Modified Drawdown In Well 2 Given Aquifer Constant Calculator

Formula Used:

\[ s_2' = s_1' - \frac{Q \cdot \ln\left(\frac{r_2}{r_1}\right)}{2.72 \cdot T} \]

Modified Drawdown 1 (s₁'):

Discharge (Q):

m³/s

Radial Distance at Well 2 (r₂):

Radial Distance at Well 1 (r₁):

Aquifer Constant (T):

m²/s

Modified Drawdown 2 (s₂'):

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1. What is Modified Drawdown Calculation?

The Modified Drawdown calculation determines the drawdown at a second observation well based on known parameters from a first observation well, discharge rate, radial distances, and aquifer transmissivity constant.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ s_2' = s_1' - \frac{Q \cdot \ln\left(\frac{r_2}{r_1}\right)}{2.72 \cdot T} \]

Where:

\( s_2' \) — Modified Drawdown at Well 2 (m)
\( s_1' \) — Modified Drawdown at Well 1 (m)
\( Q \) — Discharge rate (m³/s)
\( r_2 \) — Radial distance at Observation Well 2 (m)
\( r_1 \) — Radial distance at Observation Well 1 (m)
\( T \) — Aquifer Constant/Transmissivity (m²/s)
\( \ln \) — Natural logarithm function
2.72 — Approximation of Napier's constant (e)

Explanation: This formula calculates the modified drawdown at a second observation point based on the logarithmic relationship between radial distances and aquifer properties.

3. Importance of Modified Drawdown Calculation

Details: Accurate drawdown calculations are essential for groundwater resource management, well field design, and understanding aquifer characteristics for sustainable water extraction.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure radial distances and aquifer constant are positive values. Discharge rate must be greater than zero for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the natural logarithm in this formula?
A: The natural logarithm accounts for the logarithmic relationship between radial distance and drawdown in confined aquifers, following the Theis solution principles.

Q2: Why is 2.72 used instead of the exact value of e?
A: 2.72 is a practical approximation of Euler's number (e ≈ 2.71828) commonly used in field calculations for simplicity while maintaining reasonable accuracy.

Q3: What are typical ranges for aquifer transmissivity values?
A: Transmissivity values typically range from 0.1 to 1000 m²/day, depending on aquifer material and hydraulic conductivity.

Q4: When is this calculation method most appropriate?
A: This method is most appropriate for confined aquifers with homogeneous and isotropic properties under steady-state or quasi-steady-state conditions.

Q5: What are the limitations of this calculation approach?
A: Limitations include assumptions of aquifer homogeneity, fully penetrating wells, and negligible well storage effects. Results may need adjustment for unconfined aquifers or complex geological settings.