What governs the longitudinal gradient (slope) selected for sanitary sewers? Pick the best statement describing the factors that primarily determine sewer grade.

Introduction / Context:
The grade (slope) of a gravity sewer must be chosen to achieve self-cleansing velocities while preventing excessive velocities that could cause scouring and structural issues. Because velocity is a function of hydraulic radius and slope for a given discharge (e.g., via Manning’s equation), several variables co-determine the selected slope.

Given Data / Assumptions:

• Gravity flow in partially full circular conduits.
• Use of empirical relations like Manning’s V = (1/n) R^(2/3) S^(1/2).
• Target self-cleansing velocity, commonly around 0.6–0.75 m/s for sanitary sewers (varies by standard).

Concept / Approach:

For a specified design discharge, the chosen diameter and slope together set the hydraulic radius and thus velocity. Conversely, a required self-cleansing velocity dictates a minimum slope for a chosen diameter and expected flow. Therefore, all three—discharge, diameter, and target velocity—are linked and jointly determine the gradient.

Step-by-Step Solution:

Verification / Alternative check:

Design tables present recommended minimum slopes as a function of pipe size and anticipated flow to achieve self-cleansing—confirming multi-dependence.

Why Other Options Are Wrong:

(a), (b), and (c) alone do not fully specify the slope; the integrated view in (d) is correct.

Common Pitfalls:

Choosing minimal slopes without checking low-flow velocities; ignoring roughness n changes over time due to slime or sediment deposition.

Final Answer:

all the above.