Question

Water is flowing through a non uniform radius tube. If ratio of the radius of entry and exit end of the pipe is 3:2 then the ratio of velocities of entring and exit liquid is

• A. 4:9
• B. 9:4
• C. 8:27
• D. 1:1

Answer 1

The correct option is A 4:9

We know, for the fluid flowing through the non uniform pipe the velocity of fluid is inversely proportional to the area of cross-section.
Hence, if v1, v2 are the velocities of entry and exit end of the pipe and a1, a2 are the area of cross-sections of entry and exit end of the pipe, then
$\frac{v1}{v2}=\frac{a2}{a1}$
$\Rightarrow \frac{v1}{v2}=\frac{(r2{)}^2}{(r1{)}^2}$
$\therefore \frac{v1}{v2}=\frac{(2{)}^2}{(3{)}^2}=\frac{4}{9}$