Problem 1: Darcy's Law Application A confined aquifer has a hydraulic conductivity ($K$) of $25 \text{ m/day}$. Two observation wells located 500 meters apart along the direction of flow have measured piezometric heads of 45.0 m and 42.5 m, respectively. The aquifer has a constant thickness of 15 m and a width of 2 km. Calculate the hydraulic gradient and the total daily discharge ($Q$) through this section of the aquifer.

Problem 2: Steady Flow to a Well in a Confined Aquifer (Thiem Equation) A fully penetrating well in a confined aquifer is pumped at a constant rate of $1,500 \text{ m}^3/\text{day}$. Steady-state conditions are reached. The drawdown in an observation well 30 meters away ($r_1$) is 2.5 meters. The drawdown in a second observation well 100 meters away ($r_2$) is 1.2 meters. The aquifer has a uniform thickness of 20 meters. Calculate the Transmissivity ($T$) and Hydraulic Conductivity ($K$) of the aquifer.

Problem 3: Steady Flow to a Well in an Unconfined Aquifer (Dupuit Equation) A well penetrates fully into an unconfined aquifer with an initial saturated thickness of 30 meters. The well is pumped continuously at $1,200 \text{ m}^3/\text{day}$ until steady state is reached. Observation wells at 20 meters ($r_1$) and 80 meters ($r_2$) show piezometric heads (measured from the impermeable base) of 26 meters ($h_1$) and 28 meters ($h_2$), respectively. Calculate the hydraulic conductivity ($K$) of the aquifer.

Problem 4: Unsteady Flow (Cooper-Jacob Approximation) A pumping test is conducted in a confined aquifer. A well is pumped at $2,400 \text{ m}^3/\text{day}$. An observation well is located 50 meters away ($r = 50$). After 10 hours ($t = 0.417 \text{ days}$) of continuous pumping, the drawdown ($s$) is 1.8 meters. The aquifer has a known Transmissivity ($T$) of $500 \text{ m}^2/\text{day}$. Use the Cooper-Jacob approximation to calculate the Storage Coefficient ($S_c$) of the aquifer. (Verify that $u \le 0.01$ afterward).

Case Study 1: The Principle of Effective Stress and Land Subsidence In the San Joaquin Valley of California, intensive agricultural pumping of deep confined aquifers has caused the ground surface to sink by over 8 meters in some areas. Discuss how groundwater pumping physically causes massive land subsidence using Terzaghi's Principle of Effective Stress.

Case Study 2: Saltwater Intrusion in Coastal Aquifers Coastal cities like Miami and Jakarta heavily rely on groundwater. However, over-pumping has led to severe "saltwater intrusion," ruining drinking water supplies. Explain the hydrodynamics of saltwater intrusion using the Ghyben-Herzberg relation.