Transmissivity When Discharge And Drawdowns Are Considered Calculator

Formula Used:

\[ \tau = \frac{Q_{sf} \cdot \ln\left(\frac{r_2}{r_1}\right)}{2\pi (H_1 - H_2)} \]

Steady Flow in a Confined Aquifer (Qsf):

m³/s

Radial Distance at Observation Well 2 (r₂):

Radial Distance at Observation Well 1 (r₁):

Drawdown at Start of Recuperation (H₁):

Drawdown at a Time (H₂):

Transmissivity (τ):

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1. What is Transmissivity?

Transmissivity is the measure of how much water can be transmitted horizontally through a unit width of the entire thickness of an aquifer. It's a key parameter in hydrogeology that quantifies the ability of an aquifer to transmit groundwater.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau = \frac{Q_{sf} \cdot \ln\left(\frac{r_2}{r_1}\right)}{2\pi (H_1 - H_2)} \]

Where:

\( \tau \) — Transmissivity (m²/s)
\( Q_{sf} \) — Steady Flow in a Confined Aquifer (m³/s)
\( r_2 \) — Radial Distance at Observation Well 2 (m)
\( r_1 \) — Radial Distance at Observation Well 1 (m)
\( H_1 \) — Drawdown at Start of Recuperation (m)
\( H_2 \) — Drawdown at a Time (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: This formula calculates transmissivity based on steady flow conditions in a confined aquifer, using drawdown measurements from two observation wells at different radial distances.

3. Importance of Transmissivity Calculation

Details: Accurate transmissivity estimation is crucial for groundwater resource management, well field design, contaminant transport modeling, and predicting aquifer response to pumping.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure radial distances and drawdowns are positive values, and that H₁ and H₂ are not equal. All values must be valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for transmissivity values?
A: Transmissivity values can range from less than 1 m²/day for tight formations to over 1000 m²/day for highly productive aquifers.

Q2: How does transmissivity relate to hydraulic conductivity?
A: Transmissivity equals hydraulic conductivity multiplied by aquifer thickness (T = K × b). It represents the total transmission capacity of the entire aquifer.

Q3: When is this formula applicable?
A: This formula applies to steady-state flow in confined aquifers with fully penetrating wells and homogeneous, isotropic conditions.

Q4: What are the limitations of this approach?
A: The method assumes ideal conditions and may not account for aquifer heterogeneity, partial penetration, or boundary effects.

Q5: How should observation wells be positioned?
A: Observation wells should be placed at different radial distances from the pumping well, ideally in the same direction to minimize directional anisotropy effects.