Discharge Entering Cylindrical Surface To Well Discharge Calculator

Formula Used:

\[ Q = (2 \times \pi \times r \times H_a) \times (K \times \frac{dh}{dr}) \]

Radial Distance (r):

Width of Aquifer (H_a):

Coefficient of Permeability (K):

m/s

Change in Piezometric Head (dh):

Change in Radial Distance (dr):

Discharge Entering Cylindrical Surface into Well (Q):

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1. What is the Discharge Entering Cylindrical Surface into Well?

The Discharge Entering Cylindrical Surface into Well represents the flow rate of groundwater entering a cylindrical well or borehole. This calculation is essential for well design, groundwater management, and understanding aquifer characteristics.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ Q = (2 \times \pi \times r \times H_a) \times (K \times \frac{dh}{dr}) \]

Where:

\( Q \) — Discharge entering cylindrical surface into well (m³/s)
\( \pi \) — Mathematical constant pi (≈3.14159)
\( r \) — Radial distance from the pumped well (m)
\( H_a \) — Width of aquifer (m)
\( K \) — Coefficient of permeability (m/s)
\( dh \) — Change in piezometric head (m)
\( dr \) — Change in radial distance (m)

Explanation: The formula calculates groundwater flow into a cylindrical well surface based on Darcy's law and cylindrical geometry considerations.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for well design, determining sustainable pumping rates, assessing aquifer yield, and managing groundwater resources effectively.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for distance, m/s for permeability). Ensure all input values are positive and valid. The change in radial distance (dr) should not be zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of radial distance in this calculation?
A: Radial distance determines the cylindrical surface area through which groundwater flows into the well, directly affecting the discharge calculation.

Q2: How does aquifer width influence the discharge?
A: Aquifer width represents the vertical extent of the water-bearing formation, with wider aquifers typically allowing greater groundwater flow into wells.

Q3: What does the coefficient of permeability represent?
A: The coefficient of permeability quantifies how easily water can flow through the aquifer material, with higher values indicating more permeable formations.

Q4: Why is the change in piezometric head important?
A: The change in piezometric head represents the hydraulic gradient that drives groundwater flow toward the well.

Q5: What are typical units for discharge in groundwater applications?
A: Discharge is typically measured in cubic meters per second (m³/s) or liters per second (L/s) for groundwater applications.