Principles of Groundwater Flow ESS 454 Hydrogeology Module 3 Principles of Groundwater Flow Point water Head, Validity of Darcy’s Law Diffusion Equation Flow in Unconfined Aquifers & Refraction of Flow lines Flownets Instructor: Michael Brown brown@ess.washington.edu

Outline and Learning Goals Understand how to quantitatively calculate heads and water fluxes in unconfined aquifers Be able to qualitatively and quantitatively estimate how flow lines are bent at interfaces between materials having different hydraulic conductivities

Unconfined Aquifer q’in=Qin/y q’out=q’in Jules Dupuit’s Contribution: Assume Water Table Hydraulic gradient is slope of water table Flow is horizontal h1 q’in=Qin/y q’out=q’in h2 y x=L x=0 h x

Unconfined Aquifer Qin Qout qout qin w=Infiltration (inches/year) Water Table w=Infiltration (inches/year) Vertical Flux: Qinfiltration=w dx dy h1 qout qin h2 Horizontal Flux dy dx Qin Qout

Unconfined Aquifer Consider unconfined aquifer with infiltration Consider change in storage caused by flow in x-direction Quantity change Over distance dx Contribution from flow in y-direction

Unconfined Aquifer A trick The steady-state behavior of an unconfined aquifer Align water table gradient in x-direction

Unconfined Aquifer This is easy to solve: Just integrate twice Two integrations, two integration constants The value of the head a two points (usually the two boundaries) gives enough information to solve this

Unconfined Aquifer x=0 L w h1 w=0 x=0 -> h=h1 x=L -> h=h2 h2 flow flow xw.t.divide At divide q’=0 You can solve for h at water table divide

Diffusion Equation for Unconfined Aquifer Valid for small draw-down (small ∆h) Nearly horizontal water table b is average thickness of saturated zone

Refraction of Flow Lines Derivation given in book i Imagine flux tube intersecting boundary Conserve water through boundary K1 K2 Apply Darcy’s Law at interface Use standard trig. relationships tan(r)=K2/K1 tan(i) r Bent away if K2<K1 Bent towards if K2>K1

End of Flow in unconfined Aquifers and Refraction of flow lines Coming up: The creation of “Flownets”