Kennedy’s theory – trial design step: The iterative (trial) procedure for canal design using Kennedy’s theory primarily employs which relationship between discharge and section/velocity?

Introduction / Context:Kennedy’s regime method sizes unlined canals by ensuring that mean velocity equals the “critical velocity” which does not cause silting or scouring. The trial procedure uses continuity and Kennedy’s empirical velocity-depth relation.

Given Data / Assumptions:

• Steady, uniform flow in an alluvial canal.
• Critical velocity V relates to flow depth y and sediment via the critical velocity ratio m.
• Discharge Q must equal area A times velocity V.

Concept / Approach:Kennedy proposed V = 0.55 * m * y^0.64 (SI units, with m the critical velocity ratio). The trial begins with an assumed section (hence y and A), computes V from the critical velocity relation, and checks Q = A * V. Section parameters are iterated to satisfy both hydraulics and velocity criterion.

Step-by-Step Solution:Use continuity: Q = A * V.Use Kennedy: V = 0.55 * m * y^0.64.Iterate section dimensions until computed Q matches the design discharge and velocity equals the critical value.

Verification / Alternative check:Some designers combine Kennedy with Chezy/Manning to ensure slope adequacy; however, the cornerstone relation in the trial is the critical velocity formula with continuity.

Why Other Options Are Wrong:

• Q = A * y: Dimensionally incorrect; y is depth, not velocity.
• Chezy-only: Ignores the critical velocity criterion central to Kennedy.
• All the above: Incorrect because only option (a) captures Kennedy’s trial essence.

Common Pitfalls:Using wrong exponent in V–y relation; omitting the m-factor; failing to reconcile depth with hydraulic slope constraints.

Final Answer:Q = A * V together with V = 0.55 * m * y^0.64