question_answer

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 V, the speed of the ejection of the liquid through the holes is:

A) \[\frac{{{V}^{2}}R}{nr}\]

B) \[\frac{V{{R}^{2}}}{{{n}^{2}}{{r}^{2}}}\]

C)  \[\frac{V{{R}^{2}}}{n{{r}^{2}}}\]

D)  \[\frac{V{{R}^{2}}}{{{n}^{3}}{{r}^{2}}}\]

Correct Answer: C

Solution :

\[Av=\]constant \[\pi {{R}^{2}}V=n\pi {{r}^{2}}{{v}_{1}}\Rightarrow {{v}_{1}}=\frac{V{{R}^{2}}}{n{{r}^{2}}}\]