Discharge Due To Spherical Flow In Well Calculator

Formula Used:

\[ Q_s = 2 \pi K r' (H - h_w) \]

Coefficient of Permeability (K):

m/s

Radius of Well (r'):

Thickness of Aquifer (H):

Depth of Water (h_w):

Discharge by Spherical Flow (Q_s):

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1. What is Discharge by Spherical Flow?

Discharge by Spherical Flow refers to the flow rate of water through a well under spherical flow conditions. This occurs when water flows radially towards the well from all directions in three dimensions, typically in confined or unconfined aquifers.

2. How Does the Calculator Work?

The calculator uses the spherical flow equation:

\[ Q_s = 2 \pi K r' (H - h_w) \]

Where:

\( Q_s \) — Discharge by spherical flow (m³/s)
\( K \) — Coefficient of permeability (m/s)
\( r' \) — Radius of well (m)
\( H \) — Thickness of aquifer (m)
\( h_w \) — Depth of water in the well (m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The equation calculates the discharge rate based on the permeability of the soil, well dimensions, and the difference between aquifer thickness and water depth in the well.

3. Importance of Spherical Flow Calculation

Details: Accurate calculation of spherical flow discharge is crucial for well design, groundwater resource management, and predicting the yield of wells in various hydrogeological conditions.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters and meters per second). Ensure that the depth of water is less than the aquifer thickness for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between spherical and radial flow?
A: Spherical flow occurs in three dimensions from all directions, while radial flow typically refers to two-dimensional flow in a horizontal plane.

Q2: When is spherical flow assumption appropriate?
A: Spherical flow is appropriate for partially penetrating wells or when the well screen is much shorter than the aquifer thickness.

Q3: What factors affect the coefficient of permeability?
A: Soil type, grain size distribution, porosity, and degree of saturation all affect the permeability coefficient.

Q4: How does well radius affect discharge?
A: Larger well radius generally results in higher discharge rates due to increased surface area for water entry.

Q5: What are typical values for coefficient of permeability?
A: Values range from 10^-2 m/s for gravel to 10^-9 m/s for clay, with most soils falling between 10^-4 to 10^-6 m/s.