Time In Hours Given Time At 1st And 2nd Instance Since Pumping Started Calculator

Formula Used:

\[ Time\ in\ Hours = \frac{2.303 \times Discharge \times \log\left(\frac{Time\ of\ Drawdown\ (t2)\ in\ Wells}{Time\ of\ Drawdown\ (t1)\ in\ Wells}\right)}{4 \times \pi \times Difference\ in\ Drawdowns} \]

Discharge (Q):

m³/s

Time of Drawdown (t2) in Wells:

Time of Drawdown (t1) in Wells:

Difference in Drawdowns (Δs):

Time in Hours:

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1. What is the Time in Hours Calculation?

The Time in Hours calculation determines the time required for drawdown changes in pumping wells based on discharge rates and drawdown differences. This is essential for groundwater hydrology and well field management.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Time\ in\ Hours = \frac{2.303 \times Q \times \log\left(\frac{t2}{t1}\right)}{4 \times \pi \times \Delta s} \]

Where:

\( Q \) — Discharge rate (m³/s)
\( t2 \) — Time of drawdown at second instance (s)
\( t1 \) — Time of drawdown at first instance (s)
\( \Delta s \) — Difference in drawdowns between wells (m)
\( \pi \) — Mathematical constant pi (approximately 3.1416)
\( \log \) — Base-10 logarithm function

Explanation: The formula calculates the time in hours based on the logarithmic relationship between drawdown times and the difference in drawdown levels.

3. Importance of Time Calculation in Pumping Wells

Details: Accurate time calculation is crucial for determining optimal pumping schedules, assessing aquifer characteristics, and managing groundwater resources effectively.

4. Using the Calculator

Tips: Enter discharge in m³/s, drawdown times in seconds, and difference in drawdowns in meters. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why use logarithmic function in this calculation?
A: The logarithmic function accounts for the non-linear relationship between drawdown times and the resulting time calculation in pumping well analysis.

Q2: What are typical values for discharge in pumping wells?
A: Discharge rates vary widely but typically range from 0.01 to 10 m³/s depending on well characteristics and aquifer properties.

Q3: How accurate is this calculation method?
A: The method provides good accuracy for most practical applications in groundwater hydrology when proper input values are used.

Q4: Can this formula be used for multiple wells?
A: This specific formula is designed for calculations between two instances in time for individual wells or well pairs.

Q5: What units should be used for time values?
A: Time values should be entered in seconds, but the calculator converts the final result to hours for practical interpretation.