Proportionality Constant Per Unit Well Area Of Aquifer Calculator

Formula Used:

\[ K_0 = A \times \left( \frac{1}{T_r} \times \ln\left(\frac{H_1}{H_2}\right) \right) \]

Area of the Well (A):

m²

Time Interval (T_r):

Drawdown at the Start of Recuperation (H₁):

Drawdown at a Time (H₂):

Proportionality Constant (K₀):

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1. What is the Proportionality Constant?

The Proportionality Constant is referred as characteristics of the aquifer and the area of the well. It represents discharge per unit drawdown also called specific capacity of well.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ K_0 = A \times \left( \frac{1}{T_r} \times \ln\left(\frac{H_1}{H_2}\right) \right) \]

Where:

\( K_0 \) — Proportionality Constant (m³/s)
\( A \) — Area of the Well (m²)
\( T_r \) — Time Interval (s)
\( H_1 \) — Drawdown at the Start of Recuperation (m)
\( H_2 \) — Drawdown at a Time (m)
\( \ln \) — Natural logarithm function

Explanation: The formula calculates the specific capacity of a well by analyzing the relationship between drawdown measurements over a specific time interval and the well area.

3. Importance of Proportionality Constant Calculation

Details: Accurate calculation of the proportionality constant is crucial for determining the specific capacity of wells, assessing aquifer characteristics, and designing efficient groundwater extraction systems.

4. Using the Calculator

Tips: Enter all values in appropriate units (area in m², time in seconds, drawdown in meters). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What does the Proportionality Constant represent?
A: The Proportionality Constant represents the discharge per unit drawdown, also known as the specific capacity of the well, which characterizes the aquifer's response to pumping.

Q2: Why is the natural logarithm used in this formula?
A: The natural logarithm is used to model the exponential relationship between drawdown and time during the recuperation phase of aquifer testing.

Q3: What are typical units for the Proportionality Constant?
A: The Proportionality Constant is typically expressed in m³/s, representing the flow rate per unit drawdown.

Q4: When should this calculation be performed?
A: This calculation should be performed during aquifer pumping tests to determine the specific capacity and characterize the aquifer's hydraulic properties.

Q5: Are there limitations to this equation?
A: The equation assumes ideal aquifer conditions and may need adjustments for complex geological formations, boundary effects, or non-ideal well conditions.