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?

Difficulty: Medium

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

Explanation:


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

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