An ideal fluid is flowing in a non-uniform cross-sectional tube XY (as shown in the figure) from end X to end Y. If and are the kinetic energy per unit volume of the fluid at X and Y respectively, then the correct option is [2024]

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Solution

Q.
An ideal fluid is flowing in a non-uniform cross-sectional tube XY (as shown in the figure) from end X to end Y. If $K_{1}$ and $K_{2}$ are the kinetic energy per unit volume of the fluid at X and Y respectively, then the correct option is [2024]

1 $K_{1} = K_{2}$

2 $2 K_{1} = K_{2}$

3 $K_{1} > K_{2}$

4 $K_{1} < K_{2}$

Ans.
(3)

The cross-section area of X is smaller than the Y.

Using equation of continuity for ideal fluid, $a_{1} v_{1} = a_{2} v_{2}$

$v_{1} > v_{2}$ $(∵ a_{1} < a_{2})$

So, the $\frac{K.E.}{Volume} of x (K_{1}) > \frac{K.E.}{Volume} of y (K_{2})$

$∴$ $K_{1} > K_{2}$ $(∵ K = \frac{1}{2} ρ v^{2})$

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