Question

Discharge could be determined for suppressed rectangular weir by which of the following formulae?
(where Q= discharge (liters/second), L= Length of crest (cm), and H = head on the crest (cm))

• A. \(Q = 0.0184 \, LH^{3/2}\)
• B. \(Q = 0.0184 \, (1-0.1H)H^{3/2}\)
• C. \(Q = 0.0184 \, (1-0.2H)H^{3/2}\)
• D. \(Q = 0.184 \, LH^{3/2}\)

Hint:

Suppressed weir (no side contractions) $\implies Q = 0.0184 L H^{3/2}$.
Contracted weir (2 side contractions) $\implies Q = 0.0184(L - 0.2H)H^{3/2}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Francis' formula for discharge over a sharp-crested rectangular weir depends on whether end contractions are suppressed or present.
Key Formula or Approach:
\[ Q = \frac{2}{3} C_d \sqrt{2g} \, (L - 0.1 n H) H^{3/2} \]
where \(n\) is the number of end contractions (\(n=0\) for suppressed, \(n=2\) for contracted).

Step 2: Detailed Explanation:
In metric units where \(Q\) is in L/s, \(L\) in cm, and \(H\) in cm:
- For a suppressed rectangular weir (no end contractions, \(n=0\)):
\[ Q = 0.0184 \, L \, H^{3/2} \]
- For a contracted rectangular weir (with two end contractions, \(n=2\)):
\[ Q = 0.0184 \, (L - 0.2 H) \, H^{3/2} \]

Step 3: Final Answer:
Thus, the formula for a suppressed rectangular weir is \(Q = 0.0184 \, LH^{3/2}\), matching option (A).