Depth Of Water In Well Given Coefficient Of Transmissibility Calculator

Formula Used:

\[ h_w = H_i - \frac{Q \cdot \ln\left(\frac{R_w}{r}\right)}{2 \pi T} \]

Initial Aquifer Thickness (H_i):

Discharge (Q):

m³/s

Radius of Influence (R_w):

Radius of Well (r):

Coefficient of Transmissibility (T):

m²/s

Depth of Water (h_w):

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1. What is the Depth of Water Calculation?

The depth of water in a well given the coefficient of transmissibility calculates the water depth above the impermeable layer using aquifer properties and pumping conditions. This is essential for groundwater resource management and well design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_w = H_i - \frac{Q \cdot \ln\left(\frac{R_w}{r}\right)}{2 \pi T} \]

Where:

\( h_w \) — Depth of water in the well (m)
\( H_i \) — Initial aquifer thickness (m)
\( Q \) — Discharge rate (m³/s)
\( R_w \) — Radius of influence (m)
\( r \) — Radius of well (m)
\( T \) — Coefficient of transmissibility (m²/s)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: The formula calculates the drawdown in a well based on pumping rate, aquifer properties, and geometric factors.

3. Importance of Depth of Water Calculation

Details: Accurate calculation of water depth is crucial for determining well yield, designing pumping systems, assessing groundwater availability, and managing aquifer resources sustainably.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure radii are measured from the same reference point, and all values are positive. The radius of influence should be greater than the well radius for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is the coefficient of transmissibility?
A: The coefficient of transmissibility represents the rate of water flow through a vertical strip of aquifer under unit hydraulic gradient.

Q2: How is radius of influence determined?
A: Radius of influence is typically determined through pumping tests or estimated based on aquifer properties and pumping duration.

Q3: What are typical values for coefficient of transmissibility?
A: Values vary widely by aquifer type, ranging from 10⁻⁵ to 10² m²/s for different geological formations.

Q4: When is this calculation most accurate?
A: This calculation is most accurate for confined aquifers with homogeneous properties and steady-state pumping conditions.

Q5: What limitations does this formula have?
A: The formula assumes ideal conditions and may not account for aquifer heterogeneity, partial penetration, or time-dependent effects.