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The discharge through a V- notch varies as:
(Where H is the head)

  • A.\(H^{3/2}\)
  • B.H
  • C.\(H^{5/2}\)
  • D.\(H^{1/2}\)

Answer: C

The discharge through a V-notch varies as \(H^{5/2}\).

For a triangular notch of included angle \(\theta\):

\[ \begin{aligned} Q &= \frac{8}{15} C_d \sqrt{2g} \\ &\quad \times \tan\frac{\theta}{2}\, H^{5/2} \end{aligned} \]

The extra power compared with a rectangular weir comes from the width of the flow growing with the head. \(H^{3/2}\) is the law for a rectangular notch or weir, and \(H^{1/2}\) is the law for an orifice, where velocity alone grows as \(\sqrt{H}\). Discharge proportional to H fits none of these devices.

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