For a given open channel, if the Chezy's coefficient (C) is decreased, then how will it affect the discharge (Q) of the flow?
- AQ will decreaseCorrect
- BQ will become zero
- CQ will remain constant
- DQ will increase
Solution
Concept
In Chezy's formula, discharge is directly proportional to Chezy's coefficient C.
Formula
Q = A × C × √(R × S)
Step-by-step solution
1. Chezy's formula: V = C √(R S). 2. Discharge Q = A × V = A C √(R S). 3. For the given channel, A, R and S are fixed. 4. So Q ∝ C. 5. If C decreases, Q decreases.
Explanation
Chezy's coefficient C shows how smooth the channel is. Smaller C means a rougher channel and more resistance to flow. So velocity and discharge both become less.
Why the other options are wrong
B: Q becomes zero only if C = 0, which is not practical. C: Q depends on C, so it cannot stay constant. D: Q is directly proportional to C, so it cannot increase when C decreases.
Shortcut
Q ∝ C, so a smaller C gives a smaller Q.
Common mistake
Mixing C with Manning's n. Q is inversely proportional to n but directly proportional to C.
Correct answer: A) Q will decrease