Discharge By Spherical Flow With Base 10 Calculator

Discharge By Spherical Flow With Base 10 Formula:

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

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 is the discharge for spherical flow in well, calculated using specific parameters including discharge rate, well radius, aquifer thickness, and radius of influence.

2. How Does the Calculator Work?

The calculator uses the Spherical Flow equation:

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

Where:

\( Qs \) — Discharge by Spherical Flow (m³/s)
\( Q \) — Discharge rate (m³/s)
\( r' \) — Radius of Well (m)
\( bp \) — Aquifer Thickness During Pumping (m)
\( R \) — Radius of Influence (m)
\( \log \) — Logarithmic function with base 10

Explanation: The equation calculates spherical flow discharge by considering the geometric relationships and logarithmic scaling of well and aquifer parameters.

3. Importance of Spherical Flow Calculation

Details: Accurate calculation of spherical flow discharge is crucial for well design, groundwater management, and understanding aquifer behavior during pumping operations.

4. Using the Calculator

Tips: Enter discharge in m³/s, well radius in meters, aquifer thickness in meters, and radius of influence in meters. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 2.3 factor in the equation?
A: The 2.3 factor is a conversion constant that accounts for the relationship between natural logarithms and base-10 logarithms used in the formula.

Q2: How does well radius affect spherical flow discharge?
A: Larger well radii generally result in higher discharge rates, as they provide greater surface area for water flow into the well.

Q3: What is radius of influence and how is it determined?
A: 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 modeling.

Q4: When is spherical flow assumption appropriate?
A: Spherical flow assumptions are typically used for partially penetrating wells or in situations where three-dimensional flow patterns dominate.

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