Drawdown Calculator

Theis Equation:

\[ s_t = \frac{Q}{4\pi T} \ln\left(\frac{2.2Tt}{r^2S}\right) \]

Discharge (Q):

m³/s

Transmissivity (T):

m²/s

Time Period (t):

Distance from Pumping Well (r):

Storage Coefficient (S):

Total Drawdown (sₜ):

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1. What is the Theis Equation?

The Theis equation is used to calculate drawdown in a confined aquifer due to pumping from a well. It provides a mathematical model for predicting how water levels in an aquifer will respond to pumping over time.

2. How Does the Calculator Work?

The calculator uses the Theis equation:

\[ s_t = \frac{Q}{4\pi T} \ln\left(\frac{2.2Tt}{r^2S}\right) \]

Where:

\( s_t \) — Total drawdown (m)
\( Q \) — Discharge rate (m³/s)
\( T \) — Transmissivity (m²/s)
\( t \) — Time period (s)
\( r \) — Distance from pumping well (m)
\( S \) — Storage coefficient
\( \pi \) — Mathematical constant pi (≈3.1416)
\( \ln \) — Natural logarithm function

Explanation: The equation calculates the drawdown in an aquifer at a specific distance from a pumping well after a given time period of pumping.

3. Importance of Drawdown Calculation

Details: Accurate drawdown calculation is crucial for groundwater resource management, well design, aquifer testing, and predicting the impact of pumping on surrounding water levels.

4. Using the Calculator

Tips: Enter all values in the specified units. Discharge in m³/s, transmissivity in m²/s, time in seconds, distance in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What types of aquifers is the Theis equation applicable to?
A: The Theis equation is specifically designed for confined aquifers that are homogeneous, isotropic, and infinite in extent.

Q2: What are typical values for transmissivity and storage coefficient?
A: Transmissivity typically ranges from 10⁻⁵ to 10⁻¹ m²/s, while storage coefficient for confined aquifers ranges from 10⁻⁵ to 10⁻³.

Q3: What are the limitations of the Theis equation?
A: The equation assumes ideal conditions: homogeneous aquifer, constant pumping rate, fully penetrating well, and negligible well storage effects.

Q4: How does distance from the pumping well affect drawdown?
A: Drawdown decreases with increasing distance from the pumping well due to the spreading of the cone of depression.

Q5: What is the significance of the constant 2.2 in the equation?
A: The constant 2.2 comes from the approximation of the well function for the Theis solution and represents Euler's constant raised to a power.