Chezy’s uniform flow relation — identifying terms: In the classical form V = C √(m i) for open-channel flow, what do the symbols represent?
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AV is the mean velocity of flow
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Bm is the hydraulic mean depth (A/P)
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Ci is the head loss (slope of energy grade line) per unit length
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DAll of the above
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ENone of the above
Answer
Correct Answer: All of the above
Explanation
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:
State Chezy equation: V = C √(m i).Identify m = A/P, the hydraulic radius.Recognize i as head loss per unit length (S_f), equal to slope for uniform flow.Hence, options (a), (b), and (c) are all correct, so choose (d).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