Drawdown at Well given Coefficient of Transmissibility with Base 10 Calculator

Formula Used:

\[ Stw = \frac{Q}{\frac{2.72 \times Tenvi}{\log_{10}\left(\frac{Rw}{r}\right)}} \]

Discharge (Q):

m³/s

Coefficient of Transmissibility (Tenvi):

m²/s

Radius of Influence (Rw):

Radius of Well (r):

Total Drawdown in Well (Stw):

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1. What is Drawdown at Well?

Total Drawdown in Well in Well Hydraulics is defined as the reduction in hydraulic head observed at a well in an aquifer, typically due to pumping a well as part of an aquifer test or well test.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Stw = \frac{Q}{\frac{2.72 \times Tenvi}{\log_{10}\left(\frac{Rw}{r}\right)}} \]

Where:

\( Stw \) — Total Drawdown in Well (m)
\( Q \) — Discharge (m³/s)
\( Tenvi \) — Coefficient of Transmissibility (m²/s)
\( Rw \) — Radius of Influence (m)
\( r \) — Radius of Well (m)

Explanation: This formula calculates the drawdown at a well based on discharge rate, transmissibility coefficient, and the geometric relationship between the radius of influence and well radius.

3. Importance of Drawdown Calculation

Details: Accurate drawdown calculation is crucial for well design, aquifer characterization, and determining sustainable pumping rates to prevent over-exploitation of groundwater resources.

4. Using the Calculator

Tips: Enter discharge in m³/s, coefficient of transmissibility in m²/s, and both radii in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 2.72 constant?
A: The constant 2.72 is approximately equal to the mathematical constant e (Euler's number), which appears in the derivation of the well hydraulics equations.

Q2: How is coefficient of transmissibility different from hydraulic conductivity?
A: Coefficient of transmissibility equals hydraulic conductivity multiplied by aquifer thickness, representing the total transmissive capacity of the aquifer.

Q3: What factors affect the radius of influence?
A: Radius of influence depends on pumping rate, aquifer properties, duration of pumping, and boundary conditions.

Q4: When is this formula most applicable?
A: This formula is most applicable for confined aquifers with steady-state flow conditions and fully penetrating wells.

Q5: What are typical units for these parameters?
A: Discharge is typically in m³/s or L/s, transmissibility in m²/s, and distances in meters, though other consistent unit systems can be used.