Question

The peak runoff rate \(Q_p\) in \(\text{m}^3\text{/s}\) by the Ryves formula is given as \(Q_p = C_r A^b\), where A is the area in \(\text{km}^2\) and \(C_r\) is Ryves constant. The value of exponent b is

• A. 1
• B. \(2/3\)
• C. \(1/2\)
• D. \(3/4\)

Hint:

Exponents for Peak Flood Formulas:
Ryves Formula $\implies A^{2/3}$ (South India).
Dickens Formula $\implies A^{3/4}$ (North India).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Empirical flood peak formulas relate maximum discharge to catchment area using regional power-law exponents.
Key Formula or Approach:
\[ Q_p = C_R \cdot A^{2/3} \quad \text{(Ryves' Formula for South India)} \]
\[ Q_p = C_D \cdot A^{3/4} \quad \text{(Dickens' Formula for North/Central India)} \]

Step 2: Detailed Explanation:
In Indian engineering hydrology:
1. Ryves Formula: Developed for catchments in southern India (Tamil Nadu, Karnataka, Andhra Pradesh):
\[ Q_p = C_R \cdot A^{2/3} \]
where \(b = 2/3\) (or \(0.67\)).
2. Dickens Formula: Developed for northern and central Indian catchments:
\[ Q_p = C_D \cdot A^{3/4} \]
where the exponent is \(3/4\) (or \(0.75\)).
3. Inglis Formula: Developed for western Maharashtra catchments:
\[ Q_p = \frac{124 A}{\sqrt{A + 10.4}} \]

Step 3: Final Answer:
Thus, the value of exponent \(b\) in Ryves formula is \(2/3\), matching option (B).