Drawdown At Time Interval 't2' Calculator

Formula Used:

\[ s2 = \left( \frac{Q}{4\pi T} \ln\left(\frac{t2}{t1}\right) \right) + s1 \]

Discharge (Q):

m³/s

Transmissivity (T):

m²/s

Time of Drawdown (t1):

Time of Drawdown (t2):

Drawdown at Time Interval t1 (s1):

Drawdown at Time Interval t2 (s2):

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1. What is the Drawdown at Time Interval 't2' Formula?

The formula calculates the drawdown at a specific time interval t2 based on discharge, transmissivity, time intervals, and initial drawdown. It's derived from the Theis equation and is used in hydrogeology to analyze aquifer response to pumping.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ s2 = \left( \frac{Q}{4\pi T} \ln\left(\frac{t2}{t1}\right) \right) + s1 \]

Where:

\( s2 \) — Drawdown at time interval t2 (m)
\( Q \) — Discharge rate (m³/s)
\( T \) — Transmissivity (m²/s)
\( t1 \) — Initial time of drawdown (s)
\( t2 \) — Final time of drawdown (s)
\( s1 \) — Initial drawdown at time interval t1 (m)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: The formula calculates the additional drawdown between two time intervals and adds it to the initial drawdown to get the total drawdown at time t2.

3. Importance of Drawdown Calculation

Details: Accurate drawdown calculation is crucial for well design, aquifer testing, determining sustainable pumping rates, and assessing the impact of groundwater extraction on aquifer systems.

4. Using the Calculator

Tips: Enter all values in the specified units. Discharge and transmissivity must be positive values. Time values must be positive and t2 should be greater than t1 for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of this formula?
A: This formula helps predict how much the water level will drop in a well over time due to pumping, which is essential for sustainable groundwater management.

Q2: When is this formula applicable?
A: The formula applies to confined aquifers with homogeneous and isotropic properties, and for times when the cone of depression is still developing.

Q3: What are typical transmissivity values?
A: Transmissivity values range from 0.1 m²/day for tight formations to over 1000 m²/day for highly productive aquifers. Convert to m²/s by dividing by 86400.

Q4: How does drawdown affect well performance?
A: Excessive drawdown can lead to well failure, reduced pumping efficiency, and potential contamination from surrounding aquifers.

Q5: What are the limitations of this approach?
A: This approach assumes ideal aquifer conditions and may not account for boundary effects, aquifer heterogeneity, or partial penetration of wells.