Define non-uniform open channel flow with examples

Non-uniform (varied) flow is open channel flow in which the depth, and hence the velocity, changes from section to section along the channel: $\dfrac{\partial y}{\partial x}\neq0$. In steady non-uniform flow the discharge at a given section does not change with time, but the water surface is not parallel to the bed ($S_w\neq S_0$). It is divided into:

1. Gradually varied flow (GVF) where depth changes slowly. Example: backwater curve upstream of a weir or dam; flow in a canal with a change of bed slope.
2. Rapidly varied flow (RVF) where depth changes abruptly. Example: hydraulic jump, flow over a spillway crest or below a sluice gate.
3. Spatially varied flow (SVF) where discharge also changes along the length. Example: side weir, roadside gutter.

Natural rivers are non-uniform because their section and slope change from place to place. A uniform flow is only an idealised case of constant depth in a long prismatic channel.