Empirical sectioning for small drains (Q ≤ 15 m³/s): What relation between depth (d) and top width (B) is commonly adopted for preliminary proportioning?

Introduction / Context:
For roadside, storm-water, or small irrigation drains up to about 15 m³/s, designers often begin with empirical proportions before iterating with Manning or Chézy equations. A typical starting proportion is a depth roughly half the top width, providing a stable, maintainable section.

Given Data / Assumptions:

• Design discharge up to approximately 15 m³/s.
• Trapezoidal or prismatic open-channel section.
• Need for an initial proportion prior to hydraulic checking.

Concept / Approach:

Using a rule-of-thumb like d = 0.5 B (equivalently B ≈ 2 d) provides a reasonable hydraulic radius and side-slope economy for first sizing. The section is then refined to satisfy permissible velocities, freeboard, side slopes, and material constraints using Manning’s formula and stability checks.

Step-by-Step Solution:

Verification / Alternative check:

Sensitivity analysis against B/d ratios near 2 shows minor differences in area and hydraulic radius; final sizing is governed by Manning and stability criteria.

Why Other Options Are Wrong:

d = 0.2 B produces too shallow a section; B = 0.2 d and B = 0.5 d invert the proportion unrealistically, giving very narrow or very deep sections.

Common Pitfalls:

Keeping empirical proportions without hydraulic verification; ignoring freeboard; neglecting sediment transport and maintenance access.

Final Answer:

d = 0.5 B