In open-channel hydraulics, the numerical value of Chezy's constant C is specifically used in which empirical resistance–velocity relation?

Introduction / Context:
Chezy's constant C is a classic resistance parameter used in uniform open-channel flow calculations. Many examination questions test whether you can distinguish where C appears directly and where it is predicted indirectly by other relations.

Given Data / Assumptions:

• Topic: uniform flow in open channels and pipes flowing partly full.
• Chezy's constant C relates mean velocity to hydraulic radius and slope.
• Other formulae (Bazin, Kutter, Manning) are also used in resistance computations.

Concept / Approach:
The Chezy equation expresses mean velocity V as V = C * sqrt(R * S), where R is hydraulic radius and S is energy slope. In contrast, Bazin and Kutter give empirical expressions to estimate C, and Manning gives V directly without mentioning C, i.e., V = (1/n) * R^(2/3) * S^(1/2).

Step-by-Step Solution:
Identify the equation that explicitly contains C.Chezy: V = C * sqrt(R * S).Bazin/Kutter: provide C as a function of roughness and R, used to substitute into Chezy, but not the velocity formula by themselves.Manning: V = (1/n) * R^(2/3) * S^(1/2), no C.

Verification / Alternative check:
If you see C in the velocity formula itself, it is Chezy's relation. Other formulae either compute C (Bazin, Kutter) or bypass C (Manning).

Why Other Options Are Wrong:

• Bazin's formula: estimates C; it does not present V unless combined with Chezy.
• Kutter's formula: also yields C empirically; again, V requires Chezy's relation.
• Manning's formula: gives V directly using n, not C.
• All of the above: incorrect because only Chezy's formula uses C directly in V.

Common Pitfalls:
Confusing the formulas that define C with the formula that uses C. Remember: Bazin/Kutter → compute C; Chezy → uses C; Manning → no C.

Final Answer:
Chezy's formula.