Physics - Fluid Question with Solution | TestHub

Expression for terminal velocity can be obtained by balancing weight of the droplet with viscous retardation force and the buoyancy force. Terminal velocity is given by $v=\frac{2}{9}\left(\frac{r^2(\rho -\sigma )}{\eta }\right)$ $\therefore v\propto r^2$ Now, let $V^{\prime }$ be the terminal velocity of the merged droplet $\begin{array}{rl}& \therefore \frac{V}{V^{\prime }}=\frac{r^2}{R^2}\\ & \Rightarrow V^{\prime }=\frac{V{R}^2}{r^2}\end{array}$