Equation For Varying Dimensionless Group In Theis Equation Calculator

Theis Equation:

\[ u = \frac{r^2 \times S}{4 \times T \times t} \]

Distance From Pumping Well:

Storage Coefficient:

Transmissivity:

m²/s

Time:

hours

Varying Dimensionless Group (u):

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1. What Is The Equation For Varying Dimensionless Group In Theis Equation?

The Theis equation is used in hydrogeology to analyze drawdown in an aquifer due to pumping. The varying dimensionless group (u) is a key parameter that varies with both the position of the observation well and the time since pumping began.

2. How Does The Calculator Work?

The calculator uses the Theis equation:

\[ u = \frac{r^2 \times S}{4 \times T \times t} \]

Where:

\( r \) — Distance from pumping well (m)
\( S \) — Storage coefficient (dimensionless)
\( T \) — Transmissivity (m²/s)
\( t \) — Time since pumping began (hours)

Explanation: This dimensionless parameter helps determine the drawdown in an aquifer at a specific distance and time during pumping.

3. Importance Of Dimensionless Group Calculation

Details: Accurate calculation of the dimensionless group is crucial for predicting aquifer behavior, designing pumping tests, and managing groundwater resources effectively.

4. Using The Calculator

Tips: Enter distance in meters, storage coefficient (dimensionless), transmissivity in m²/s, and time in hours. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of the dimensionless group u?
A: The parameter u represents the ratio of storage to transmissivity effects at a given distance and time, helping characterize aquifer response to pumping.

Q2: What are typical ranges for u values?
A: u values typically range from 10⁻⁶ to 10, with smaller values indicating greater distance from the well or longer pumping times.

Q3: How does u relate to drawdown calculations?
A: The value of u is used to determine the well function W(u), which is then used to calculate the actual drawdown in the aquifer.

Q4: Are there limitations to this equation?
A: The Theis equation assumes ideal conditions: homogeneous isotropic aquifer, fully penetrating well, and constant pumping rate.

Q5: When should this equation not be used?
A: The equation may not be appropriate for leaky aquifers, fractured rock formations, or when boundary effects are significant.