Identify the named relationship used to determine the average linear velocity of groundwater flow (in metres per day) based on hydraulic conductivity, hydraulic gradient, and effective porosity.

Introduction / Context:Groundwater movement is commonly analyzed using Darcy-based relationships. Translating discharge to average linear (seepage) velocity requires the concept of effective porosity to account for the actual flow pathways.

Given Data / Assumptions:

• Steady laminar groundwater flow through a porous medium.
• Hydraulic conductivity K, hydraulic gradient i, and effective porosity n_e.

Concept / Approach:Darcy’s law states Q = K i A. The Darcy or superficial velocity v_d = Q/A = K i. The average linear (seepage) velocity v is v = v_d / n_e = (K i) / n_e.

Step-by-Step Solution:Start with Darcy: Q = K i A.Superficial velocity: v_d = Q/A = K i.Average linear velocity accounting for flow through voids: v = v_d / n_e = (K i)/n_e.This velocity is often expressed in metres per day when K and i are in compatible units.

Verification / Alternative check:Field tracer tests typically show that groundwater moves at the seepage velocity which exceeds the Darcy velocity by roughly 1/n_e.

Why Other Options Are Wrong:

• Hazen, Slichter, Meinzer: associated with empirical correlations for K from grain-size data, not the fundamental velocity relation.

Common Pitfalls:

• Confusing Darcy velocity with seepage velocity; forgetting to divide by effective porosity.

Final Answer:Darcy’s formula