Radial Distance of Well 1 Based on Discharge of Two Wells under Consideration Calculator

Formula Used:

\[ R1 = \frac{r2}{\exp\left(\frac{\pi \times K_{soil} \times (h2^2 - h1^2)}{Q}\right)} \]

Radial Distance at Observation Well 2:

Coefficient of Permeability of Soil Particle:

m/s

Depth of Water 2:

Depth of Water 1:

Discharge:

m³/s

Radial Distance 1:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Radial Distance Calculation?

The radial distance calculation determines the distance from a well based on the discharge rate, soil permeability, and water depth measurements from observation wells. This is essential in hydrogeology for understanding groundwater flow patterns and well interference.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R1 = \frac{r2}{\exp\left(\frac{\pi \times K_{soil} \times (h2^2 - h1^2)}{Q}\right)} \]

Where:

\( R1 \) — Radial Distance 1 (m)
\( r2 \) — Radial Distance at Observation Well 2 (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 (m³/s)
\( \pi \) — Mathematical constant (approximately 3.14159)
\( \exp \) — Exponential function

Explanation: The formula calculates the radial distance from well 1 based on the difference in water depths, soil permeability, and discharge rate between two observation wells.

3. Importance of Radial Distance Calculation

Details: Accurate radial distance calculation is crucial for determining well spacing, predicting drawdown effects, designing efficient well fields, 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). Ensure all values are positive and measurements are accurate for reliable results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of radial distance in well hydraulics?
A: Radial distance helps determine the zone of influence of a pumping well and is essential for designing well spacing to avoid interference between adjacent wells.

Q2: How does soil permeability affect the radial distance calculation?
A: Higher soil permeability allows water to move more easily through the soil, resulting in a larger zone of influence and greater radial distances for the same discharge rate.

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 10⁻⁵ m/s), gravel (10⁻¹ to 10⁻³ m/s). The specific value depends on soil composition and compaction.

Q4: When is this calculation most applicable?
A: This calculation is most applicable in confined aquifers with steady-state flow conditions and when wells are fully penetrating the aquifer thickness.

Q5: What are the limitations of this approach?
A: The calculation assumes homogeneous, isotropic aquifer conditions, steady-state flow, and may not account for boundary effects, partial penetration, or time-dependent drawdown.