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Open channel flow, where water flows with a free surface, differs from closed conduit flow due to the influence of gravity and surface effects. 

Energy considerations are essential for understanding flow behavior in rivers, canals, and engineered channels.

The flow’s specific energy, which includes gravitational potential and kinetic energy, varies with depth and velocity and is represented as E.

For any given flow rate, specific energy yields two possible depths where subcritical is deep and slow, while supercritical is shallow and fast.

The Froude number, F_r, classifies these regimes. Subcritical flow, with a Froude number less than one, is gravity-driven, while supercritical flow, with a Froude number greater than one, is inertia-driven.

Critical flow occurs when the Froude number is one, which minimizes energy at a critical depth.

Channel slope impacts depth variation. In gradually varied flow, the depth gradient shows that subcritical and supercritical flows adjust differently.

For uniform flow, depth is stabilized when slope S₀ equals friction slope S_f.

These energy principles are crucial for designing efficient channels that predict and manage flow behavior across hydraulic systems.