Chezy’s uniform flow relation — identifying terms: In the classical form V = C √(m i) for open-channel flow, what do the symbols represent?

Introduction / Context:
Chezy’s formula is a foundational empirical relation for steady, uniform open-channel flow. It links the mean velocity to channel characteristics and slope through the Chezy coefficient C.

Given Data / Assumptions:

• Uniform flow: depth and velocity do not vary along the channel reach.
• Steady conditions; prismatic channel.
• Hydraulic mean depth m = A/P, where A = area and P = wetted perimeter.

Concept / Approach:

The relation is V = C √(m i). Here V is the section-averaged velocity, m is the hydraulic radius (often denoted R = A/P, also called hydraulic mean depth in many texts), and i is the energy gradient (loss of head per unit length), equal to the bed slope in uniform flow.

Step-by-Step Solution:

Verification / Alternative check:

Manning’s equation V = (1/n) m^(2/3) i^(1/2) is consistent and can be rearranged to a Chezy form with C related to n and m.

Why Other Options Are Wrong:

(e) contradicts standard definitions used across hydraulics literature.

Common Pitfalls:

Confusing m with depth y; mixing up slope of bed with water surface—only equal in uniform flow.

Final Answer:

All of the above