Final answer:
Hydraulic conductivity is related to the equation of continuity, which states that the product of cross-sectional area and velocity remains constant in incompressible fluid flow, so velocity increases as cross-sectional area decreases and vice versa.
Step-by-step explanation:
The concept of equivalent hydraulic conductivity when dealing with varying cross-sectional areas derives from the equation of continuity in fluid mechanics. According to this principle, for any incompressible fluid, the product of cross-sectional area (A) and the average velocity (v) at any point along the flow path remains constant (A1V1 = A2V2). Therefore, if the cross-sectional area decreases, the velocity must increase to maintain the flow rate, and conversely, if the area increases, the velocity decreases. While hydraulic conductivity generally refers to a material's ability to conduct fluid through its pore spaces, in the context of pipes with varying cross-sectional areas, it essentially illustrates how the fluid flow (velocity and rate) adapts to the size changes in the conduit. An increase in velocity in a reduced cross-sectional area may seem like an increase in hydraulic conductivity, but it's a testament to the fluid maintaining its continuity.