The letters following each Review Question refer to the corresponding Learning Objective from the Chapter Opener. What does Darcy's law tell us about rates of discharge in groundwater? (A)

Darcy's law is a fundamental principle in groundwater flow and hydrogeology. It states that the discharge of groundwater through an aquifer depends on the hydraulic conductivity of the porous media, the cross-sectional area through which water flows, and the hydraulic gradient (the head difference) in the system. Mathematically, Darcy's law can be expressed as: \(Q = -KA(\frac{dh}{dl})\) Where: - Q is the discharge rate of groundwater (m³/s) - K is the hydraulic conductivity of the porous medium (m/s) - A is the cross-sectional area through which water flows (m²) - \(dh\) is the change in hydraulic head (m) - \(dl\) is the change in distance over which the head change occurs (m)

To determine the discharge rates in groundwater, we first need to analyze the components of Darcy's law. - Hydraulic Conductivity (K): This represents the ease with which water can move through the porous media. Higher conductivity values indicate that water can flow more freely, while lower values suggest resistance to flow. - Cross-sectional Area (A): This is the area through which groundwater flows. Larger areas allow more water to pass through, resulting in higher discharge rates. - Hydraulic Gradient (\(\frac{dh}{dl}\)): This is the driving force for the groundwater flow. It represents the change in hydraulic head per unit distance. A larger hydraulic gradient implies a greater force driving the groundwater flow, leading to higher discharge rates.

With the understanding of Darcy's law and its components, we can now calculate the discharge rate in groundwater systems. 1. Determine the hydraulic conductivity, cross-sectional area, and hydraulic gradient for the given groundwater system. This information can be obtained from field measurements, laboratory tests, or available data. 2. Plug the values into the Darcy's law equation and solve for the discharge rate (Q): \(Q = -KA(\frac{dh}{dl})\) 3. The result will be the discharge rate of groundwater in the system, expressed in cubic meters per second (m³/s). In conclusion, Darcy's law tells us that the discharge rate of groundwater in a system is proportional to the hydraulic conductivity of the porous media, the cross-sectional area through which water flows, and the hydraulic gradient of the system. By understanding and applying Darcy's law, we can determine the rates of discharge in various groundwater systems.