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Hydrogeology: Transmissivity Evaluation via Cooper-Jacob Time-Drawdown Analysis

 The Cooper-Jacob Method simplifies the non-steady Theis equation for drawdown (s) near a pumping well in a confined aquifer. When parameter $u = \frac{r^2 \cdot S}{4 \cdot T \cdot t} \le 0.01$ (i.e., small radial distance r or extended pumping time t), the infinite well series converts to a logarithmic approximation: $s = \frac{2.303 \cdot Q}{4 \pi \cdot T} \cdot \log_{10}\left( \frac{2.25 \cdot T \cdot t}{r^2 \cdot S} \right)$ ​Where $Q$ is pumping rate, $T$ is transmissivity, and $S$ is storativity. On a semi-log plot of drawdown (s) versus time (t), data points form a straight line. Transmissivity (T) and storativity (S) are calculated using the drawdown per log cycle $(\Delta s)$ and zero-drawdown time intercept $(t_0):$ $T = \frac{2.303 \cdot Q}{4 \pi \cdot \Delta s} \quad \text{and} \quad S = \frac{2.25 \cdot T \cdot t_0}{r^2}$ ​In deep alluvial aquifers across the Indo-Gangetic basin, manual water level measurements during multi-hour pumping tests often introduce human obse...