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

The Correct Option is B

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

According to the equation of continuity for an incompressible fluid, $A_1v_1 = A_2v_2$, where A represents the cross-sectional area.

As the area increases from X to Y, the velocity decreases.

Consequently, since $K \propto v^2$, it follows that $K_1>K_2$.