Understanding Dicken's Formula for Maximum Flood

Dicken's formula is an empirical method used in hydrology and civil engineering to estimate the peak discharge (maximum flood flow) from a river catchment or drainage area.

This formula helps engineers predict the highest flow rate a river might experience, which is crucial for designing structures like bridges, culverts, and dams to ensure they can withstand flood conditions safely.

Dicken's Formula Equation

The standard form of Dicken's formula is represented as:

$Q_p = C \times A^{\frac{3}{4}}$

Explanation of Terms

• $Q_p$: Represents the peak discharge or maximum flood flow, typically measured in cubic meters per second (m³/s) or cubic feet per second (cfs).
• $C$: This is a constant coefficient. Its value depends on the characteristics of the drainage basin, such as topography, soil type, and land use. It is often determined based on regional data or specific empirical studies. For instance, values might range from around 10 to 30 or higher, depending on the context.
• $A$: Represents the area of the drainage basin contributing to the flood, usually measured in square kilometers (km²) or square miles (mi²). The exponent $\frac{3}{4}$ indicates that the discharge is related to the area raised to the power of three-quarters.

Analyzing the Options for Dicken's Formula

Let's examine the provided options in relation to the standard Dicken's formula ($Q_p = CA^{3/4}$):

• Option 1: $Q_p = CA^{\frac{3}{4}}$
  This option precisely matches the widely accepted form of Dicken's formula, where the peak discharge ($Q_p$) is directly proportional to the drainage area ($A$) raised to the power of 3/4, multiplied by a constant ($C$).
• Option 2: $Q_p = C_1A^{\frac{2}{3}}$
  This formula uses a different exponent ($\frac{2}{3}$) for the area. While other empirical flood formulas exist with similar structures, this is not Dicken's formula.
• Option 3: $Q_p = C\sqrt{A}$
  This formula simplifies to $Q_p = C \times A^{\frac{1}{2}}$. The exponent $\frac{1}{2}$ (or square root) is different from the $\frac{3}{4}$ characteristic of Dicken's formula.
• Option 4: $Q_p = 177p\sqrt{A}$
  This formula includes different variables ($p$ and $\sqrt{A}$) and a specific constant (177). It does not represent the general form of Dicken's formula.

Based on the standard definition and common usage in hydrology, Option 1 accurately represents Dicken's formula for determining maximum flood discharge.