Chezy application to a full rectangular channel (b = 6 m, y = 3 m) A rectangular channel is 6 m wide and 3 m deep, running full on a bed slope S = 1/2000. If Chezy’s constant C = 54.8, identify the correct specifications (hydraulic mean depth, velocity, and discharge).

Introduction / Context:Chezy’s formula is widely used for uniform open-channel flow to relate mean velocity to hydraulic radius and slope. This problem checks competence in computing section properties and applying the velocity formula correctly.

Given Data / Assumptions:

• Rectangular section: width b = 6 m; depth y = 3 m (running full).
• Chezy constant C = 54.8; bed slope S = 1/2000.
• Uniform, steady flow; prismatic channel; water at ordinary conditions.

Concept / Approach:

Hydraulic mean depth (hydraulic radius) R = A / P for open channels. Chezy’s velocity: V = C * √(R * S). Discharge: Q = A * V.

Step-by-Step Solution:

Verification / Alternative check:

Dimensions: R in meters, S dimensionless; V in m/s; Q in m^3/s. Values are internally consistent and typical for a channel of this size and slope.

Why Other Options Are Wrong:

Since (a), (b), and (c) are all correct, any option omitting one of them is incomplete.

Common Pitfalls:

Using hydraulic depth A/b instead of hydraulic radius A/P; arithmetic slips with slope; forgetting the square root in Chezy’s relation.

Final Answer:

All of the above