Depth Of Water In Well Given Coefficient Of Transmissibility With Base 10 Calculator

Formula Used:

\[ h_{well} = b_w - \frac{Q \cdot \log_{10}\left(\frac{R_w}{r}\right)}{2.72 \cdot T_{envi}} \]

Aquifer Thickness (b_w):

Discharge (Q):

m³/s

Radius of Influence (R_w):

Radius of Well (r):

Coefficient of Transmissibility (T_envi):

m²/s

Depth of Water in Well (h_well):

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1. What is Depth of Water in Well?

Depth of Water in Well is measured above the impermeable layer and represents the water level in a well under specific pumping conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_{well} = b_w - \frac{Q \cdot \log_{10}\left(\frac{R_w}{r}\right)}{2.72 \cdot T_{envi}} \]

Where:

\( h_{well} \) — Depth of Water in Well (m)
\( b_w \) — Aquifer Thickness (m)
\( Q \) — Discharge rate (m³/s)
\( R_w \) — Radius of Influence (m)
\( r \) — Radius of Well (m)
\( T_{envi} \) — Coefficient of Transmissibility (m²/s)

Explanation: This formula calculates the depth of water remaining in a well after accounting for drawdown effects caused by pumping, using logarithmic relationships between well geometry and aquifer properties.

3. Importance of Depth Calculation

Details: Accurate calculation of water depth in wells is crucial for groundwater resource management, well design, pumping system optimization, and sustainable water extraction practices.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m³/s for discharge, m²/s for transmissibility). Ensure all values are positive and physically meaningful (Radius of Influence should be greater than Radius of Well).

5. Frequently Asked Questions (FAQ)

Q1: What is the Coefficient of Transmissibility?
A: Coefficient of transmissibility is defined as the rate of flow of water through a vertical strip of the aquifer under unit hydraulic gradient.

Q2: Why use base-10 logarithm in this formula?
A: The base-10 logarithm is used because it provides a convenient scaling for the radial flow equations in groundwater hydrology.

Q3: What is the significance of the constant 2.72?
A: The constant 2.72 is derived from the conversion factors and empirical relationships in the derivation of the well flow equations.

Q4: How is Radius of Influence determined?
A: Radius of Influence is typically measured from the center of the well to the point where the drawdown curve meets the original water table, often determined through field testing.

Q5: What are typical values for these parameters?
A: Parameter values vary widely depending on aquifer characteristics, but typical ranges are: Aquifer Thickness (5-100 m), Discharge (0.001-0.1 m³/s), Radius of Influence (100-1000 m), Well Radius (0.1-0.5 m), Transmissibility (0.001-0.1 m²/s).