Radial Distance of Well 1 Based on Discharge from Two Wells with Base 10 Calculator

Formula Used:

\[ R1 = \frac{r2}{10^{\frac{1.36 \times K_{soil} \times (h2^2 - h1^2)}{Q}}} \]

Radial Distance at Observation Well 2 (r2):

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 1 (R1):

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1. What is Radial Distance of Well 1 Based on Discharge from Two Wells with Base 10?

This formula calculates the radial distance of well 1 based on discharge measurements from two wells using a base 10 logarithmic relationship. It's used in hydrogeology to determine the influence radius of wells and analyze groundwater flow patterns.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R1 = \frac{r2}{10^{\frac{1.36 \times K_{soil} \times (h2^2 - h1^2)}{Q}}} \]

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)

Explanation: The formula calculates the radial distance from well 1 based on the hydraulic properties of the soil, water depths in observation wells, and discharge rate.

3. Importance of Radial Distance Calculation

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

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure radial distances are in meters, permeability in m/s, water depths in meters, and discharge in m³/s. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 1.36 coefficient?
A: The 1.36 coefficient is derived from empirical relationships and unit conversions that make the formula dimensionally consistent for the given parameters.

Q2: When is this formula most applicable?
A: This formula is most applicable in confined aquifers with steady-state flow conditions and homogeneous soil properties.

Q3: What are typical values for soil permeability?
A: Soil permeability varies widely: gravel (10^-1-10^-2 m/s), sand (10^-3-10^-5 m/s), clay (10^-7-10^-9 m/s).

Q4: How does water depth affect radial distance?
A: Greater differences in water depths between wells typically result in larger calculated radial distances, indicating broader influence areas.

Q5: What are the limitations of this approach?
A: This approach assumes homogeneous aquifer conditions, steady-state flow, and may not account for complex geological features or transient conditions.