Question

An incompressible non viscous fluid flows steadily through a cylindrical pipe which has radius $2R$ 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

• A. $\frac{V}{2}$
• B. $4V$
• C. $2V$
• D. $V$

Answer 1

Answer: (B)

We know that, from continuity equation,
$A_1 V_1=A_2 V_2$
(Symbols have usual meanings)
$\pi(2 R)^2 V=\pi R^2 V_B$
$\left(V_B=\right.$ Velocity of the fluid at point $\left.B\right)$
$\Rightarrow \pi(2 R)^2 V=\pi R^2 V_B$
$\Rightarrow \pi 4 R^2 V=\pi R^2 V_B$
$4 V=V_B$
$\therefore V_B=4 V$