Radial Distance From Well 1 Given Aquifer Constant Calculator

Formula Used:

\[ r_1 = \frac{r_2}{10^{\frac{2.72 \times T \times (s_1 - s_2)}{Q}}} \]

Radial Distance at Observation Well 2 (r₂):

Aquifer Constant (T):

Drawdown in Well 1 (s₁):

Drawdown in Well 2 (s₂):

Discharge (Q):

m³/s

Radial Distance at Observation Well 1 (r₁):

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1. What is the Radial Distance Formula?

The radial distance formula calculates the distance from an observation well to a pumping well in hydrogeology. It's essential for determining aquifer characteristics and understanding groundwater flow patterns around extraction points.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_1 = \frac{r_2}{10^{\frac{2.72 \times T \times (s_1 - s_2)}{Q}}} \]

Where:

\( r_1 \) — Radial distance at observation well 1 (m)
\( r_2 \) — Radial distance at observation well 2 (m)
\( T \) — Aquifer constant (coefficient of transmissibility)
\( s_1 \) — Drawdown in well 1 (m)
\( s_2 \) — Drawdown in well 2 (m)
\( Q \) — Discharge rate (m³/s)

Explanation: This formula calculates the radial distance at one observation well based on measurements from another observation well, accounting for aquifer properties and pumping effects.

3. Importance of Radial Distance Calculation

Details: Accurate radial distance calculations are crucial for determining the zone of influence of pumping wells, designing well fields, and assessing potential interference between extraction points in aquifer systems.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for distances, m³/s for discharge). Ensure drawdown measurements are taken at the same time for both observation wells for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the aquifer constant (T)?
A: The aquifer constant, or coefficient of transmissibility, represents the rate at which water is transmitted through a unit width of aquifer under a unit hydraulic gradient.

Q2: Why is the 2.72 factor used in the formula?
A: The factor 2.72 comes from the conversion between natural logarithms and base-10 logarithms used in the derivation of the formula (2.72 ≈ 1/ln(10)).

Q3: What are typical ranges for radial distances in well testing?
A: Radial distances typically range from a few meters to several hundred meters, depending on aquifer properties, pumping rate, and duration of pumping.

Q4: How does drawdown difference affect the calculation?
A: A larger difference in drawdown between the two observation wells results in a more significant adjustment to the radial distance calculation.

Q5: When is this formula most applicable?
A: This formula is most applicable in confined aquifers where the Theis assumptions hold true, including homogeneous, isotropic aquifer properties and fully penetrating wells.