Depression Head In Well At Time T After Pumping Stopped Calculator

Formula Used:

\[ Depression\ Head = \frac{Initial\ Depression\ Head}{\exp(Specific\ Capacity \times Time)} \] \[ h_2 = \frac{h_1}{\exp(KA \times t)} \]

Depression Head at Time T (h₂):

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1. What is Depression Head Calculation?

The depression head calculation determines the water level depression in a well at a specific time after pumping has stopped. This is important for understanding aquifer recovery rates and well performance characteristics.

2. How Does the Calculator Work?

The calculator uses the exponential decay formula:

\[ h_2 = \frac{h_1}{\exp(KA \times t)} \]

Where:

\( h_2 \) — Depression head at time T (Meter)
\( h_1 \) — Initial depression head when pumping stopped (Meter)
\( KA \) — Specific capacity of the well (Meter per Second)
\( t \) — Time after pumping stopped (Hour)
\( \exp \) — Exponential function

Explanation: The formula models how the depression head decreases exponentially over time as the aquifer recovers after pumping cessation.

3. Importance of Depression Head Calculation

Details: Accurate depression head calculation is crucial for well design, aquifer characterization, and determining sustainable pumping rates for groundwater extraction.

4. Using the Calculator

Tips: Enter initial depression head in meters, specific capacity in meters per second, and time in hours. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is specific capacity?
A: Specific capacity is the discharge per unit drawdown, typically expressed as the pumping rate divided by the drawdown in the well.

Q2: Why does the depression head decrease exponentially?
A: The exponential decrease occurs because the rate of recovery is proportional to the remaining depression head, following natural decay patterns.

Q3: What time units should be used?
A: Time should be entered in hours to maintain consistency with the specific capacity units (meters per second).

Q4: Are there limitations to this formula?
A: This formula assumes ideal conditions and may not account for complex aquifer heterogeneity or boundary effects.

Q5: When is this calculation most accurate?
A: The calculation is most accurate for confined aquifers with relatively homogeneous properties and sufficient distance from boundaries.