Depression Head In Well At Time T Given Pumping Stopped And Constant Calculator

Formula Used:

\[ h_2 = \frac{h_1}{\exp\left(\frac{K \cdot t}{A_{cs}}\right)} \]

Depression Head When Pumping Stopped (h₁):

Constant (K):

m³/s

Time (t):

Cross-Sectional Area (A_cs):

m²

Depression Head At Time T (h₂):

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1. What Is The Depression Head Formula?

The depression head formula calculates the water level depression in a well at a specific time after pumping has stopped. It's based on the exponential decay relationship between the initial depression head and various hydrogeological parameters.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ h_2 = \frac{h_1}{\exp\left(\frac{K \cdot t}{A_{cs}}\right)} \]

Where:

\( h_2 \) — Depression head at time T (m)
\( h_1 \) — Depression head when pumping stopped (m)
\( K \) — Constant depending on soil properties (m³/s)
\( t \) — Time after pumping stopped (s)
\( A_{cs} \) — Cross-sectional area of the well (m²)
\( \exp \) — Exponential function

Explanation: The formula describes how the water level in a well recovers exponentially after pumping ceases, with the recovery rate influenced by soil permeability and well geometry.

3. Importance Of Depression Head Calculation

Details: Accurate calculation of depression head recovery is crucial for groundwater resource management, well design, and understanding aquifer properties. It helps determine the sustainable yield of wells and assess aquifer characteristics.

4. Using The Calculator

Tips: Enter all values in the specified units. Ensure positive values for all parameters. The constant K depends on soil type and can be determined through pumping tests or obtained from hydrogeological studies.

5. Frequently Asked Questions (FAQ)

Q1: What Does The Constant K Represent?
A: The constant K represents the soil's hydraulic conductivity and storage properties at the base of the well. It varies with soil type and aquifer characteristics.

Q2: How Is Cross-Sectional Area Determined?
A: Cross-sectional area is calculated based on the well's geometry. For circular wells, it's πr² where r is the radius of the well.

Q3: What Time Units Should Be Used?
A: Time should be entered in seconds to maintain consistency with the SI units used for other parameters.

Q4: When Is This Formula Most Accurate?
A: This formula provides the most accurate results for confined aquifers and wells that fully penetrate the aquifer. Accuracy may vary for unconfined aquifers or partially penetrating wells.

Q5: How Can The Constant K Be Determined Experimentally?
A: The constant K can be determined through pumping tests where both drawdown and recovery data are measured and analyzed to characterize the aquifer properties.