Subtopic: Steady and unsteady flow in confined and unconfined aquifers
Question Statement:
In a pumping test conducted on a confined aquifer at a constant discharge of $Q = 2400.0\text{ m}^3/\text{day}$, drawdown is measured in an observation well. Using the Cooper-Jacob semilogarithmic time-drawdown analysis, the drawdown increases by $\Delta s = 1.80\text{ m}$ per logarithmic cycle of time ($t_2 / t_1 = 10$). Taking $\pi = 3.1416$, the transmissivity ($T$) of the aquifer in square meters per day ($\text{m}^2/\text{day}$) is ________ (round off to one decimal place).
Answer Key:
244.4
Step-by-Step Solution & Explanation
1. Cooper-Jacob slope equation for one log cycle of time:
$\Delta s = \frac{2.303 Q}{4 \pi T} \implies T = \frac{2.303 Q}{4 \pi \Delta s}$
2. Substituting given values:
- $Q = 2400.0\text{ m}^3/\text{day}$
- $\Delta s = 1.80\text{ m}$
- $\pi = 3.1416$
$T = \frac{2.303 \times 2400.0\text{ m}^3/\text{day}}{4 \times 3.1416 \times 1.80\text{ m}} = \frac{5527.20}{22.6195} = 244.355\text{ m}^2/\text{day} \approx 244.4\text{ m}^2/\text{day}$