A liquid drop of mass m and radius r is falling from great height. Its velocity is proportional to .

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9-1.Fluid Mechanics

medium

A liquid drop of mass $m$ and radius $r$ is falling from great height. Its velocity is proportional to ............

$\frac{m}{r}$

$\frac{m}{r^2}$

$\frac{m}{r^3}$

$\frac{m}{r^4}$

Solution

(a)

When a drop fall in air the terminal velocity of the drop is $V _0=\frac{ mg -\frac{4}{3} \pi r ^3 \rho g}{6 \pi \eta r }$ where $\rho$ is density of air $\eta$ is the viscosity of air From the above equation $V _0 \propto \frac{ m }{ r }$

Standard 11

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