Define non-prismatic channel

A non-prismatic channel is an open channel whose cross-sectional shape or size, or the bed slope, changes along its length. Its area depends on both depth and distance, $A=f(y,x)$.

Examples: all natural rivers and streams, a canal with transitions (contraction or expansion), a channel with a change of bed slope, or a channel with a change in width at a bridge.

 Plan view of a transition
 ________
         \______   narrower section
 ________/ ______

Analysis (for example critical depth) of non-prismatic channels is done section by section, because properties such as $A$, $T$ and $R$ vary from one section to the next.