Radial Distance of Well 2 Given Coefficient of Transmissibility and Discharge Calculator

Formula Used:

\[ R2 = r1 \times 10^{\frac{2.72 \times T_{envi} \times (h2 - h1)}{Q0}} \]

Radial Distance at Observation Well 1 (r1):

Coefficient of Transmissibility (T_envi):

m²/s

Depth of Water 2 (h2):

Depth of Water 1 (h1):

Discharge at Time t=0 (Q0):

m³/s

Radial Distance at Well 2 (R2):

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1. What is the Radial Distance Calculation?

This calculator determines the radial distance at well 2 based on the coefficient of transmissibility, discharge rate, and water depth measurements. It's essential for groundwater flow analysis and well field design in hydrogeology.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R2 = r1 \times 10^{\frac{2.72 \times T_{envi} \times (h2 - h1)}{Q0}} \]

Where:

\( R2 \) — Radial distance at well 2 (m)
\( r1 \) — Radial distance at observation well 1 (m)
\( T_{envi} \) — Coefficient of transmissibility (m²/s)
\( h2 \) — Depth of water in well 2 (m)
\( h1 \) — Depth of water in well 1 (m)
\( Q0 \) — Discharge at time t=0 (m³/s)

Explanation: This formula calculates the radial distance at a second well based on the transmissibility coefficient, water depth differences, and initial discharge rate.

3. Importance of Radial Distance Calculation

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

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure radial distances and water depths are positive values. The discharge rate must be greater than zero for valid calculations.

5. Frequently Asked Questions (FAQ)

Q1: What is the coefficient of transmissibility?
A: The coefficient of transmissibility represents the rate of water flow through a vertical strip of aquifer under unit hydraulic gradient.

Q2: Why is the 2.72 constant used in the formula?
A: The constant 2.72 is derived from the natural logarithm base (e) and is used in the conversion between logarithmic forms of the well flow equations.

Q3: What are typical values for coefficient of transmissibility?
A: Values vary widely depending on aquifer material, ranging from 0.1 m²/day for clay to over 1000 m²/day for highly permeable gravel aquifers.

Q4: How does water depth difference affect the calculation?
A: A greater difference in water depths (h2 - h1) increases the calculated radial distance, indicating a larger zone of influence around the pumping well.

Q5: What are the limitations of this calculation?
A: This approach assumes homogeneous, isotropic aquifer conditions and steady-state flow, which may not represent all real-world scenarios accurately.