Dickens Formula and Peak Runoff Estimation

The Dickens formula is a well-known empirical formula used in hydrology to estimate the peak rate of runoff ($Q_p$) from a catchment area during a flood event. Empirical formulas are based on observations and data collected over time rather than purely theoretical principles.

Parameters in Dickens Formula

The Dickens formula is expressed as:

\(Q_p = C_D A^{3/4}\)

Where:

• \(Q_p\) is the peak discharge or peak rate of runoff (typically in m³/s or ft³/s).
• \(C_D\) is the Dickens coefficient. This coefficient is empirical and depends on various factors like the shape and characteristics of the catchment, the type of storm, and the region. Its value varies significantly.
• \(A\) is the drainage area or the area of the catchment (typically in km² or sq mi).

From the formula \(Q_p = C_D A^{3/4}\), it is clear that the peak rate of runoff ($Q_p$) is directly related to the drainage area or the area of the catchment ($A$). The exponent 3/4 indicates the nature of this relationship.

Analyzing the Options

Let's look at the given options in the context of the Dickens formula:

• length of longest drain: While the length of the longest drain can influence the time of concentration and thus affect runoff characteristics, it is not the primary parameter directly used in the standard Dickens formula structure.
• Drainage density: Drainage density (total length of streams per unit area) is an important catchment characteristic, but it is not a direct parameter in the Dickens formula. It might indirectly influence the coefficient \(C_D\).
• Depth of rainfall: The depth of rainfall is a critical input for flood estimation, but the basic Dickens formula relates peak runoff primarily to the catchment area via the coefficient \(C_D\) which implicitly accounts for rainfall characteristics and intensity for a region. It's not an explicit parameter like area in the formula itself.
• Area of catchment: As seen in the formula \(Q_p = C_D A^{3/4}\), the area of the catchment ($A$) is a direct and primary parameter influencing the estimated peak runoff ($Q_p$).

Therefore, the Dickens formula is used for estimating the peak rate of runoff during a flood from a catchment, and it is most directly related to the Area of catchment.