Open channel flow, where a fluid flows with a free surface exposed to the atmosphere, is primarily governed by gravitational and surface effects, distinguishing it from closed conduit or pipe flow. In open channels such as rivers, canals, and artificial channels, energy analysis provides valuable insights into flow behavior and the relationship between depth, velocity, and slope.

Specific Energy and Flow Depth

In open channel flow, the specific energy, E, combines the gravitational potential energy associated with fluid depth, and the kinetic energy tied to flow velocity. For a given discharge or flow rate, there are typically two possible depths, known as alternate depths, at which the specific energy remains the same. One is deeper and slower, known as subcritical, and the other is shallower and faster, known as supercritical. Subcritical flow, with a lower velocity, has a depth that results in a tranquil, gravity-driven movement. In contrast, supercritical flow, at a shallow depth and high velocity, is dominated by inertial forces.

Froude Number and Flow Classification

The Froude number F_r​ is a dimensionless indicator of flow regimes, representing the ratio of inertial forces to gravitational forces in the channel. It is defined by:

Here, V is the flow velocity, g is gravitational acceleration, and y is the hydraulic depth. The Froude number categorizes flow regimes. Subcritical flow occurs when F_r​ is less than one, indicating that gravity governs the flow behavior. Supercritical flow, where F_r​ is greater than one, is inertia-driven, and the water moves rapidly with less depth. Critical flow, where F_r​ is equal to one, represents the condition of minimum specific energy occurring at a critical depth. This necessary condition is essential for designing structures like weirs and spillways that control flow transitions between subcritical and supercritical states.

Role of Channel Slope

Channel slope also plays a significant role in determining flow characteristics. In gradually varied flow, the channel’s slope and bed geometry influence how depth changes along the flow. For instance, subcritical flow is sustained in a mild slope, while supercritical flow typically prevails in a steep slope. In cases of uniform flow, the flow depth stabilizes when the channel’s bed slope S₀​ matches the friction slope S_f, representing the balance between gravitational and frictional forces. This uniform depth is crucial in designing stable and efficient channels where flow is consistent and predictable over long distances.

Understanding these energy principles and classifications in open channel flow is essential for hydraulic engineering. It enables accurate predictions of flow behavior, effective channel designs, and improved management of hydraulic systems across various applications.