Modified Drawdown In Well 1 Given Aquifer Constant Calculator

Formula Used:

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

Modified Drawdown 2 (s₂'):

Discharge (Q):

m³/s

Radial Distance at Observation Well 2 (r₂):

Radial Distance at Observation Well 1 (r₁):

Aquifer Constant (T):

m²/s

Modified Drawdown 1 (s₁'):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Modified Drawdown Formula?

The Modified Drawdown formula calculates the drawdown in one observation well based on known parameters from another observation well, discharge rate, radial distances, and aquifer constant. It's essential for analyzing groundwater flow in confined aquifers.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( s_1' \) — Modified Drawdown at well 1 (m)
\( s_2' \) — Modified Drawdown at well 2 (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 (base e)
2.72 — Approximation of Napier's constant (e)

Explanation: The formula accounts for the logarithmic relationship between drawdown and radial distance in confined aquifers.

3. Importance of Modified Drawdown Calculation

Details: Accurate drawdown calculation is crucial for determining aquifer characteristics, predicting groundwater behavior, and designing efficient well systems for water extraction.

4. Using the Calculator

Tips: Enter all values in appropriate units. Modified drawdown values should be non-negative, discharge and aquifer constant must be positive, and radial distances must be positive values with r₂ > r₁ 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 distribution of drawdown around a pumping well in a confined aquifer, following Theis's solution principles.

Q2: Why use 2.72 instead of the exact value of e (2.71828...)?
A: 2.72 is a practical approximation commonly used in field calculations for simplicity while maintaining sufficient accuracy for engineering purposes.

Q3: What are typical ranges for aquifer constant values?
A: Aquifer constant (transmissivity) typically ranges from 0.1 to 1000 m²/day, with higher values indicating more productive aquifers.

Q4: When is this formula most applicable?
A: This formula is most applicable for confined aquifers with steady-state conditions and homogeneous, isotropic properties.

Q5: What are the limitations of this approach?
A: The formula assumes ideal conditions and may not accurately represent complex aquifer systems with heterogeneity, boundary effects, or unsteady flow conditions.