Depth of Water in 1st Well given Coefficient of Transmissibility Calculator

Formula Used:

\[ h1 = h2 - \frac{Q \cdot \log_{10}(r2/r1)}{2.72 \cdot T} \]

Depth of Water 2 (h2):

Discharge (Q):

m³/s

Radial Distance at Observation Well 2 (r2):

Radial Distance at Observation Well 1 (r1):

Coefficient of Transmissibility (T):

m²/s

Depth of Water 1 (h1):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Depth of Water in 1st Well Formula?

The formula calculates the depth of water in the first observation well based on the coefficient of transmissibility, discharge rate, and radial distances from the pumping well. It's derived from the Theis equation for confined aquifers.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h1 = h2 - \frac{Q \cdot \log_{10}(r2/r1)}{2.72 \cdot T} \]

Where:

\( h1 \) — Depth of water in 1st well (m)
\( h2 \) — Depth of water in 2nd well (m)
\( Q \) — Discharge rate (m³/s)
\( r2 \) — Radial distance at observation well 2 (m)
\( r1 \) — Radial distance at observation well 1 (m)
\( T \) — Coefficient of transmissibility (m²/s)

Explanation: The formula calculates the difference in water levels between two observation wells based on the logarithmic relationship between radial distance and drawdown.

3. Importance of the Calculation

Details: This calculation is essential for groundwater hydrology studies, well field design, and determining aquifer characteristics. It helps in understanding how water levels respond to pumping at different distances.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for distances, m³/s for discharge, m²/s for transmissibility). Ensure all values are positive and r2 > r1 for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What is the coefficient of transmissibility?
A: The coefficient of transmissibility represents the rate at which water is transmitted through a unit width of aquifer under a unit hydraulic gradient.

Q2: Why use logarithmic scale for distances?
A: The logarithmic relationship accounts for the decreasing rate of drawdown with increasing distance from the pumping well.

Q3: What are typical values for coefficient of transmissibility?
A: Values range from 10⁻⁵ to 10⁻¹ m²/s depending on aquifer material, with higher values indicating more permeable aquifers.

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

Q5: What are the limitations of this approach?
A: The formula assumes homogeneous, isotropic aquifers and doesn't account for boundary conditions or time-dependent effects.