MediumChemistryHigh School (11–12)States of MatterNumericalAP A-Level IB

An Ostwald viscometer is filled with the same volume of each liquid at 20 °C…

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An Ostwald viscometer is filled with the same volume of each liquid at $20\ ^\circ\text{C}$ . Water, with $\rho = 998\ \text{kg/m}^3$ and $\eta = 1.002\ \text{mPa s}$ , takes $84\ \text{s}$ to flow between the marks. Ethanol, with $\rho = 789\ \text{kg/m}^3$ , takes $114\ \text{s}$ . Find the viscosity of ethanol, in mPa s and in poise.

Need a reminder? The key ideaShow

Poiseuille: $Q = \dfrac{\pi\Delta Pr^4}{8\eta L}$ . Stokes: a steady speed $v = \dfrac{2r^2(\rho_s - \rho)g}{9\eta}$ , valid when $Re = \dfrac{\rho vd}{\eta}$ is below about $1$ . Ostwald viscometer: $\dfrac{\eta_1}{\eta_2} = \dfrac{\rho_1t_1}{\rho_2t_2}$ . For a liquid, $\eta = Ae^{E/RT}$ , which falls as $T$ rises.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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← A steel ball of radius 2.0 mm and density 7800 kg/m³ is dropped into a tall jar of glycerol…Water, with η = 1.002 mPa s, flows through a horizontal capillary tube of radius 0.50 mm and length… →

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