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FLOW NETS

FLOW NETS. Techniques for Finding “Solutions” to Groundwater Flow”. Techniques for Finding “Solutions” to Groundwater Flow” Inspection (intuition) Graphical Techniques. Techniques for Finding “Solutions” to Groundwater Flow” Inspection (intuition) Graphical Techniques Analog Models.

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FLOW NETS

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  1. FLOW NETS

  2. Techniques for Finding “Solutions” to Groundwater Flow”

  3. Techniques for Finding “Solutions” to Groundwater Flow” • Inspection (intuition) • Graphical Techniques

  4. Techniques for Finding “Solutions” to Groundwater Flow” • Inspection (intuition) • Graphical Techniques • Analog Models

  5. Techniques for Finding “Solutions” to Groundwater Flow” • Inspection (intuition) • Graphical Techniques • Analog Models • Analytical Mathematical Techniques (Calculus)

  6. Techniques for Finding “Solutions” to Groundwater Flow” • Inspection (intuition) • Graphical Techniques • Analog Models • Analytical Mathematical Techniques (Calculus) • Numerical Mathematical Techniques (Computers)

  7. I. Introduction A. Overview

  8. I. Introduction A. Overview • one of the most powerful tools for the analysis of groundwater flow.

  9. I. Introduction A. Overview • one of the most powerful tools for the analysis of groundwater flow. • provides a solution to LaPlaces Equation for 2-D, steady state, boundary value problem.

  10. I. Introduction A. Overview • one of the most powerful tools for the analysis of groundwater flow. • provides a solution to LaPlaces Equation for 2-D, steady state, boundary value problem. • To solve, need to know:

  11. I. Introduction A. Overview • one of the most powerful tools for the analysis of groundwater flow. • provides a solution to LaPlaces Equation for 2-D, steady state, boundary value problem. • To solve, need to know: • have knowledge of the region of flow

  12. I. Introduction A. Overview • one of the most powerful tools for the analysis of groundwater flow. • provides a solution to LaPlaces Equation for 2-D, steady state, boundary value problem. • To solve, need to know: • have knowledge of the region of flow • boundary conditions along the perimeter of the region

  13. To solve, need to know: • have knowledge of the region of flow • boundary conditions along the perimeter of the region • spatial distribution of hydraulic head in region.

  14. Composed of 2 sets of lines • equipotential lines (connect points of equal hydraulic head) • flow lines (pathways of water as it moves through the aquifer.

  15. Composed of 2 sets of lines • equipotential lines (connect points of equal hydraulic head) • flow lines (pathways of water as it moves through the aquifer. d2h + d2h = 0 gives the rate of change of dx2 dy2 h in 2 dimensions

  16. II. Assumptions Needed For Flow Net Construction

  17. Assumptions Needed For Flow Net Construction • Aquifer is homogeneous, isotropic • Aquifer is saturated

  18. Assumptions Needed For Flow Net Construction • Aquifer is homogeneous, isotropic • Aquifer is saturated • There is no change in head with time

  19. Assumptions Needed For Flow Net Construction • Aquifer is homogeneous, isotropic • Aquifer is saturated • There is no change in head with time • Soil and water are incompressible

  20. Assumptions Needed For Flow Net Construction • Aquifer is homogeneous, isotropic • Aquifer is saturated • there is no change in head with time • soil and water are incompressible • Flow is laminar, and Darcys Law is valid

  21. Assumptions Needed For Flow Net Construction • Aquifer is homogeneous, isotropic • Aquifer is saturated • there is no change in head with time • soil and water are incompressible • flow is laminar, and Darcys Law is valid • All boundary conditions are known.

  22. III. Boundaries

  23. III. Boundaries A. Types

  24. III. Boundaries • Types 1. Impermeable 2. Constant Head 3. Water Table

  25. III. Boundaries • Types 1. Impermeable 2. Constant Head 3. Water Table

  26. B. Calculating Discharge Using Flow Nets III. Boundaries Q’ = Kph f Where: Q’ = Discharge per unit depth of flow net (L3/t/L) K = Hydraulic Conductivity (L/t) p = number of flow tubes h = head loss (L) f = number of equipotential drops

  27. IV. Refraction of Flow Lines

  28. IV. Refraction of Flow Lines • The derivation • The general relationships • An example problem

  29. IV. Flow Nets: Isotropic, Heterogeneous Types • “Reminder” of the conditions needed to draw a flow net for homogeneous, isotropic conditions • An Example of Iso, Hetero

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