The analysis of flow patterns of water surface shape, velocity, shear stress and discharge through a stream reach falls under the heading Open Channel Flow.

Open Channel Flow is defined as fluid flow with a free surface open to the atmosphere. Examples include streams, rivers and culverts not flowing full. Open channel flow assumes that the pressure at the surface is constant and the hydraulic grade line is at the surface of the fluid

Steady and unsteady flow depend on whether flow depth and velocity change with time at a point. In general if the quantity of water entering and leaving the reach does not change, then the flow is considered steady.

Steady flow in a channel can be either Uniform or Non-uniform (varied).When the average velocities in successive cross sections of a channel are the same, the flow is uniform. This occurs only when the cross section is constant. Non-uniform flow results from gradual or sudden changes in the cross sectional area.

Uniform flow and varied flow describe the changes in depth and velocity with respect to distance. If the water surface is parallel to the channel bottom flow is uniform and the water surface is at normal depth. Varied flow or non-uniform flow occurs when depth or velocity change over a distance, like in a constriction or over a riffle. Gradually varied flow occurs when the change is small, and rapidly varied flow occurs when the change is large, for example a wave,  waterfall, or the rapid transition from a stream channel into the inlet of a culvert.

See also: Continuity Equation, Gradually Varied Flow