Time In Hours Given Constant Depression Head And Area Of Well Calculator

Formula Used:

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

Cross-Sectional Area (A_cs):

m²

Constant Depression Head (H):

Depression Head 1 (h₁):

Depression Head 2 (h₂):

Discharge (Q):

m³/s

Time (t):

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1. What is the Time Calculation Formula?

The time calculation formula estimates the time required for water level changes in a well based on cross-sectional area, constant depression head, depression head measurements, and discharge rate. This is particularly useful in hydrogeology and well testing applications.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the time required for the water level to change from depression head h₁ to h₂ based on the well's characteristics and discharge rate.

3. Importance of Time Calculation

Details: Accurate time calculation is crucial for well testing, aquifer characterization, and determining the efficiency of water extraction systems. It helps in planning pumping schedules and understanding aquifer response to pumping.

4. Using the Calculator

Tips: Enter all values in the specified units. Cross-sectional area and depression heads must be positive values. Discharge rate must be greater than zero for valid calculations.

5. Frequently Asked Questions (FAQ)

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

Q2: Why use logarithmic function in the formula?
A: The logarithmic function accounts for the non-linear relationship between head differences and time in unsteady flow conditions.

Q3: What are typical values for cross-sectional area?
A: Cross-sectional area values depend on well diameter. For a typical 6-inch well, the area is approximately 0.018 m², while larger wells can have areas up to 1 m² or more.

Q4: How accurate is this calculation?
A: The calculation provides a theoretical estimate. Actual field conditions may vary due to aquifer heterogeneity, well efficiency, and other factors.

Q5: Can this formula be used for all well types?
A: This formula is most applicable to confined aquifers with certain assumptions. For unconfined aquifers or complex geological conditions, modified approaches may be needed.