Coefficient Of Transmissibility Given Discharge Calculator

Coefficient Of Transmissibility Formula:

\[ T = \frac{Q}{\frac{2\pi(b_w - h_{well})}{\ln\left(\frac{R_w}{r}\right)}} \]

Discharge (Q):

m³/s

Aquifer Thickness (b_w):

Depth of Water in Well (h_well):

Radius of Influence (R_w):

Radius of Well (r):

Coefficient of Transmissibility (T):

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1. What is Coefficient of Transmissibility?

The coefficient of transmissibility is defined as the rate of flow of water through a vertical strip of the aquifer under unit hydraulic gradient. It represents the ability of an aquifer to transmit water through its entire saturated thickness.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T = \frac{Q}{\frac{2\pi(b_w - h_{well})}{\ln\left(\frac{R_w}{r}\right)}} \]

Where:

\( T \) — Coefficient of transmissibility (m²/s)
\( Q \) — Discharge rate (m³/s)
\( b_w \) — Aquifer thickness (m)
\( h_{well} \) — Depth of water in well (m)
\( R_w \) — Radius of influence (m)
\( r \) — Radius of well (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: This formula calculates the transmissibility coefficient based on well discharge and aquifer characteristics, using the relationship between drawdown and radial distance from the well.

3. Importance of Coefficient Calculation

Details: Accurate calculation of transmissibility coefficient is crucial for groundwater resource assessment, well design, pumping test analysis, and predicting aquifer response to pumping.

4. Using the Calculator

Tips: Enter all values in consistent units (meters and cubic meters per second). Ensure aquifer thickness is greater than water depth, and radius of influence is greater than well radius for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between transmissibility and permeability?
A: Transmissibility refers to the ability of the entire aquifer to transmit water, while permeability refers to the ability of the aquifer material itself to transmit fluids.

Q2: What are typical values for transmissibility coefficient?
A: Values range from 0.1 m²/day for tight formations to over 1000 m²/day for highly productive aquifers. The unit conversion is 1 m²/s = 86,400 m²/day.

Q3: When is this formula most applicable?
A: This formula is most applicable for confined aquifers with steady-state flow conditions and fully penetrating wells.

Q4: What are the limitations of this approach?
A: The formula assumes homogeneous, isotropic aquifer conditions and may not be accurate for unconfined aquifers or complex geological settings.

Q5: How does well construction affect the results?
A: Well screen length, placement, and development can significantly influence the calculated transmissibility values in field applications.