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 :

P - \frac{1}{2} δ V^{2}

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P - δ V^{2}

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P + δ V^{2}

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P - 7.5 δ V^{2}

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Solution

The correct options are
A $P - δ V^{2}$
C $P - \frac{1}{2} δ V^{2}$
We know that, from continuity equation,
$A_{1} V_{2} = A_{2} V_{2}$
(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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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 :

The correct options are A P−δV2 C P−12δV2We know that, from continuity equation,A1V2=A2V2(Symbols have usual meanings)π(2R)2V=πR2VB(VB= Velocity of the fluid at point B)⇒π(2R)2V=πR2VB⇒π4R2V=πR2VB4V=VB∴VB=4V

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 :