In open-channel hydraulics, Chezy's constant (C) is primarily used in which velocity–discharge relationship or formula? Provide the formulation context where C directly multiplies the hydraulic terms.

Introduction / Context:
Chezy's constant (C) is a classical roughness/flow coefficient used to compute mean velocity in open channels. Knowing where and how this constant is employed helps students connect historical formulas (Chezy, Bazin, Kutter) to modern practice (Manning), and avoid mixing up which parameter belongs to which equation.

Given Data / Assumptions:

• We are dealing with steady, uniform open-channel flow.
• Hydraulic radius R and bed slope S are well defined.
• Chezy's constant C appears as a multiplier in a velocity equation.

Concept / Approach:
Chezy's formula relates mean velocity V to channel properties as V = C * sqrt(R * S). In this expression, C encapsulates the combined effects of boundary roughness and flow regime. Bazin's and Kutter's formulas were developed mainly to estimate C for given conditions, not to replace Chezy's velocity form. Manning's equation uses a different coefficient n and does not include C explicitly.

Step-by-Step Solution:
1) Recall Chezy: V = C * sqrt(R * S).2) Identify where C multiplies sqrt(R * S) directly: Chezy's formula.3) Recognize that Bazin and Kutter give empirical expressions for C itself, which are then substituted back into Chezy's velocity form.4) Note that Manning expresses V = (1/n) * R^(2/3) * S^(1/2), no C present.

Verification / Alternative check:
Dimensionally, with V proportional to sqrt(RS), C is dimensionless in SI (if R and S are in consistent units), matching the Chezy formulation; Manning instead requires n with different dimensional handling.

Why Other Options Are Wrong:

• Bazin's formula: Used to estimate C, not the velocity directly without Chezy's form.
• Kutter's formula: Also estimates C; it feeds into Chezy's velocity expression.
• Manning's formula: Uses n, not C.
• Darcy–Weisbach equation: Pipe/head loss relation; does not employ Chezy's C.

Common Pitfalls:
Confusing the empirical correlations for C (Bazin/Kutter) with the velocity equation where C is actually used (Chezy).

Final Answer:
Chezy's formula