Depression Head In Well At Time T After Pumping Stopped With Base 10 In Coarse Sand Calculator

Formula Used:

\[ h_2 = \frac{h_1}{10^{\left(\frac{1 \times t/3600}{2.303}\right)}} \]

Depression Head At Time T (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 a base 10 logarithmic relationship that is particularly applicable to coarse sand aquifers.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ h_2 = \frac{h_1}{10^{\left(\frac{1 \times t/3600}{2.303}\right)}} \]

Where:

\( h_1 \) — Initial depression head when pumping stopped (m)
\( t \) — Time elapsed after pumping stopped (s)
3600 — Conversion factor from seconds to hours
2.303 — Conversion factor from natural log to base 10 log

Explanation: This formula models the recovery of water levels in coarse sand aquifers after pumping cessation, using a base 10 logarithmic decay relationship.

3. Importance Of Depression Head Calculation

Details: Accurate depression head calculation is crucial for understanding aquifer recovery rates, determining well efficiency, and planning sustainable groundwater extraction in coarse sand formations.

4. Using The Calculator

Tips: Enter the initial depression head in meters and the time elapsed in seconds. Both values must be positive numbers for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why Use Base 10 Instead Of Natural Logarithm?
A: Base 10 is commonly used in hydrogeological calculations for coarse sand aquifers as it provides a more practical scaling for the logarithmic recovery relationship observed in these formations.

Q2: What Are Typical Depression Head Values?
A: Depression head values vary significantly based on aquifer characteristics, pumping rates, and duration. Values typically range from 0.1 to 10 meters in coarse sand aquifers.

Q3: When Should This Calculation Be Used?
A: This calculation is specifically designed for coarse sand aquifers where the recovery follows a base 10 logarithmic pattern after pumping cessation.

Q4: Are There Limitations To This Formula?
A: This formula is specifically calibrated for coarse sand aquifers and may not accurately represent recovery patterns in other aquifer types such as clay, silt, or fractured rock formations.

Q5: How Does Time Conversion Affect The Calculation?
A: The time conversion from seconds to hours (divided by 3600) and the log base conversion (divided by 2.303) are essential for maintaining dimensional consistency and proper scaling of the logarithmic relationship.