
Techniques for Finding “Solutions” to Groundwater Flow” • Inspection (intuition) • Graphical Techniques
Techniques for Finding “Solutions” to Groundwater Flow” • Inspection (intuition) • Graphical Techniques • Analog Models
Techniques for Finding “Solutions” to Groundwater Flow” • Inspection (intuition) • Graphical Techniques • Analog Models • Analytical Mathematical Techniques (Calculus)
Techniques for Finding “Solutions” to Groundwater Flow” • Inspection (intuition) • Graphical Techniques • Analog Models • Analytical Mathematical Techniques (Calculus) • Numerical Mathematical Techniques (Computers)
I. Introduction A. Overview
I. Introduction A. Overview • one of the most powerful tools for the analysis of groundwater flow.
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.
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:
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
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
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.
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.
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
Assumptions Needed For Flow Net Construction • Aquifer is homogeneous, isotropic • Aquifer is saturated
Assumptions Needed For Flow Net Construction • Aquifer is homogeneous, isotropic • Aquifer is saturated • There is no change in head with time
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
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
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.
III. Boundaries A. Types
III. Boundaries • Types 1. Impermeable 2. Constant Head 3. Water Table
III. Boundaries • Types 1. Impermeable 2. Constant Head 3. Water Table
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
IV. Refraction of Flow Lines • The derivation • The general relationships • An example problem
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