An unconfined sandy aquifer has a tested hydraulic conductivity ($K$) of $2.5 \times 10^{-4} \text{ m/s}$. Two observation wells, located $150 \text{ m}$ apart along the direction of groundwater flow, measure water table elevations of $45.2 \text{ m}$ and $43.7 \text{ m}$ above sea level, respectively. The aquifer has an average saturated thickness of $12 \text{ m}$ and a width of $500 \text{ m}$. Calculate the total groundwater flow rate ($Q$) through this section of the aquifer.

A confined limestone aquifer has a uniform thickness ($b$) of $35 \text{ m}$. A pumping test determines that the aquifer has a transmissivity ($T$) of $8.4 \times 10^{-3} \text{ m}^2/\text{s}$. What is the hydraulic conductivity ($K$) of the limestone?

Using the data from Problem 1 (where $K = 2.5 \times 10^{-4} \text{ m/s}$ and $i = 0.01$), calculate both the specific discharge (Darcy velocity, $v$) and the actual average linear velocity (seepage velocity, $v_s$) of a water molecule traveling between the two wells. The porosity ($n$) of the sandy aquifer is $30\%$. How long (in days) will it take a contaminant plume to travel the $150 \text{ m}$ between the wells?

A large underground subway station is being constructed via the "cut-and-cover" method in a dense urban environment. The $25 \text{ m}$ deep excavation must penetrate through a thick layer of stiff, impermeable clay (an aquitard) and terminate directly above a $10 \text{ m}$ thick layer of highly permeable, water-bearing gravel (a confined aquifer). The piezometric surface (artesian pressure head) of the gravel aquifer is located $5 \text{ m}$ below ground surface (i.e., $20 \text{ m}$ above the bottom of the planned excavation).

A rapidly expanding coastal city relies heavily on a large unconfined freshwater aquifer for its municipal water supply. Due to severe drought and a massive population boom, the city's municipal pumping wells, located $2 \text{ km}$ inland, have vastly increased their daily extraction rates.