Q. Water is flowing through a tube of non-uniform cross-section. Ratio of the radius at entry and exit end of the pipe is 3:2. Then the ratio of velocities at entry and exit of liquid is
A) 4 : 9
B) 9 : 4
C) 8 : 27
D) 1 : 1
Explanation
(a) If velocities of water at entry and exit points are $v_{1}$ and $v_{2}$, then according to equation of continuity
$A_{1}v_{1} = A_{2}v_{2} \Rightarrow \frac{v_{1}}{v_{2}} = \frac{A_{2}}{A_{1}} = \left( \frac{r_{2}}{r_{1}} \right)^{2} = \left( \frac{2}{3} \right)^{2} = \frac{4}{9}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.