Question Bank • QB_EXP_IDE_UNS_003 MSQ • 2 Marks

Section 5: Irrigation and Drainage Engineering

Unsteady Flow to Wells: Theis & Cooper-Jacob Solutions

Subtopic: Theis non-equilibrium equation characteristics

Question Statement:

Which of the following statements regarding the Theis non-equilibrium formula $s = \frac{Q}{4 \pi T} W(u)$ is/are TRUE?

Options:

  • (A) It models transient, unsteady drawdown in an elastic confined aquifer
  • (B) The well function $W(u)$ is evaluated mathematically as the exponential integral $\int_u^\infty \frac{e^{-\eta}}{\eta} d\eta$
  • (C) Water is assumed to be released instantaneously from storage with decline in head
  • (D) The cone of depression stops expanding after 10 minutes of pumping

Answer Key:

A, B, C

Step-by-Step Solution & Explanation

1. Theis solved the 2D heat-conduction analogy for transient confined aquifer drawdown (A is true). 2. $W(u) = \int_u^\infty \frac{e^{-\eta}}{\eta} d\eta$ is the standard exponential integral (B is true). 3. Elastic storage decompression is assumed instantaneous (C is true). 4. In an infinite aquifer without recharge boundaries, the cone of depression expands indefinitely with time (D is false).
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