For computing mean velocity of flow in sanitary sewers with known slope and roughness, which empirical relation is most widely used in modern practice?

Introduction / Context:
Hydraulic design of gravity sewers requires a reliable formula linking velocity, hydraulic radius, slope, and roughness. Among several historical relations, one has become the de facto standard in sewer design manuals.

Given Data / Assumptions:

• Open-channel (partially full) or full-flow gravity conditions.
• Steady, uniform flow assumption for sizing.
• Use of a roughness parameter calibrated for pipe material.

Concept / Approach:
Manning's formula expresses velocity as V = (1/n) * R^(2/3) * S^(1/2), where n is Manning's roughness coefficient, R is hydraulic radius, and S is slope of energy grade line. It is simple, dimensionally consistent in SI, and supported by abundant tabulations of n for sewer materials.

Step-by-Step Solution:
Identify the design need: mean velocity under steady, uniform flow.Select formula with widely available roughness data: Manning's.Apply for partial flow by using actual wetted area and perimeter to compute R.

Verification / Alternative check:
Chezy, Kutter, and Bazin are predecessors and can be interrelated, but modern codes almost universally present charts/tables in terms of Manning's n for pipes and channels.

Why Other Options Are Wrong:

• Chezy/Kutter/Bazin: Historically important but less convenient; require coefficients that vary with R and S.
• Williams–Hazen: Suited to pressurized water mains; not ideal for open-channel sewer hydraulics.

Common Pitfalls:
Using inappropriate n values; forgetting that sediment or slime layers increase effective roughness; applying full-flow hydraulic radius to partial-flow conditions.

Final Answer:
Manning's formula