Equation For Residual Drawdown Calculator

Equation For Residual Drawdown:

\[ s' = \frac{Q}{4\pi T} \times (W(u) - W(u')) \]

Discharge (Q):

m³/s

Transmissibility (T):

m²/s

Well Function of u (W(u)):

Well Function after Cessation (W(u')):

Residual Drawdown (s'):

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1. What is the Equation For Residual Drawdown?

The Equation For Residual Drawdown calculates the change in groundwater level after the cessation of pumping. It is derived from Theis' solution and accounts for the difference in well functions before and after pumping stops.

2. How Does the Calculator Work?

The calculator uses the equation:

\[ s' = \frac{Q}{4\pi T} \times (W(u) - W(u')) \]

Where:

\( s' \) — Residual Drawdown (m)
\( Q \) — Discharge (m³/s)
\( T \) — Transmissibility (m²/s)
\( W(u) \) — Well Function of u
\( W(u') \) — Well Function after Cessation of Pumping
\( \pi \) — Archimedes' constant (approx. 3.1416)

Explanation: The equation calculates the residual drawdown by considering the difference between the well function during pumping and after cessation, scaled by the discharge and transmissibility.

3. Importance of Residual Drawdown Calculation

Details: Accurate residual drawdown estimation is crucial for assessing aquifer recovery, determining sustainable yield, and evaluating the impact of pumping on groundwater resources.

4. Using the Calculator

Tips: Enter discharge in m³/s, transmissibility in m²/s, and well function values. All values must be valid (discharge > 0, transmissibility > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is residual drawdown?
A: Residual drawdown is the change in groundwater level that persists after pumping has stopped, indicating aquifer recovery.

Q2: How is transmissibility different from hydraulic conductivity?
A: Transmissibility is hydraulic conductivity multiplied by aquifer thickness, representing the ability to transmit water through the entire saturated thickness.

Q3: What are typical values for well functions?
A: Well function values typically range from 0 to 10, depending on the time since pumping started/stopped and aquifer properties.

Q4: When should this equation be used?
A: This equation is used in pumping test analysis to determine aquifer properties and assess recovery after pumping cessation.

Q5: Are there limitations to this equation?
A: The equation assumes ideal conditions: homogeneous isotropic aquifer, fully penetrating well, and negligible well storage effects.