Canal cross-drainage works: In a canal syphon (inverted syphon), what is the nature of flow through the barrel(s)?

Introduction / Context:

A canal syphon—often called an inverted syphon—is a cross-drainage work used when a canal must pass beneath a natural drain/river or an obstruction, while maintaining discharge continuity. The canal is conveyed through one or more closed barrels running full, which changes the flow regime from open-channel to pressure (pipe) flow.

Given Data / Assumptions:

• The structure is a canal syphon (inverted syphon), not an aqueduct or super-passage.
• The barrel is closed and designed to run full.
• Approach and exit transitions convert between open-channel flow in the canal and pressure flow in the barrel.

Concept / Approach:

In an inverted syphon the water surface is not free to adjust to atmospheric pressure within the barrel. Instead, the conduit runs full, and energy grade line calculations use head losses (entrance, friction, exit, bends) typical of pressure flow. The hydraulic grade line and piezometric head determine the capacity and required barrel diameter(s).

Step-by-Step Solution:

Verification / Alternative check:

Design methods (e.g., Darcy–Weisbach/Hazen–Williams, entrance/exit loss coefficients) are applied, confirming pressure-flow behavior. Open-channel formulas (Manning, critical depth) are not applicable inside the running-full barrel.

Why Other Options Are Wrong:

• Under atmospheric pressure: That describes open-channel flow, not valid inside the closed, full barrel.
• Critical velocity: A specific open-channel control condition, not representative of syphon barrels.
• Under negative pressure: Properly designed syphons avoid sub-atmospheric pressures that risk cavitation/air binding.
• Mixed regime: Within a given barrel, the regime is pressure; the regime change occurs only in transitions.

Common Pitfalls:

• Confusing inverted syphons (pressure flow) with aqueducts/super-passages (open channel).
• Ignoring entrance/exit losses and bend losses, which leads to undersized barrels.

Final Answer:

Pipe flow (pressure flow through closed barrel)