Discharge By Radial Flow Given Discharge By Spherical Flow Calculator

Formula Used:

\[ Q = \frac{Q_s}{\left(\frac{r'}{b_p}\right) \cdot \log\left(\frac{R}{r'}, e\right)} \]

Discharge by Spherical Flow (Qs):

m³/s

Radius of Well (r'):

Aquifer Thickness During Pumping (bp):

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, taking into account spherical flow discharge, well radius, aquifer thickness, and radius of influence. This formula is essential in environmental engineering for groundwater flow analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q = \frac{Q_s}{\left(\frac{r'}{b_p}\right) \cdot \log\left(\frac{R}{r'}, e\right)} \]

Where:

\( Q \) — Discharge (m³/s)
\( Q_s \) — Discharge by Spherical Flow (m³/s)
\( r' \) — Radius of Well (m)
\( b_p \) — Aquifer Thickness During Pumping (m)
\( R \) — Radius of Influence (m)
\( e \) — Napier's constant (approximately 2.71828)
\( \log \) — Natural logarithm function

Explanation: The formula accounts for the relationship between spherical and radial flow discharge rates in well hydraulics, incorporating geometric and logarithmic factors.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for well design, groundwater resource management, and environmental impact assessments. It helps determine sustainable pumping rates and predict drawdown effects.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m³/s for discharge rates). All input values must be positive numbers. Ensure radius of influence is greater than well radius for valid logarithmic calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between spherical 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 natural logarithm in this formula?
A: The natural logarithm accurately models the logarithmic pressure distribution that occurs in radial flow systems in porous media.

Q3: What is radius of influence?
A: Radius of influence is the distance from the well center to the point where drawdown becomes negligible and the water table remains unaffected.

Q4: When is this formula most applicable?
A: This formula is particularly useful for partially penetrating wells or in confined aquifers where both radial and spherical flow components are significant.

Q5: What are typical values for these parameters?
A: Well radii typically range from 0.1-0.5m, aquifer thickness from 5-50m, radius of influence from 10-1000m, and discharge rates from 0.001-1.0 m³/s depending on aquifer properties.