Question

Find out the terminal velocity of rain water drop of radius 1 mm. Viscous coefficient for air is $1.8\times {10}^{-5}Ns/m^2$ and density $1.2kg/m^3$, density of water is ${10}^{3}kg/m^3$, ($g=10m/s^2$).

Answer 1

Given, $r=1mm=1\times {10}^{-3}m$;

$\eta =1.8\times {10}^{-2}Ns/m^{-2}$

$p={10}^{3}kg{m}^{-3};\sigma =1.2kg{m}^{-3};g=10m{s}^{-2}$

$v_t=?$

$\therefore v_t=\frac{2r^2(p-\sigma )g}{9\eta }=\frac{2\times {10}^{-6}(1000-1.2)\times 10}{9\times 1.8\times {10}^{-2}}$

$=\frac{2\times 998.8}{9\times 1.8}\times {10}^{-3}$

$=123.3\times {10}^{-3}=0.123m/s=12.3cm/s$