Inverted siphon (cross-drainage): The uplift pressure on the roof (crown) of an inverted siphon barrel is maximum under which operating condition?

Introduction / Context:
Inverted siphons carry canal water or drainage under crossings under pressure. The roof (crown) may be subjected to external hydrostatic pressure from floodwater above (e.g., a drain flowing over the siphon). Uplift checks are critical for structural safety.

Given Data / Assumptions:

• We consider external water level above the barrel and internal counter-pressure from barrel contents.
• Uplift is the net upward pressure acting on the roof slab.

Concept / Approach:
Uplift on the roof is driven by the head of water above acting downward on the surroundings while the underside pressure depends on the internal water level. The worst condition is when the external water level is highest and the internal counterbalancing pressure is least. High external level occurs at the drain H.F.L.; if the canal were empty (dry), counterpressure would be further reduced, but the key single condition indicating maximum external head is the drain at H.F.L.

Step-by-Step Solution:
List scenarios and compare external head over roof.Maximum external head corresponds to drain at H.F.L.Hence uplift on the roof is maximized in option (d).

Verification / Alternative check:
Design checks often consider the combination “drain at H.F.L., canal empty” as the absolute worst case; among the single conditions provided, H.F.L. of drain represents the controlling uplift.

Why Other Options Are Wrong:

• (a) Drain dry → minimal external head.
• (b) Canal dry → reduces internal counterpressure but needs high external water to be critical.
• (c) Canal at F.S.L. increases internal pressure, reducing uplift risk.

Common Pitfalls:
Ignoring combination states; misidentifying which watercourse produces external head.

Final Answer:
Drain is running at highest flood level (H.F.L.)