Physics - Fluid Question with Solution | TestHub

Viscous force acting on spherical drop $F_v=6\pi \eta rv$ $\therefore$ Terminal velocity, $v=\frac{2}{9}\frac{r^2(\sigma -\rho )g}{\eta }$ where, $\eta =$ coefficient of viscosity of liquid $\sigma =$ density of material of spherical drop $\rho =$ density of liquid Power imparted by viscous force = Rate of production of heat $\begin{array}{rl}P& =\frac{dH}{dt}=F_v\cdot v=6\pi \eta r{v}^2\\ & =6\pi \eta r\cdot {\left(\frac{2}{9}\frac{r^2(\sigma -\rho )g}{\eta }\right)}^2\\ \Rightarrow \frac{dH}{dt}& \propto r^5\end{array}$