Download Presentation
## FLOW NETS

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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