Discharge By Radial Flow Given Discharge By Spherical Flow With Base 10 Calculator

Formula Used:

\[ Q = \frac{Q_s}{2.3 \times \left(\frac{r'}{b_w}\right) \times \log\left(\frac{R}{r'}, 10\right)} \]

Discharge by Spherical Flow (Qs):

m³/s

Radius of Well (r'):

Aquifer Thickness (bw):

Radius of Influence (R):

Discharge (Q):

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1. What is the Discharge by Radial Flow Formula?

The Discharge by Radial Flow formula calculates the discharge rate for radial flow in wells based on spherical flow discharge, well radius, aquifer thickness, and radius of influence. This equation is essential in environmental engineering for groundwater flow analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q = \frac{Q_s}{2.3 \times \left(\frac{r'}{b_w}\right) \times \log\left(\frac{R}{r'}, 10\right)} \]

Where:

\( Q \) — Discharge (m³/s)
\( Q_s \) — Discharge by Spherical Flow (m³/s)
\( r' \) — Radius of Well (m)
\( b_w \) — Aquifer Thickness (m)
\( R \) — Radius of Influence (m)
\( \log \) — Logarithm base 10 function

Explanation: The formula accounts for the geometric relationships between well dimensions and flow characteristics in aquifer systems.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for well design, groundwater resource management, and environmental impact assessments of water extraction projects.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m³/s for discharge rates). Ensure all values are positive and physically meaningful for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between spherical flow and radial flow?
A: Spherical flow occurs in three dimensions around a point source, while radial flow occurs in two dimensions around a line source (like a well).

Q2: Why use base 10 logarithm in this formula?
A: The base 10 logarithm is commonly used in hydrological equations and provides convenient scaling for the range of values typically encountered in groundwater studies.

Q3: What factors affect the radius of influence?
A: The radius of influence depends on aquifer properties, pumping rate, duration of pumping, and boundary conditions of the aquifer system.

Q4: When is this formula most applicable?
A: This formula is particularly useful for analyzing flow to partially penetrating wells in confined aquifers with specific boundary conditions.

Q5: Are there limitations to this equation?
A: The equation assumes ideal conditions and may need adjustment for complex aquifer geometries, heterogeneous materials, or transient flow conditions.