Question

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 :

• A. $K_1 = K_2$
• B. $2K_1 = K_2$
• C. $K_1 > K_2$
• D. $K_1 < K_2$

Answer 1

Answer: (B)

$2K_1 = K_2$

Answer 2

Kinetic energy per unit volume is $\frac{1}{2}\rho v^2$, where $\rho$ is the density and $v$ is the velocity.

By the equation of continuity (for an incompressible fluid), $A_1v_1 = A_2v_2$, where A is the cross-sectional area.

From X to Y, the area increases, so the velocity decreases.

Since $K \propto v^2$, $K_1 > K_2$.