Chezy’s formula for uniform flow: In V = C r s, on what does the Chezy constant C primarily depend?

Introduction / Context:
Chezy’s formula, V = C * sqrt(R * S), is a classic relation for mean velocity in open channels and partially full conduits. The empirical constant C encapsulates resistance characteristics of the flow system.

Given Data / Assumptions:

• V: mean velocity; R: hydraulic radius; S: slope of energy grade line.
• C: dimensioned coefficient reflecting resistance.
• Application to sewers flowing partially full or as open channels.

Concept / Approach:
Empirically, C depends on surface roughness (material and condition) and, to a degree, on flow depth and section geometry because these influence turbulence and the resistance regime. Thus, size and shape matter indirectly via hydraulic radius and Reynolds number effects.

Step-by-Step Solution:
1) Recognize that smoother surfaces yield higher C (less resistance).2) Larger sections (size) and different shapes alter hydraulic radius and boundary layer development, affecting C in empirical calibrations.3) Conclude that C is influenced by material roughness and section characteristics; hence “all of the above”.

Verification / Alternative check:
Relations such as the Manning-Chezy link, C = (1/n) * R^(1/6), explicitly show C varying with both roughness (n) and hydraulic radius (a function of size/shape), reinforcing the multi-factor dependence.

Why Other Options Are Wrong:
Single-factor choices (size, shape, roughness, hydraulic characteristics alone) are incomplete descriptions of what influences C.

Common Pitfalls:

• Assuming C is a pure material constant independent of hydraulic radius.
• Using a single C value across widely different depths without verification.

Final Answer:
All of the above (material roughness and section characteristics)