Constant Used in Flood Discharge by Fuller's Formula Calculator

Fuller's Formula:

\[ C_{FL} = \frac{Q_{FL}}{(A_{km}^{0.8}) \times (1 + 0.8 \times \log(T_m, e)) \times (1 + 2.67 \times A_{km}^{-0.3})} \]

Flood Discharge by Fuller's Formula (Q_FL):

m³/s

Catchment Area for Flood Discharge (A_km):

m²

Time Period for a Flood Discharge (T_m):

seconds

Fuller's Constant (C_FL):

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1. What is Fuller's Constant?

Fuller's Constant refers to an empirical coefficient used in Fuller's formula to estimate peak flood discharge, adjusted for regional hydrological conditions. It is a crucial parameter in flood discharge calculations that accounts for catchment characteristics and regional variations.

2. How Does the Calculator Work?

The calculator uses Fuller's formula:

\[ C_{FL} = \frac{Q_{FL}}{(A_{km}^{0.8}) \times (1 + 0.8 \times \log(T_m, e)) \times (1 + 2.67 \times A_{km}^{-0.3})} \]

Where:

\( C_{FL} \) — Fuller's Constant
\( Q_{FL} \) — Flood Discharge by Fuller's Formula (m³/s)
\( A_{km} \) — Catchment Area for Flood Discharge (m²)
\( T_m \) — Time Period for a Flood Discharge (seconds)
\( e \) — Napier's constant (≈2.71828)

Explanation: The formula calculates Fuller's Constant based on flood discharge, catchment area, and time period, incorporating logarithmic relationships and area-dependent coefficients.

3. Importance of Fuller's Constant

Details: Fuller's Constant is essential for accurate flood discharge estimation in hydrological studies. It helps in designing flood control structures, urban drainage systems, and water resource management by providing region-specific coefficients that improve prediction accuracy.

4. Using the Calculator

Tips: Enter flood discharge in m³/s, catchment area in m², and time period in seconds. All values must be positive and valid for accurate calculation of Fuller's Constant.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of Fuller's Constant values?
A: Fuller's Constant typically ranges between 0.1 to 0.3, but can vary significantly based on regional hydrological characteristics and catchment properties.

Q2: How does catchment area affect Fuller's Constant?
A: Larger catchment areas generally result in smaller Fuller's Constant values due to the inverse relationship in the formula, reflecting the distributed nature of runoff in larger basins.

Q3: Why is Napier's constant (e) used in the formula?
A: Napier's constant is used as the base for the logarithmic function to model the exponential decay relationship between time period and flood discharge characteristics.

Q4: Can this constant be used for all types of catchments?
A: While Fuller's formula is widely applicable, the constant may need regional calibration for specific catchment types, particularly in areas with unusual geological or climatic conditions.

Q5: How accurate is Fuller's Constant for flood prediction?
A: Fuller's Constant provides good accuracy for most practical applications when properly calibrated, though it should be used with other methods for critical flood risk assessments.