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CE 3354 Engineering Hydrology

Learn about the direct application of Darcy's Law in groundwater hydrology, including the use of groundwater maps, flowlines, confined and unconfined aquifers, transmissivity, and flow between ditches. Explore different material properties and understand the concepts of porosity, hydraulic conductivity, gradients, and head in steady flow solutions. Discover what will be covered in the next lecture on transient solutions and well hydraulics.

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CE 3354 Engineering Hydrology

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  1. CE 3354 Engineering Hydrology Lecture 22: Groundwater Hydrology Concepts – Part 2

  2. Outline • Direct Application of Darcy’s Law • Steady flow solutions • Rectilinear flow • Flow to wells

  3. Direct Application of Darcy’s Law • A groundwater map is a topographic representation of the 3-D piezometric or water table surface. • Darcy’s law implies that flow should be perpendicular to the lines of constant head (or potential) • unless the medium is anisotropic (permeability is direction dependent).

  4. Direct Application of Darcy’s Law • Flowlines are thus usually plotted perpendicular to the water level distribution. • Flowlines diverge away from a recharge area or source of water to the subsurface, • Flowlines converge towards a discharge area. • The concept is similar to water flowing downhill in a surface water system.

  5. Direct Application of Darcy’s Law

  6. Direct Application of Darcy’s Law

  7. Direct Application of Darcy’s Law • Another example using a plan-view groundwater map is that the flow between any two flow lines is determined by the head change along the path of flow, the width between the flow lines, the thickness of the aquifer and the hydraulic conductivity

  8. Confined-Rectilinear • Darcy’s Law • Rearrange into differential equation • Integrate to recover the equation of head

  9. Unconfined – Rectilinear • Darcy’s Law • Rearrange into differential equation • Recall some calculus

  10. Confined – Cylindrical • Now consider a circular, confined aquifer with a well in the center

  11. Confined – Cylindrical • Calculus • Darcy’s Law • Differential Equation • Integrate

  12. Unconfined – Cylindrical • Unconfined aquifer on circular island

  13. Unconfined – Cylindrical • Unconfined aquifer on circular island

  14. Unconfined – Cylindrical • Unconfined aquifer on circular island

  15. Transmissivity • Transmissivity is the term that refers to the amount of water that will flow through an entire thickness of aquifer • The term Kb is the transmissivity it represents the discharge per unit width under unit gradient through an aquifer • The usual symbol is T

  16. Flow Between Two Ditches

  17. Flow Between Two Ditches

  18. Flow Between Two Ditches

  19. Flow Between Two Ditches

  20. Different material properties • Use hydraulics principles (head loss) to find average K (or T)

  21. Different material properties • Use hydraulics principles (head loss) to find average K (or T)

  22. Summary • Porosity, Specific Yield • Storage • Darcy’s Law – Hydraulic Conductivity • Gradients and head • Some steady flow solutions – use geometry, Darcy’s law, and calculus

  23. Next Time • Transient (time-varying) solutions • Superposition of solutions • Well hydraulics

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