Depth of Water in Well given Discharge for Fully Penetrating Well Calculator

Formula Used:

\[ h_w = \sqrt{(2 \times b_p \times H_i) - \left(\frac{Q \times \ln\left(\frac{R}{r'}\right)}{\pi \times k}\right) + (b_p)^2} \]

Aquifer Thickness During Pumping (b_p):

Initial Aquifer Thickness (H_i):

Discharge (Q):

m³/s

Radius of Influence (R):

Radius of Well (r'):

Coefficient of Permeability (k):

cm/s

Depth of Water (h_w):

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

The formula calculates the depth of water in a well above the impermeable layer for a fully penetrating well. It considers aquifer properties, pumping conditions, and well characteristics to determine the water depth during pumping operations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_w = \sqrt{(2 \times b_p \times H_i) - \left(\frac{Q \times \ln\left(\frac{R}{r'}\right)}{\pi \times k}\right) + (b_p)^2} \]

Where:

\( h_w \) — Depth of water in the well (m)
\( b_p \) — Aquifer thickness during pumping (m)
\( H_i \) — Initial aquifer thickness (m)
\( Q \) — Discharge rate (m³/s)
\( R \) — Radius of influence (m)
\( r' \) — Radius of well (m)
\( k \) — Coefficient of permeability (converted to m/s)
\( \pi \) — Archimedes' constant (3.14159)
\( \ln \) — Natural logarithm function

Explanation: The formula accounts for the relationship between pumping discharge, aquifer properties, and well geometry to determine the water depth in the well during pumping operations.

3. Importance of Depth of Water Calculation

Details: Accurate calculation of water depth in wells is crucial for designing efficient pumping systems, assessing aquifer performance, and managing groundwater resources effectively.

4. Using the Calculator

Tips: Enter all values in the specified units. Aquifer thickness, discharge, radii, and permeability must be positive values. The coefficient of permeability is automatically converted from cm/s to m/s for calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a fully penetrating well?
A: A fully penetrating well is one that extends through the entire thickness of the aquifer, allowing water to enter from all sections of the aquifer.

Q2: How is the radius of influence determined?
A: The radius of influence is the distance from the well center to where the drawdown curve meets the original water table, typically determined through field testing or empirical relationships.

Q3: Why convert permeability from cm/s to m/s?
A: The formula requires consistent units, and converting to m/s ensures all length measurements are in meters for accurate calculation.

Q4: What are typical values for coefficient of permeability?
A: Permeability values range from 10⁻⁷ cm/s for clay to 10² cm/s for gravel, with most aquifers falling between 10⁻³ to 10 cm/s.

Q5: When is this formula most applicable?
A: This formula is most accurate for confined aquifers with fully penetrating wells under steady-state pumping conditions.