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Standard XII

Physics

Equation of Continuity

Water enters ...

Question

Water enters through end A with a speed v₁ and leaves through end B with a speed v₂ of a cylindrical tube AB. The tube is always completely filled with water. In case I the tube is horizontal, in case II it is vertical with the end A upward and in case III it is vertical with the end B upward. We have v₁ = v₂ for

Case I

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Case II

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Case III

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each case

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Solution

The correct option is D. each case.
Take any orientation of cylindrical tube [uniform cross section]

Now, in any orientation the continuity equation is valid.
Therefore, $A_{1} v_{1} = A_{2} v_{2}$
But $A_{1} = A_{2}$
$\Rightarrow v_{1} = v_{2}$

Hence option (D) is correct.

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The correct option is D. each case.Take any orientation of cylindrical tube [uniform cross section] Now, in any orientation the continuity equation is valid.Therefore, A1v1=A2v2 But A1=A2 ⇒v1=v2 Hence option (D) is correct.

The correct option is D. each case.
Take any orientation of cylindrical tube [uniform cross section]

Now, in any orientation the continuity equation is valid.
Therefore, $A_{1} v_{1} = A_{2} v_{2}$
But $A_{1} = A_{2}$
$\Rightarrow v_{1} = v_{2}$

Hence option (D) is correct.