Deccan’s Formula for Drain Design

 Deccan’s Formula for Drain Design

Deccan’s Formula for Drain Design is an empirical formula widely used in India for designing small to medium surface drains, especially in semi-arid regions like the Deccan plateau. It is primarily used to estimate the discharge (Q) of stormwater or surface runoff from an area, and accordingly design an open channel or drain to carry this discharge safely.

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🔹 Deccan’s Formula:

The formula is expressed as:

$$Q = C \cdot A^{3/4}$$

Where:

• $Q$ = Peak discharge (in cubic feet per second or cusecs)

• $A$ = Drainage area (in acres)

• $C$ = Runoff coefficient (depends on land use, soil type, slope, etc.)

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🔍 Explanation of Terms:

1. Peak Discharge (Q):

• This is the maximum expected rate of flow of water (due to rainfall or storm) at a certain location in the drainage system.

• It is critical for designing the capacity of the drain.

2. Drainage Area (A):

• The area from which the surface runoff is collected and directed into the drain.

• The area should be measured accurately using maps, satellite images, or survey data.

3. Coefficient (C):

• This is an empirical value derived from field observations and past records.

• It takes into account:

  • Soil type (clay, loam, sandy)

  • Land use (urban, rural, agricultural)

  • Vegetation cover

  • Slope of land

  • Rainfall intensity

• Typically, values of C range from 0.5 to 2.5, depending on these conditions.

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💡 Why Use Deccan’s Formula?

• It is simple and quick to use for preliminary drain design.

• Especially useful in rural or undeveloped areas where detailed rainfall and hydrological data may not be available.

• Best suited for the Deccan region (India) but used more generally across similar regions.

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📐 Steps in Drain Design Using Deccan’s Formula:

Step 1: Determine the Catchment Area (A)

• Measure in acres.

• Use survey tools or mapping software.

Step 2: Choose an Appropriate Value of C

• Based on experience or regional guidelines.

• Example: C = 1.2 for moderately sloping agricultural land.

Step 3: Calculate Peak Discharge (Q)

$$Q = C \cdot A^{3/4}$$

Step 4: Design the Channel

Use the discharge $Q$ to design the drain:

• Cross-sectional shape (rectangular, trapezoidal, etc.)

• Dimensions (depth, width, side slopes)

• Slope of bed

• Use Manning’s equation for more detailed flow capacity checks.

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✅ Example:

Let’s say you have a catchment area of 16 acres, and the runoff coefficient (C) is 1.2:

$$Q = 1.2 \cdot (16)^{3/4} = 1.2 \cdot (16^{0.75}) = 1.2 \cdot 8 = 9.6 \text{ cusecs}$$

This means the drain should be designed to carry 9.6 cusecs of flow.

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⚠️ Limitations of Deccan’s Formula:

• Not suitable for large catchment areas.

• Doesn’t consider rainfall duration or intensity explicitly.

• Being empirical, it may not be accurate for unusual terrains or land use types.

• Should be used with judgment and local calibration.

📊 Runoff Coefficient (C) for Deccan’s Formula — Based on Area Unit

Terrain / Land Use	C (for km²)	C (for Acres)	C (for Hectares)
Flat cultivated land (low slope)	1.0 – 1.2	2.0 – 2.2	1.5 – 1.7
Undulating agricultural land	1.2 – 1.5	2.2 – 2.5	1.7 – 2.0
Rolling terrain with sparse cover	1.5 – 1.8	2.5 – 2.8	2.0 – 2.2
Hilly area with good vegetation	1.6 – 2.0	2.7 – 3.0	2.1 – 2.4
Urban area (residential)	2.0 – 2.5	3.0 – 3.5	2.5 – 3.0
Urban area (paved/commercial)	2.5 – 3.0	3.5 – 4.0	3.0 – 3.5

If my catchment area is 14 square kilometer then Design Drain from Deccan's Formula and take the value of C of Banda district of UP, India

Designing a drain using Deccan’s Formula involves determining the peak discharge ($Q$) based on the catchment area ($A$) and the runoff coefficient ($C$). Given your catchment area of 14 square kilometers in Banda district, Uttar Pradesh, let's proceed with the calculations.

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1. Determine the Runoff Coefficient ($C$) for Banda District

The runoff coefficient $C$ depends on factors like soil type, land use, and topography. Banda district features irregular uplands with rock outcrops and lowlands prone to water accumulation during the rainy season. The soil types include Rakar, Mar, Kabar, and Padua, with significant agricultural activity. ​Banda District

Considering these characteristics, a moderate runoff coefficient is appropriate. For semi-arid regions with mixed land use (agriculture and wastelands), $C$ typically ranges from 1.2 to 1.5 when using Deccan's Formula with area in square kilometers. Given Banda's terrain and soil composition, selecting $C = 1.5$ is reasonable.​

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2. Calculate Peak Discharge ($Q$)

Using Deccan’s Formula:

$$Q = C \times A^{3/4}$$

Substituting the values:

• $C = 1.5$

• $A = 14$ km²

$$Q = 1.5 \times 14^{3/4}$$

Calculating $14^{3/4}$:​

$$14^{3/4} \approx 7.237$$

Now, multiplying by $C$:​

$$Q = 1.5 \times 7.237 \approx 10.856 \text{ cusecs}$$

Peak Discharge ($Q$) ≈ 10.856 cusecs

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3. Designing the Drain

With $Q$ determined, design the drain to handle this discharge. Consider:

• Cross-sectional Shape: Trapezoidal sections are common for open drains due to stability and ease of construction.​

• Dimensions: Calculate the bottom width, depth, and side slopes based on $Q$, using Manning’s equation for flow capacity.​

• Slope: Ensure a sufficient bed slope to maintain self-cleansing velocity, preventing sediment deposition.​

• Freeboard: Include an additional height above the design water level to accommodate unexpected flows.​

For precise dimensions, detailed hydrological and hydraulic analyses are recommended, considering local rainfall intensity, soil infiltration rates, and existing drainage infrastructure.​

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4. Additional Considerations

• Soil Erosion Control: Implement measures like grass lining or riprap to prevent erosion of the drain banks, especially given the soil types in Banda.​

• Maintenance Access: Design the drain with accessible pathways for regular inspection and maintenance.​

• Environmental Impact: Ensure the drain design minimizes disruption to local ecosystems and agricultural activities.​