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In open channels, gradually varying flow, or GVF, occurs when the depth of water changes slowly along the channel due to varying factors, such as a non-uniform bottom slope, changing channel shape, or obstructions.

This type of flow occurs when the flow depth adjusts gradually due to an equilibrium between gravitational forces, flow inertia, and friction. It is characterized by a low rate of depth change, denoted by dy over dx. 

GVF profiles are typically used in rivers, canals, and natural streams, where flow depth gradually increases or decreases over long distances.

When the slope of the channel bed differs from the energy slope, the flow adjusts accordingly.

For example, when the bed slope is steeper, the depth tends to decrease, while gentler slopes result in an increase in depth.

This adjustment is driven by gravity and shear forces, which change the velocity and depth to meet continuity and energy requirements.

Optimal hydraulic cross sections, such as rectangular, trapezoidal, or triangular shapes, are often used in design to support efficient flow.

Understanding GVF enables the prediction of flow behavior and the designing of channels to minimize abrupt flow changes.