The cylindrical tube of a spray pump has radius R, one end of which has $n$ fine holes, each of radius $r$. If the speed of the liquid in the tube is $\mathrm{V}$, the speed of the ejection of the liquid through the holes is : (1) $\frac{V^{2} R}{n r}$ (2) $\frac{V R^{2}}{n^{2} r^{2}}$ (3) $\frac{V R^{2}}{n r^{2}}$ (4) $\frac{V R^{2}}{n^{3} r^{2}}$

contexto.120

3 years ago

The solution is option 3

Volume inflow rate = volume anflow rate
$
\pi R^{2} V=n \pi r^{2} \quad \Rightarrow \quad v=\frac{\pi R^{2} V}{n \pi r^{2}}=\frac{V R^{2}}{\mathrm{nr}^{2}}
$