Discharge In Well Given Constant Depression Head And Area Of Well Calculator

Formula Used:

\[ Q = \frac{2.303 \times A_{cs} \times H \times \log\left(\frac{h_1}{h_2}\right)}{t} \]

Cross-Sectional Area (A_cs):

m²

Constant Depression Head (H):

Depression Head 1 (h₁):

Depression Head 2 (h₂):

Time (t):

Discharge (Q):

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1. What is the Discharge Calculation Formula?

The discharge calculation formula estimates the rate of flow of water in a well system based on cross-sectional area, constant depression head, depression head measurements, and time. This formula is particularly useful in hydrogeology and well hydraulics.

2. How Does the Calculator Work?

The calculator uses the discharge formula:

\[ Q = \frac{2.303 \times A_{cs} \times H \times \log\left(\frac{h_1}{h_2}\right)}{t} \]

Where:

\( Q \) — Discharge (m³/s)
\( A_{cs} \) — Cross-sectional area (m²)
\( H \) — Constant depression head (m)
\( h_1 \) — Depression head 1 (m)
\( h_2 \) — Depression head 2 (m)
\( t \) — Time (s)

Explanation: The formula calculates the discharge rate by considering the logarithmic relationship between the depression head ratio and the other hydraulic parameters.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for well design, groundwater resource management, and understanding aquifer characteristics. It helps in determining the sustainable yield of wells and planning water extraction strategies.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for heads, square meters for area, seconds for time). Ensure all values are positive and depression head 2 is not zero to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: What is constant depression head?
A: Constant depression head refers to the steady-state difference between the water table level and the water level in the well during pumping operations.

Q2: Why use logarithmic function in the formula?
A: The logarithmic function accounts for the non-linear relationship between head differences and discharge rates in well hydraulics.

Q3: What are typical units for discharge calculation?
A: Discharge is typically measured in cubic meters per second (m³/s), though other units like liters per second may also be used.

Q4: When is this formula most applicable?
A: This formula is most applicable for calculating discharge in confined aquifers or in situations where constant depression head conditions can be maintained.

Q5: What factors can affect the accuracy of this calculation?
A: Factors include well construction, aquifer characteristics, measurement accuracy of heads, and maintenance of constant pumping conditions.