An incompressible fluid flows steadily through a cylindrical pipe having radius R at point A and ( 3 R ) at point B further along the direction of flow of liquid. If the velocity at point A is &#039

Question

An incompressible fluid flows steadily through a cylindrical pipe having radius R at point A and ( 3 R ​ ) at point B further along the direction of flow of liquid. If the velocity at point A is ' V ' then that at point B is

TestHub · Accepted Answer

According to the equation of continuity for steady flow of an incompressible fluid:

$A_{A} V_{A} = A_{B} V_{B}$

The area of cross-section at point A is $A_{A} = π R^{2}$ and the area at point B is $A_{B} = π (\frac{R}{3})^{2} = \frac{π R ^{2}}{9}$ .

Substituting the given values into the equation of continuity:

$π R^{2} V = \frac{π R ^{2}}{9} V_{B}$

$V_{B} = 9 V$

Answer: 9V

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