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(C) For a horizontal pipe, the height $h$ of the pipe remains constant at all points. Since the potential energy per unit volume is given by $\rho gh$

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Potential energy per unit volume

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(C) For a horizontal pipe, the height $h$ of the pipe remains constant at all points. Since the potential energy per unit volume is given by $\rho gh$, where $\rho$ is the density of the liquid, $g$ is the acceleration due to gravity, and $h$ is the height, this quantity remains constant throughout the flow. In a non-uniform pipe, the cross-sectional area $A$ changes, which causes the velocity $v$ to change according to the equation of continuity $(A_1v_1 = A_2v_2)$. Consequently, the kinetic energy per unit volume $(\frac{1}{2}\rho v^2)$ and the pressure energy $(P)$ change along the pipe to satisfy Bernoulli's principle. Therefore, the potential energy per unit volume is the quantity that remains unchanged.

$A$ liquid is flowing in a horizontal pipe of non-uniform cross-section. Which of the following quantities may remain unchanged with respect to time?

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