If \(\eta_{1}\) and \(\eta_{2}\) are coefficients of viscosity of two liquids, \(d_{1}\) and \(d_{2}\) are their densities and \(t_{1}\) and \(t_{2}\) are their flow times in an Ostwald's viscometer then (a) \(\frac{\eta_{1}}{\eta_{2}}=\frac{d_{1} t_{2}}{d_{2} t_{1}}\) (b) \(\frac{\eta_{1}}{\eta_{2}}=\frac{d_{2} t_{2}}{d_{1} t_{1}}\) (c) \(\frac{\eta_{1}}{\eta_{2}}=\frac{d_{1} t_{1}}{d_{2} t_{2}}\) (d) \(\frac{\eta_{1}}{\eta_{2}}-\frac{d_{2} t_{1}}{d_{1} t_{2}}\)

Short Answer

Expert verified
The correct formula is (c) \(\frac{\eta_{1}}{\eta_{2}}=\frac{d_{1} t_{1}}{d_{2} t_{2}}\)

Step by step solution

01

Understanding the Ostwald's viscometer

An Ostwald's viscometer is a device used to measure the viscosity of liquids. The viscometer measures the time it takes for a liquid to flow through a thin capillary tube. The longer the flow time, the higher the viscosity. The coefficient of viscosity (\(\eta\)) of a liquid in an Ostwald's viscometer is given as \(\eta = \gamma \rho t\), where \(\gamma\) is a constant, \(\rho\) is the density of the liquid and \(t\) is the flow times.
02

Apply the formula for each liquid

We have to apply the formula \(\eta = \gamma \rho t\) for each liquid, the coefficient of viscosity for the first liquid \(\eta_{1} = \gamma \rho_{1} t_{1}\) and for the second liquid \(\eta_{2} = \gamma \rho_{2} t_{2}\).
03

Calculate the ratio

Taking the ratio of \(\eta_{1}\) to \(\eta_{2}\) we get \(\frac{\eta_{1}}{\eta_{2}}=\frac{\gamma \rho_{1} t_{1}}{\gamma \rho_{2} t_{2}}\). As the same viscometer is used for both the liquids, the constant gamma can be eliminated from the equation resulting in the formula \(\frac{\eta_{1}}{\eta_{2}}=\frac{\rho_{1} t_{1}}{\rho_{2} t_{2}}\).

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