Question:medium

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:

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.
  • (B) and (C) only.
  • (A) and (C) only.
  • (A) and (B) only.
  • (C) only.
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Recall the correct exponent in the general rectangular weir formula.
Discharge over a rectangular sharp crested weir is derived by integrating the velocity profile over the head, and it comes out proportional to head raised to the power three-halves, not two-thirds, so a formula written as \( Q = 0.0186 L H^{2/3} \) has the wrong exponent and cannot be a genuine weir formula, making statement A false.
Step 2: Recall the correct exponent for a triangular, V-notch, weir.
A triangular notch weir integrates over a triangular flow area and comes out proportional to head raised to the power five-halves, not seven-halves, so \( Q = 0.0184 L H^{7/2} \) is also not a genuine standard weir relation, making statement B false as well.
Step 3: Check the general form given in statement C.
Every specific weir formula, rectangular, triangular or trapezoidal, can be written in the general shape \( Q = C L H^m \), where C bundles the discharge coefficient and constants and m is the exponent for that weir shape, so this generic template is always a correct way to represent weir flow, making statement C true.
Step 4: Combine the findings.
Only the general form in C is valid, since A and B use non-standard exponents.
\[ \boxed{(C) only.} \]
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