Transmissivity When Discharge At Drawdown Is Considered Calculator

Formula Used:

\[ T = \frac{Q_u \cdot \ln\left(\frac{r}{R_w}\right)}{2 \pi s_w} \]

Steady Flow of an Unconfined Aquifer (Q_u):

m³/s

Radius at the Edge of Zone of Influence (r):

Radius of the Pumping Well (R_w):

Drawdown at the Pumping Well (s_w):

Transmissivity of an Unconfined Aquifer (T):

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1. What is Transmissivity When Discharge At Drawdown Is Considered?

Transmissivity of an unconfined aquifer refers to the ability of the aquifer to transmit groundwater throughout its entire saturated thickness. This calculation considers the discharge rate and drawdown at the pumping well to determine the aquifer's transmissive properties.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T = \frac{Q_u \cdot \ln\left(\frac{r}{R_w}\right)}{2 \pi s_w} \]

Where:

\( T \) — Transmissivity of an Unconfined Aquifer (m²/s)
\( Q_u \) — Steady Flow of an Unconfined Aquifer (m³/s)
\( r \) — Radius at the Edge of Zone of Influence (m)
\( R_w \) — Radius of the Pumping Well (m)
\( s_w \) — Drawdown at the Pumping Well (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: This formula calculates the transmissivity based on the steady flow conditions, well geometry, and observed drawdown in an unconfined aquifer system.

3. Importance of Transmissivity Calculation

Details: Accurate transmissivity estimation is crucial for groundwater resource management, well field design, contaminant transport modeling, and sustainable aquifer development.

4. Using the Calculator

Tips: Enter all values in consistent units (meters and cubic meters per second). Ensure all input values are positive and the radius at zone of influence is greater than the pumping well radius.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between confined and unconfined aquifer transmissivity?
A: In confined aquifers, transmissivity remains constant with drawdown, while in unconfined aquifers, it decreases as the water table drops and saturated thickness reduces.

Q2: What are typical transmissivity values for aquifers?
A: Transmissivity values range from less than 1 m²/day for tight formations to over 1000 m²/day for highly productive aquifers.

Q3: When is this formula most applicable?
A: This formula is most applicable for steady-state conditions in homogeneous, isotropic unconfined aquifers with fully penetrating wells.

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

Q5: How does drawdown affect transmissivity calculations?
A: In unconfined aquifers, significant drawdown can reduce the saturated thickness, thereby affecting the actual transmissivity value.