Cross-Sectional Area Of Well Given Constant Depending Upon Soil At Base Calculator

Formula Used:

\[ Cross-Sectional Area = \frac{Constant}{(1/Time) \times \log(Depression head 1/Depression head, e)} \]

Constant (K):

m³/s

Time (t):

seconds

Depression Head 1 (h1):

meters

Depression Head (h2):

meters

Cross-Sectional Area:

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1. What is Cross-Sectional Area Of Well Given Constant Depending Upon Soil At Base?

This calculator determines the cross-sectional area of a well based on the constant that depends on the soil at the base of the well, time, and depression head measurements. It's used in hydrogeology to analyze well characteristics and groundwater flow.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Cross-Sectional Area = \frac{Constant}{(1/Time) \times \log(Depression head 1/Depression head, e)} \]

Where:

\( Constant \) — Constant depending on the soil at the base of the well (m³/s)
\( Time \) — Time after pumping stopped (seconds)
\( Depression head 1 \) — Depression head in the well when pumping stopped (meters)
\( Depression head \) — Depression head in the well at a time T after pumping stopped (meters)
\( e \) — Napier's constant (approximately 2.71828)

Explanation: The formula calculates the cross-sectional area by considering the logarithmic relationship between depression heads and the time factor.

3. Importance of Cross-Sectional Area Calculation

Details: Calculating the cross-sectional area is crucial for understanding well characteristics, groundwater flow analysis, and designing efficient water extraction systems. It helps in determining the well's capacity and performance.

4. Using the Calculator

Tips: Enter the constant value in m³/s, time in seconds, and depression head values in meters. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the constant depending on soil at base?
A: The constant represents soil permeability and other soil characteristics that affect water flow into the well.

Q2: Why use natural logarithm (base e) in the formula?
A: Natural logarithm is used because it provides a mathematical relationship that accurately models the decay of depression head over time.

Q3: What are typical values for depression heads?
A: Depression head values vary depending on well characteristics and pumping conditions, typically ranging from a few centimeters to several meters.

Q4: How accurate is this calculation?
A: The accuracy depends on precise measurement of depression heads and time intervals, as well as proper determination of the soil constant.

Q5: Can this formula be used for all types of wells?
A: This formula is primarily used for unconfined aquifers and may need adjustments for different well types or aquifer conditions.