Radial Distance Of Well 2 Based On Discharge From Two Wells With Base 10 Calculator

Formula Used:

\[ R2 = r1 \times 10^{\frac{1.36 \times K_{soil} \times (h2^2 - h1^2)}{Q}} \]

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 based on discharge measurements from two observation wells. This formula is essential in hydrogeology for analyzing groundwater flow and well interference effects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R2 = r1 \times 10^{\frac{1.36 \times K_{soil} \times (h2^2 - h1^2)}{Q}} \]

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 in well 2 (m)
\( h1 \) — Depth of water in well 1 (m)
\( Q \) — Discharge rate (m³/s)

Explanation: The formula calculates the radial distance at well 2 based on the hydraulic properties of the soil and the water depth differences between two observation wells.

3. Importance of Radial Distance Calculation

Details: Accurate radial distance calculation is crucial for well field design, groundwater resource management, and predicting interference effects between adjacent wells in aquifer systems.

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 within reasonable physical ranges for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the coefficient 1.36 in the formula?
A: The coefficient 1.36 is derived from the integration of the Thiem equation and represents a conversion factor that accounts for the logarithmic nature of radial flow in confined aquifers.

Q2: When is this formula most applicable?
A: This formula is most applicable for steady-state radial flow to a well in a confined aquifer with homogeneous and isotropic properties.

Q3: What are typical values for soil permeability coefficient?
A: Permeability coefficients vary widely: gravel (10⁻¹-10⁻² m/s), sand (10⁻³-10⁻⁵ m/s), silt (10⁻⁶-10⁻⁸ m/s), clay (10⁻⁹-10⁻¹² m/s).

Q4: How does well interference affect the results?
A: Well interference occurs when the cone of depression of one well affects another. This formula helps quantify that interference effect.

Q5: What are the limitations of this approach?
A: The formula assumes homogeneous aquifer properties, steady-state conditions, and fully penetrating wells. Results may be less accurate in heterogeneous aquifers or under transient conditions.