Dicken's Formula for Flood Discharge Estimation

Dicken's formula is an empirical formula used primarily in Northern India for estimating the peak flood discharge from a catchment area. It relates the peak flood discharge (Q) to the catchment area (A) and a flood coefficient (C).

Understanding Dicken's Formula

The formula proposed by Dicken is:

Q = CA^3/4

Where:

• Q represents the peak flood discharge, typically measured in m³/s or ft³/s.
• A represents the catchment area, typically measured in km² or miles².
• C is a coefficient known as Dicken's coefficient. This coefficient depends on various factors such as the region, rainfall intensity, soil type, and terrain characteristics of the catchment area.

Explanation of Terms

Let's break down the components of the formula:

• Flood Discharge (Q): This is the maximum rate at which water flows through a river or channel during a flood event. Estimating this value is crucial for designing hydraulic structures like bridges, culverts, and spillways.
• Catchment Area (A): This is the geographical area from which rainfall runoff drains into a specific point on a river or stream. A larger catchment area generally results in a higher potential flood discharge, given the same rainfall intensity.
• Flood Coefficient (C): This empirical coefficient adjusts the formula based on local conditions. Typical values for C vary widely depending on the location and its susceptibility to high runoff. For example, values might range from 6 to 30 in different parts of India, depending on rainfall and ground conditions.

Analyzing the Options

Let's look at the given options and compare them to the standard Dicken's formula:

1. Q = CA^3/4, where A is the catchment area and C is flood coefficient. - This matches the widely accepted form of Dicken's formula.
2. Q = 123A^1/2, where A is the catchment area.  - This is not Dicken's formula. It resembles Ryves' formula (Q=CAR^2/3) or might be a simplified form not related to Dicken.
3. Q = CA^5/6, where A is the catchment area and C is flood coefficient.  - This is the form of Ryves' formula (Q=CAR^2/3, where R is rainfall intensity or average annual rainfall, leading to exponent closer to 5/6 or 2/3 on A depending on interpretation). This is not Dicken's formula.
4. Q = CA^2/3, where A is the catchment area and C is flood coefficient.  - This is the form of Inglis formula, used for specific areas like Maharashtra, India. It is not Dicken's formula.

Based on the standard definition, the first option correctly represents Dicken's formula.