Equation for Residual Drawdown for Small Values of Distance and Large Values of Time Calculator

Residual Drawdown Equation:

\[ s' = \frac{2.302 \times Q}{4 \times \pi \times T} \times \log_{10}\left(\frac{t}{t'}\right) \]

Discharge (Q):

m³/s

Transmissibility (T):

m²/s

Time from Start of Pump (t):

seconds

Time since Stoppage of Pumping (t'):

seconds

Residual Drawdown (s'):

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1. What is the Residual Drawdown Equation?

The Residual Drawdown Equation estimates the change in groundwater level after pumping has stopped. It's particularly useful for small values of distance from the pumping well and large values of time, providing insights into aquifer recovery behavior.

2. How Does the Calculator Work?

The calculator uses the Residual Drawdown equation:

\[ s' = \frac{2.302 \times Q}{4 \times \pi \times T} \times \log_{10}\left(\frac{t}{t'}\right) \]

Where:

\( s' \) — Residual drawdown (m)
\( Q \) — Discharge rate (m³/s)
\( T \) — Transmissibility (m²/s)
\( t \) — Time from start of pump (seconds)
\( t' \) — Time since stoppage of pumping (seconds)
\( \pi \) — Mathematical constant pi (≈3.1416)

Explanation: The equation calculates how much the water level remains depressed after pumping stops, based on the pumping rate, aquifer properties, and timing factors.

3. Importance of Residual Drawdown Calculation

Details: Calculating residual drawdown is essential for understanding aquifer recovery, assessing well efficiency, and planning sustainable groundwater extraction. It helps hydrogeologists determine how quickly an aquifer rebounds after pumping ceases.

4. Using the Calculator

Tips: Enter discharge in m³/s, transmissibility in m²/s, and both time values in seconds. All values must be positive numbers. Ensure time since stoppage (t') is less than total pumping time (t) for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: When is this equation most applicable?
A: This equation works best for small distances from the pumping well and large time values, typically in confined aquifers with relatively homogeneous properties.

Q2: What are typical values for transmissibility?
A: Transmissibility values vary widely but typically range from 0.001 to 0.1 m²/s for most aquifers, with higher values indicating more permeable formations.

Q3: How does residual drawdown differ from drawdown?
A: Drawdown occurs during pumping, while residual drawdown is the remaining depression of the water table after pumping has stopped.

Q4: What assumptions does this equation make?
A: The equation assumes a homogeneous, isotropic aquifer of infinite extent, fully penetrating well, and negligible well storage effects.

Q5: Can this be used for unconfined aquifers?
A: While primarily designed for confined aquifers, it can provide reasonable estimates for unconfined aquifers when drawdown is small relative to aquifer thickness.