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ESS 454 Hydrogeology

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.

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ESS 454 Hydrogeology

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  1. 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

  2. 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

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

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

  5. 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

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

  7. 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

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

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

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

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

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