An incompressible non viscous fluid flows steadily through a cylindrical pipe which has radius 2 R at point A and radius R at point B farther along the flow direction. If the velocity of the fluid at

Question

An incompressible non viscous fluid flows steadily through a cylindrical pipe which has radius 2 R at point A and radius R at point B farther along the flow direction. If the velocity of the fluid at point A is V , its velocity at the point B will be

TestHub · Accepted Answer

We know that, from continuity equation,

$A_{1} V_{1} = A_{2} V_{2}$

(Symbols have usual meanings)

$π ({2 R)}^{2} V = π R^{2} V_{B}$

( $V_{B} =$ Velocity of the fluid at point $B$ )

$\Rightarrow π (2 {R)}^{2} V = π R^{2} V_{B}$

$\Rightarrow π 4 R^{2} V = π R^{2} V_{B}$

$4 V = V_{B}$

$∴ V_{B} = 4 V$

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