Kennedy’s critical velocity formula: According to Kennedy, the critical (non-silting, non-scouring) mean velocity V0 (m/s) in a channel of depth D (m) is

Introduction / Context:
Kennedy’s method sizes alluvial canals by equating the actual mean velocity to a “critical velocity” that avoids silting and scouring.

Given Data / Assumptions:

• D in metres, V0 in m/s.
• m = critical velocity ratio accounting for sediment characteristics.
• Uniform flow and representative sediment.

Concept / Approach:
Kennedy proposed the empirical relation V0 = 0.55 * m * D^0.64 (SI form). Designers iterate canal dimensions so computed actual velocity matches V0.

Step-by-Step Solution:
Write V0 as function of depth D: V0 = 0.55 * m * D^0.64.Choose m based on silt character; m ≈ 1 for average silt.Use continuity Q = A * V and geometric relations to size the section accordingly.

Verification / Alternative check:
For D = 1 m, m = 1 → V0 ≈ 0.55 m/s, a plausible value for non-silting/non-scouring velocity in fine-silt canals.

Why Other Options Are Wrong:

• Option b ignores m, which varies by silt type.
• Options c and d use wrong coefficients/exponents.
• Option e inverts dependence contrary to observations.

Common Pitfalls:
Using wrong units; applying exponent to hydraulic radius rather than depth; forgetting to adjust m.

Final Answer:
V0 = 0.55 * m * D^0.64