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

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) (V/2) (B) 4V (C) 2V (D) V

Tardigrade Admin · 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

Q. 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

$\frac{V}{2}$

$4 V$

$2 V$

$V$

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

Q. 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

2V​

4V

2V

V

We know that, from continuity equation, A1​V1​=A2​V2​ (Symbols have usual meanings) π(2R)2V=πR2VB​ (VB​= Velocity of the fluid at point B) ⇒π(2R)2V=πR2VB​ ⇒π4R2V=πR2VB​ 4V=VB​ ∴VB​=4V

Q. 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

$\frac{V}{2}$

$4 V$

$2 V$

$V$