Radial Distance of Well 2 Based on Discharge of Two Wells under Consideration Calculator

Formula Used:

\[ R2 = r1 \times \exp\left(\frac{\pi \times K_{soil} \times (h2^2 - h1^2)}{Q}\right) \]

Radial Distance at Observation Well 1 (r1):

Coefficient of Permeability of Soil Particle (K_soil):

m/s

Depth of Water 2 (h2):

Depth of Water 1 (h1):

Discharge (Q):

m³/s

Radial Distance at Well 2 (R2):

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1. What is the Radial Distance Calculation?

The radial distance calculation determines the distance from a well where the water table reaches a specific level, based on soil permeability, water depths, and discharge rate. This is essential in hydrogeology for well field design and groundwater management.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R2 = r1 \times \exp\left(\frac{\pi \times K_{soil} \times (h2^2 - h1^2)}{Q}\right) \]

Where:

\( R2 \) — Radial distance at well 2 (m)
\( r1 \) — Radial distance at observation well 1 (m)
\( K_{soil} \) — Coefficient of permeability of soil particle (m/s)
\( h2 \) — Depth of water 2 (m)
\( h1 \) — Depth of water 1 (m)
\( Q \) — Discharge rate (m³/s)
\( \pi \) — Archimedes' constant (approximately 3.1416)
\( \exp \) — Exponential function

Explanation: The formula calculates how the radial distance changes based on the difference in water depths, soil permeability, and discharge rate.

3. Importance of Radial Distance Calculation

Details: Accurate radial distance calculation is crucial for determining well interference, designing well spacing, and managing groundwater resources effectively.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for distances, m/s for permeability, m³/s for discharge). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the exponential function in this formula?
A: The exponential function accounts for the non-linear relationship between radial distance and the ratio of permeability times head difference to discharge.

Q2: How does soil permeability affect the radial distance?
A: Higher permeability allows water to move more easily through the soil, resulting in a larger radial distance for the same discharge and head difference.

Q3: What are typical values for soil permeability coefficients?
A: Permeability coefficients vary widely: clay (10⁻⁸ to 10⁻¹⁰ m/s), sand (10⁻³ to 10⁻⁶ m/s), gravel (10⁻¹ to 10⁻³ m/s).

Q4: When is this calculation most applicable?
A: This calculation is most applicable for confined aquifers with steady-state flow conditions and homogeneous, isotropic soil properties.

Q5: What are the limitations of this approach?
A: The formula assumes ideal conditions and may not account for aquifer heterogeneity, transient flow conditions, or boundary effects.