}_{2}}{{t}_{2}}}{{{d}_{1}}{{t}_{1}}}$
C. $\dfrac{{{\eta }_{1}}}{{{\eta }_{2}}}=\dfrac{{{d}_{1}}{{t}_{1}}}{{{d}_{2}}{{t}_{2}}}$
D. $\dfrac{{{\eta }_{1}}}{{{\eta }_{2}}}=\dfrac{{{d}_{2}}{{t}_{1}}}{{{d}_{1}}{{t}_{2}}}$

Answer 1

Hint: Ostwald viscometer or U-tube viscometer or capillary viscometer, a device used to measure the density or viscosity of a liquid. If we know the viscosity of one liquid we can calculate the viscosity of another liquid.

Complete step by step answer:
Viscosity is nothing but the density of a liquid. It is a measure of a fluid’s resistance to flow. The SI unit of viscosity is square meters per second (${{m}^{2}}/s$) but square centimeter per second ($c{{m}^{2}}/s$) is more commonly used.
There are three main types of viscometer; capillary, coaxial cylinder and falling sphere.
In this Ostwald’s viscometer, the instrument consists of measuring time for a volume of a liquid which is known which flows through the capillary under the influence of gravity.
For measuring viscosity, the temperature of the substance is precisely controlled because small changes in temperature can cause major change in viscosity.
First, the instrument is calibrated with materials of known viscosity such as deionized water or pure water.
The liquid is added and pulled into the upper reservoir and then allowed to drain back by gravity. The relative viscosity is measured in the following way:
${{\eta }_{rel}}=\dfrac{\eta }{{{\eta }_{0}}}=\dfrac{dt}{{{d}_{0}}{{t}_{0}}}$

Hence, the correct option is C which is $\dfrac{{{\eta }_{1}}}{{{\eta }_{2}}}=\dfrac{{{d}_{1}}{{t}_{1}}}{{{d}_{2}}{{t}_{2}}}$.

Note: The Oswald’s viscometer works on the principle that the device is used to measure the viscosity of the liquid with a known density.