Kennedy’s theory of stable channels: For a unique (single) design solution using Kennedy’s approach, which geometric information must be known in advance?

Introduction / Context:
Kennedy’s regime theory relates non-silting, non-scouring velocity to flow depth for silt-laden channels. Because the theory does not directly yield both width and depth simultaneously, an additional geometric relation is required to arrive at a unique section.

Given Data / Assumptions:

• Kennedy’s velocity–depth relation: V = m * y^(1/6) (m depends on silt grade).
• Discharge Q is known and continuity must be satisfied (Q = A * V).
• A shape assumption is needed to close the problem.

Concept / Approach:
With V tied to y, and Q known, we still have two unknowns (width and depth) for a rectangular (or nearly rectangular) section. Specifying the ratio B/D provides the necessary closure to determine both B and D uniquely.

Step-by-Step Solution:
Use V = m * y^(1/6) to relate velocity to depth.Apply Q = A * V with A = B * y to link width and depth.Provide B/D to close the system and solve for B, y uniquely.

Verification / Alternative check:
Design examples in texts specify side slopes and B/D to determine a unique section under Kennedy’s theory, followed by stability checks.

Why Other Options Are Wrong:

• Only breadth or only depth does not close the system with the given relations.
• “All of the above” is false; only B/D provides the necessary closure.

Common Pitfalls:
Assuming Kennedy alone gives unique B and D; forgetting to adopt a shape parameter; confusing with Lacey’s set where additional parameters are available.

Final Answer:
Only the ratio of breadth to depth (B/D)