Radial Distance of Well 1 given Confined Aquifer Discharge Calculator

Formula Used:

\[ R1 = r2/10^{((2.72 \times KWH \times bp \times (h2-h1))/Q0)} \]

Radial Distance at Observation Well 2:

Coefficient of Permeability:

m/s

Aquifer Thickness During Pumping:

Depth of Water 2:

Depth of Water 1:

Discharge at Time t=0:

m³/s

Radial Distance 1 (R1):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Radial Distance of Well 1?

Radial Distance of Well 1 is the distance from the pumping well to the first observation well in a confined aquifer system. It is a critical parameter in well hydraulics for determining the extent of the cone of depression and analyzing aquifer properties.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R1 = r2/10^{((2.72 \times KWH \times bp \times (h2-h1))/Q0)} \]

Where:

\( R1 \) — Radial Distance 1 (m)
\( r2 \) — Radial Distance at Observation Well 2 (m)
\( KWH \) — Coefficient of Permeability in Well Hydraulics (m/s)
\( bp \) — Aquifer Thickness During Pumping (m)
\( h2 \) — Depth of Water 2 (m)
\( h1 \) — Depth of Water 1 (m)
\( Q0 \) — Discharge at Time t=0 (m³/s)

Explanation: This formula calculates the radial distance to the first observation well based on the drawdown characteristics and aquifer properties observed at the second well.

3. Importance of Radial Distance Calculation

Details: Accurate calculation of radial distances is crucial for designing well fields, determining safe pumping rates, and assessing the impact of pumping on surrounding wells and the aquifer system.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for distances, m/s for permeability, m³/s for discharge). Ensure all values are positive and measurements are accurate for reliable results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the coefficient 2.72 in the formula?
A: The coefficient 2.72 is derived from the natural logarithm base (e) and is used in the conversion between natural logarithms and base-10 logarithms commonly used in well hydraulics equations.

Q2: How does aquifer thickness affect the radial distance calculation?
A: Aquifer thickness directly influences the transmissivity of the aquifer. Thicker aquifers generally result in smaller drawdowns at given distances, affecting the calculated radial distances.

Q3: What are typical values for coefficient of permeability?
A: Permeability values vary widely by aquifer material: gravel (10⁻¹-10⁻² m/s), sand (10⁻³-10⁻⁵ m/s), silt (10⁻⁶-10⁻⁸ m/s), clay (10⁻⁹-10⁻¹² m/s).

Q4: When is this formula most applicable?
A: This formula is specifically designed for confined aquifers with steady-state conditions and fully penetrating wells where the Dupuit-Forchheimer assumptions apply.

Q5: What are the limitations of this approach?
A: The formula assumes homogeneous, isotropic aquifer conditions, constant pumping rates, and negligible well losses. It may not be accurate for unconfined aquifers or complex hydrogeological settings.