Question:
Which of the following statements regarding basic equation for flow through the weir are correct?
(A). \(Q = 0.0186 L H^{2/3}\)
(B). \(Q = 0.0184 L H^{7/2}\)
(C). \(Q = C L H^m\)
Choose the correct answer from the options given below:
Which of the following statements regarding basic equation for flow through the weir are correct?
(A). \(Q = 0.0186 L H^{2/3}\)
(B). \(Q = 0.0184 L H^{7/2}\)
(C). \(Q = C L H^m\)
Choose the correct answer from the options given below:
(A). \(Q = 0.0186 L H^{2/3}\)
(B). \(Q = 0.0184 L H^{7/2}\)
(C). \(Q = C L H^m\)
Choose the correct answer from the options given below:
Show Hint
The exponent for any rectangular weir discharge formula is always \(3/2\) (or 1.5).
For a triangular weir (V-notch), the exponent is \(5/2\) (or 2.5). This is a critical distinction in exams.
For a triangular weir (V-notch), the exponent is \(5/2\) (or 2.5). This is a critical distinction in exams.
Updated On: Jul 7, 2026
- (B) and (C) only.
- (A) and (C) only.
- (A) and (B) only.
- (C) only.
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Weir flow equations are derived by integrating the theoretical velocity of water over the vertical cross-sectional area of flow above the crest.
Step 3: Detailed Explanation:
The general discharge equation for a rectangular weir is:
\[ Q = \frac{2}{3} C_d L \sqrt{2g} H^{3/2} \] This standard equation can be simplified into the general empirical form:
\[ Q = C L H^m \] where:
\(C\) = discharge coefficient
\(L\) = length of the weir crest
\(H\) = head of water above the crest
\(m\) = exponent, which is theoretically \(1.5\) (or \(3/2\)) for a rectangular weir.
Analyzing the statements:
- Statement (A) uses an incorrect exponent of \(2/3\).
- Statement (B) uses an incorrect exponent of \(7/2\).
- Statement (C) matches the correct generalized form of the weir discharge equation.
Therefore, only statement (C) is correct.
Step 4: Final Answer:
The correct option is 4, which corresponds to (C) only.
Weir flow equations are derived by integrating the theoretical velocity of water over the vertical cross-sectional area of flow above the crest.
Step 3: Detailed Explanation:
The general discharge equation for a rectangular weir is:
\[ Q = \frac{2}{3} C_d L \sqrt{2g} H^{3/2} \] This standard equation can be simplified into the general empirical form:
\[ Q = C L H^m \] where:
\(C\) = discharge coefficient
\(L\) = length of the weir crest
\(H\) = head of water above the crest
\(m\) = exponent, which is theoretically \(1.5\) (or \(3/2\)) for a rectangular weir.
Analyzing the statements:
- Statement (A) uses an incorrect exponent of \(2/3\).
- Statement (B) uses an incorrect exponent of \(7/2\).
- Statement (C) matches the correct generalized form of the weir discharge equation.
Therefore, only statement (C) is correct.
Step 4: Final Answer:
The correct option is 4, which corresponds to (C) only.
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