Question

Given below are the two statements.
Statement I: Triangular weirs do not have any element or effects of weir length.
Statement II: Triangular weirs are the best option of flow stage measurements when the discharges or flow depths are relatively very high.
In light of the above statements, choose the most appropriate answer from the options given below

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is correct but Statement II is false
• D. Statement I is incorrect but Statement II is true

Hint:

Triangular (V-notch) weir: $Q \propto H^{5/2}$, no crest length ($L$), best for low discharges. Rectangular weir: $Q \propto L H^{3/2}$, best for high discharges.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Sharp-crested triangular (V-notch) weirs provide high measurement precision at low discharges without requiring horizontal crest length adjustments.
Key Formula or Approach:
\[ Q = \frac{8}{15} C_d \sqrt{2g} \tan\left(\frac{\theta}{2}\right) H^{5/2} \]

Step 2: Detailed Explanation:
1. Statement I: The discharge formula for a triangular weir \(Q = \frac{8}{15} C_d \sqrt{2g} \tan(\theta/2) H^{5/2}\) contains no crest length parameter \(L\). The flow area is determined solely by the notch angle \(\theta\) and the head \(H\). Hence, Statement I is correct.
2. Statement II: Triangular V-notch weirs are ideal for measuring small to moderate discharges because a small change in discharge produces a substantial, easily measurable change in head. For high discharges, broad-crested or long rectangular weirs are preferred. Hence, Statement II is false.

Step 3: Final Answer:
Therefore, Statement I is correct but Statement II is false, corresponding to option (C).