Unsteady Flow to Wells: Theis & Cooper-Jacob Solutions
Subtopic: Transmissivity from Cooper-Jacob drawdown per log cycle
Question Statement:
A pumping test is conducted at a constant discharge of $Q = 1200\text{ m}^3/\text{day}$. A semi-logarithmic plot of drawdown versus time at an observation well yields a straight line with a drawdown slope of $\Delta s = 1.50\text{ m}$ per log cycle of time. Using the Cooper-Jacob method, the transmissivity ($T$) of the aquifer is ________ $\text{m}^2/\text{day}$ (round off to one decimal place).
Answer Key:
146.6
Step-by-Step Solution & Explanation
From the Cooper-Jacob approximation, drawdown per log cycle is:
$\Delta s = \frac{2.303 Q}{4 \pi T} \implies T = \frac{2.303 Q}{4 \pi \Delta s}$
Given $Q = 1200\text{ m}^3/\text{day}$ and $\Delta s = 1.50\text{ m}$:
$T = \frac{2.303 \times 1200}{4 \pi \times 1.50} = \frac{2763.6}{18.8496} = 146.6\text{ m}^2/\text{day}$