Depression Head In Well At Time T After Pumping Stopped With Known Discharge And Time Calculator

Formula Used:

\[ h_2 = \frac{h_1}{10^{\frac{Q \cdot t/3600}{A_{cs} \cdot H \cdot 2.303}}} \]

Depression Head When Pumping Stopped (h1):

Discharge (Q):

m³/s

Time (t):

Cross-Sectional Area (Acs):

m²

Constant Depression Head (H):

Depression Head At Time T (h2):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is The Depression Head Calculation?

The depression head calculation determines the water level depression in a well at a specific time after pumping has stopped, using known discharge rates and time intervals. This is essential for understanding aquifer recovery and well performance.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ h_2 = \frac{h_1}{10^{\frac{Q \cdot t/3600}{A_{cs} \cdot H \cdot 2.303}}} \]

Where:

\( h_2 \) — Depression head at time T after pumping stopped (m)
\( h_1 \) — Depression head when pumping stopped (m)
\( Q \) — Discharge rate (m³/s)
\( t \) — Time after pumping stopped (s)
\( A_{cs} \) — Cross-sectional area (m²)
\( H \) — Constant depression head (m)

Explanation: This formula calculates the remaining depression in the well based on the initial conditions and time elapsed since pumping cessation.

3. Importance Of Depression Head Calculation

Details: Accurate depression head calculation is crucial for assessing well recovery rates, determining aquifer characteristics, and planning sustainable groundwater extraction strategies.

4. Using The Calculator

Tips: Enter all values in the specified units. Ensure depression head values are positive, discharge is in m³/s, time in seconds, area in m², and constant head in meters.

5. Frequently Asked Questions (FAQ)

Q1: Why is time converted in the formula?
A: The time conversion (t/3600) converts seconds to hours to maintain dimensional consistency with other parameters in the equation.

Q2: What is the significance of the constant 2.303?
A: The constant 2.303 is the conversion factor from natural logarithm to base-10 logarithm (ln(10) ≈ 2.303).

Q3: How does cross-sectional area affect the result?
A: Larger cross-sectional areas result in slower depression head recovery, as the water has more volume to fill the well.

Q4: When is this calculation most accurate?
A: This calculation is most accurate in confined aquifers with relatively homogeneous properties and steady initial conditions.

Q5: Can this be used for multiple pumping cycles?
A: This formula is designed for single pumping cessation events. For multiple cycles, more complex modeling approaches are needed.