A horizontal pipe carries an incompressible, non-viscous liquid in steady flow. At one section the pipe gradually narrows and then widens again farther downstream.
(i) State the fundamental conservation principle that governs the constancy of the volume flow rate in such a situation.
(ii) Explain qualitatively, without doing any numerical calculation, why the speed of the liquid must increase in the narrow portion of the pipe and decrease again in the wider portion.
(iii) Give one everyday example (other than water flowing in household plumbing) where the same reasoning accounts for an observable change in fluid speed, and briefly describe how the example illustrates the principle.