Question

Match LIST-I with LIST-II:\[\begin{array}{|c|l|l|} \hline \textbf{LIST-I (Flow parameter of a channel flow)} & & \textbf{LIST-II (Proportional to)} \\ \hline \text{A. Mean velocity in a Lacey regime channel} & & \text{IV. $Q^{2/3}$} \\ \hline \text{B. Mean velocity in a lined channel} & & \text{II. $S^{1/3}$} \\ \hline \text{C. Normal scour depth in an alluvial channel} & & \text{III. $Q^{1/2}$} \\ \hline \text{D. Wetted perimeter of a Lacey regime channel} & & \text{I. $S^{1/2}$} \\ \hline \end{array}\] where $S$ is slope of channel and $Q$ is discharge. Choose the most appropriate match from the options given below:

• A. A - I, B - II, C - III, D - IV
• B. A - II, B - I, C - IV, D - III
• C. A - I, B - I, C - II, D - III
• D. A - III, B - I, C - II, D - IV

Hint:

Remember: Lacey's regime equations link velocity to slope ($S^{1/2}$) and wetted perimeter to discharge ($Q^{2/3}$).

Answer 1

The Correct Option is A

Step 1: Establish relationships.
- (A) Mean velocity in Lacey regime channel is proportional to $S^{1/2}$, corresponding to I.
- (B) Mean velocity in a lined channel is proportional to $S^{1/3}$, corresponding to II.
- (C) Normal scour depth in an alluvial channel is proportional to $Q^{1/2}$, corresponding to III.
- (D) Wetted perimeter in Lacey's regime is proportional to $Q^{2/3}$, corresponding to IV.

Step 2: Correlate the items.
\[ A \to I, B \to II, C \to III, D \to IV \]

Step 3: Finalize the answer.
Therefore, the correct pairing is option (1).