Depression Head in Well at Time T given Pumping Stopped and Constant with Base 10 Calculator

Formula Used:

\[ Depression Head = \frac{Depression Head}{10^{\left(\frac{Constant \times Time}{Cross-Sectional Area \times 2.303}\right)}} \] \[ h_2 = \frac{h_1}{10^{\left(\frac{K \times t}{A_{cs} \times 2.303}\right)}} \]

Depression Head (h1):

Constant (K):

m³/s

Time (t):

Cross-Sectional Area (Acs):

m²

Depression Head (h2):

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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 soil constants and well characteristics. This is important for understanding aquifer recovery and well performance.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_2 = \frac{h_1}{10^{\left(\frac{K \times t}{A_{cs} \times 2.303}\right)}} \]

Where:

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

Explanation: This formula calculates how the depression head decreases over time as the well recovers after pumping stops, accounting for soil properties and well geometry.

3. Importance of Depression Head Calculation

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

4. Using the Calculator

Tips: Enter initial depression head in meters, soil constant in m³/s, time in seconds, and cross-sectional area in m². All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is depression head in well hydrology?
A: Depression head refers to the vertical distance the water level in a well is lowered below the static water level due to pumping.

Q2: How is the soil constant (K) determined?
A: The soil constant is typically determined through pump tests and depends on the permeability and characteristics of the aquifer material.

Q3: Why use base 10 in this formula?
A: The base 10 logarithm is used in this particular formulation of the recovery equation, which is derived from empirical observations of well recovery patterns.

Q4: What factors affect the accuracy of this calculation?
A: Accuracy depends on proper determination of soil constants, well construction details, and measurement precision of initial conditions.

Q5: Can this formula be used for all well types?
A: This formula is most applicable to fully penetrating wells in confined aquifers with specific boundary conditions. Modifications may be needed for other well configurations.