A liquid enters tube of variable cross section with a velocity 3 ms^-1 through the wider end and leaves from the narrower end whose radius is half of the wider one. The velocity with which is laves the tube is ___________ ms^-1

According to the equation of continuity, the flow's volume rate stays constant throughout the flow. The continuity equation can be written as,

${\mathrm{A}}_1{\mathrm{v}}_1={\mathrm{A}}_2{\mathrm{v}}_2$

$\Rightarrow \mathrm{\pi }{{\mathrm{r}}_1}^2{\mathrm{v}}_1=\mathrm{\pi }{{\mathrm{r}}_2}^2{\mathrm{v}}_2$

$\Rightarrow {\mathrm{r}}^2\times 3={\left(\frac{\mathrm{r}}{2}\right)}^2{\mathrm{v}}_2 \Rightarrow {\mathrm{r}}^2\times 3=\frac{{\mathrm{r}}^2}{4}{\mathrm{v}}_2\Rightarrow {\mathrm{v}}_2=12\mathrm{m}/\sec$

Hence the correct answer is 12.