Chezy’s resistance constant C used in the Chezy equation for open-channel flow was empirically correlated/estimated by which classical investigator?

Introduction / Context:
The Chezy equation V = C √(R S) uses an empirical resistance coefficient C. Historically, engineers proposed correlations to estimate C from channel roughness and hydraulic radius. Knowing the names helps track which formula you are applying in design problems.

Given Data / Assumptions:

• Steady uniform flow in open channels.
• Chezy form V = C √(R S), where R is hydraulic radius and S is slope.

Concept / Approach:

Kutter proposed a widely used formula to compute Chezy’s C in terms of a roughness coefficient and hydraulic radius. Bazin also developed a relation for C, but “Kutter’s formula” is the classic association students are often tested on. Manning, meanwhile, introduced an alternative equation V = (1/n) R^(2/3) S^(1/2) with roughness n rather than C.

Step-by-Step Solution:

Verification / Alternative check:

Many handbooks list “Kutter’s formula for C” near the Chezy equation, reinforcing this pairing.

Why Other Options Are Wrong:

(a) Bazin did propose a C-relation, but exam convention often associates Kutter more directly. (c) Manning corresponds to a different formula using n. (d) Powell is unrelated in this context. (e) Darcy pertains to closed conduit head loss, not Chezy’s C.

Common Pitfalls:

Confusing the Chezy and Manning formulations; assuming the same roughness parameter applies across them without conversion.

Final Answer:

Kutter