Subtopic: Steady and unsteady flow in confined and unconfined aquifers
Question Statement:
Two parallel canals 50 m apart fully penetrate a homogeneous unconfined aquifer resting on a horizontal impermeable layer. The aquifer has a hydraulic conductivity of 3 m day⁻¹ and an effective porosity of 0.25. Steady groundwater flow occurs from the upper canal (water level 10 m above aquifer bottom) to the lower canal (8.5 m). If a sediment layer 4 cm thick with hydraulic conductivity 1.2×10⁻² m day⁻¹ is deposited on the inflow face, the groundwater discharge per 1000 m width between the two canals in m³ day⁻¹ will be _______________
Official Answer Key:
694
Step-by-Step Solution & Explanation
This is a two-media-in-series unconfined (Dupuit) flow problem: flow must first pass through the thin, low-conductivity sediment layer (thickness t=0.04 m, K_sed=0.012 m/day) at the inflow face, then through the remaining aquifer (length ≈50 m, K=3 m/day) to the outflow canal, with continuity of discharge q across both media and an unknown intermediate head h_m at the sediment/aquifer interface.
Using the Dupuit equation for each segment: q = K_sed(h₁²−h_m²)/(2t) = K(h_m²−h₂²)/(2L_aquifer)
Solving this pair simultaneously (h₁=10 m, h₂=8.5 m) gives h_m ≈ 9.766 m and q ≈ 0.694 m³/day per metre width.
For 1000 m width: Q ≈ 694 m³/day (the thin, low-K sediment layer creates a substantial additional resistance, reducing the discharge from the ≈832 m³/day that would occur without it).
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