Equivalent egg-shaped sewer: If D is the diameter of a circular sewer and D' is the top horizontal diameter of an hydraulically equivalent egg-shaped section, which relation is typically used?

Introduction / Context:
Egg-shaped sections are sometimes designed to be hydraulically equivalent to a circular pipe—meaning they deliver similar discharge under specified conditions. The proportions relate key egg-shaped dimensions to an equivalent circular diameter for comparison and substitution in design problems.

Given Data / Assumptions:

• Hydraulic equivalence considered at running-full condition under the same slope and roughness.
• D is equivalent circular diameter; D' is top horizontal diameter of the egg-shaped section.
• Standard proportion set for the “new egg-shaped” geometry.

Concept / Approach:

Design tables provide dimensional ratios for egg-shaped sections to match the carrying capacity of a reference circular pipe. Among these, the top horizontal diameter D' commonly relates to circular D by a fixed multiple. A frequently cited relation in exam-oriented references is D' ≈ 0.84 D for equivalence based on capacity at full flow.

Step-by-Step Solution:

Verification / Alternative check:

Cross-check with proportion tables for egg-shaped sewers used in civil engineering texts and past competitive examinations that employ the 0.84 D ratio.

Why Other Options Are Wrong:

0.64 D and 0.74 D are too small and would understate capacity; 0.94 D is too large for the top horizontal dimension in the standard equivalence set; 1.04 D overstates the dimension relative to circular D.

Common Pitfalls:

Mixing “equivalent” for full-flow capacity with geometric similarity; confusing top horizontal diameter with overall depth or crown radius of the egg-shaped section.

Final Answer:

D' = 0.84 D