Discharge by Spherical Flow Calculator

Discharge by Spherical Flow Formula:

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

Discharge (Q):

m³/s

Radius of Well (r'):

Aquifer Thickness (bₚ):

Radius of Influence (R):

Discharge by Spherical Flow (Qₛ):

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1. What is Discharge by Spherical Flow?

Discharge by Spherical Flow represents the discharge for spherical flow in a well system. It's an important parameter in environmental engineering for analyzing groundwater flow patterns and well performance.

2. How Does the Calculator Work?

The calculator uses the spherical flow equation:

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

Where:

\( Q_s \) — Discharge by spherical flow (m³/s)
\( Q \) — Total discharge rate (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: This equation calculates the spherical flow component of discharge by considering well geometry, aquifer characteristics, and the natural logarithmic relationship between radius of influence and well radius.

3. Importance of Spherical Flow Calculation

Details: Accurate calculation of spherical flow discharge is crucial for well design, groundwater resource management, and environmental impact assessments. It helps engineers optimize well performance and predict drawdown patterns.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for lengths, m³/s for discharge rates). Ensure all input 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 is two-dimensional. Spherical flow is more relevant for partially penetrating wells or point sources.

Q2: When is the spherical flow assumption appropriate?
A: Spherical flow models are appropriate for wells that partially penetrate aquifers or when flow converges three-dimensionally toward a well screen.

Q3: What is the radius of influence?
A: The radius of influence is the distance from the well center to the point where the drawdown curve meets the original water table or becomes negligible.

Q4: How does aquifer thickness affect spherical flow?
A: Aquifer thickness directly influences the flow geometry. Thicker aquifers may exhibit more pronounced spherical flow characteristics, especially for partially penetrating wells.

Q5: Are there limitations to this equation?
A: This equation assumes homogeneous aquifer properties, steady-state conditions, and ideal spherical flow geometry. Real-world conditions may require more complex modeling approaches.