Question

A large bottle fitted with a siphon made of capillary glass tubing. Compare the times taken to empty a bottle when it is filled with water and with kerosene of specific gravity 0.8 . The viscosities of water and kerosene are 0.01poise and 0.02 poise respectively.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Let}{\mathrm{t}}_1\mathrm{and}{\mathrm{t}}_2\mathrm{bt}\mathrm{the}\mathrm{time}\mathrm{taken}\mathrm{to}\mathrm{empty}\mathrm{the}\mathrm{bottle}\mathrm{filled}\mathrm{with}\mathrm{water}\mathrm{and}\mathrm{petroleum}\mathrm{resp}. \\ \mathrm{If}{\mathrm{n}}_1\mathrm{and}{\mathrm{\rho }}_1\mathrm{are}\mathrm{the}\mathrm{viscosity}\mathrm{and}\mathrm{density}\mathrm{of}\mathrm{water}\mathrm{and}{\mathrm{n}}_2\mathrm{and}{\mathrm{\rho }}_2\mathrm{of}\mathrm{petroleum},\mathrm{then}, \\ {\mathrm{n}}_1=0.01\mathrm{poise} \\ {\mathrm{n}}_2=0.02\mathrm{poise} \\ \mathrm{specific}\mathrm{gravity},\frac{{\mathrm{\rho }}_2}{{\mathrm{\rho }}_1}=0.8 \\ {\mathrm{t}}_1=\frac{8{\mathrm{n}}_1\mathrm{lA}}{{\mathrm{\pi \rho }}_1{\mathrm{gr}}^4}{\log }_{\mathrm{e}}\mathrm{H} \\ \mathrm{and}{\mathrm{t}}_2=\frac{8{\mathrm{n}}_2\mathrm{lA}}{{\mathrm{\pi \rho }}_2{\mathrm{gr}}^4}{\log }_{\mathrm{e}}\mathrm{H} \\ \frac{{\mathrm{t}}_1}{{\mathrm{t}}_2}=\frac{{\mathrm{n}}_1}{{\mathrm{n}}_2}\times \frac{{\mathrm{\rho }}_2}{{\mathrm{\rho }}_1} \\ \frac{{\mathrm{t}}_1}{{\mathrm{t}}_2}=\frac{0.01}{0.02}\times 0.8=\frac{0.4}{1} \\ \frac{{\mathrm{t}}_1}{{\mathrm{t}}_2}=\frac{4}{10} \\ \frac{{\mathrm{t}}_1}{{\mathrm{t}}_2}=\frac{2}{5} \end{gathered}$$