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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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slide3
Techniques for Finding “Solutions” to Groundwater Flow”
  • Inspection (intuition)
  • Graphical Techniques
slide4
Techniques for Finding “Solutions” to Groundwater Flow”
  • Inspection (intuition)
  • Graphical Techniques
  • Analog Models
slide5
Techniques for Finding “Solutions” to Groundwater Flow”
  • Inspection (intuition)
  • Graphical Techniques
  • Analog Models
  • Analytical Mathematical Techniques (Calculus)
slide6
Techniques for Finding “Solutions” to Groundwater Flow”
  • Inspection (intuition)
  • Graphical Techniques
  • Analog Models
  • Analytical Mathematical Techniques (Calculus)
  • Numerical Mathematical Techniques (Computers)
slide7
I. Introduction

A. Overview

slide8
I. Introduction

A. Overview

  • one of the most powerful tools for the analysis of groundwater flow.
slide9
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.
slide10
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:
slide11
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
slide12
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
slide13
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.
slide14
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.
slide15
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

slide17
Assumptions Needed For Flow Net Construction
  • Aquifer is homogeneous, isotropic
  • Aquifer is saturated
slide18
Assumptions Needed For Flow Net Construction
  • Aquifer is homogeneous, isotropic
  • Aquifer is saturated
  • There is no change in head with time
slide19
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
slide20
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
slide21
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.
slide24
III. Boundaries
  • Types

1. Impermeable

2. Constant Head

3. Water Table

slide25
III. Boundaries
  • Types

1. Impermeable

2. Constant Head

3. Water Table

slide26

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

slide28
IV. Refraction of Flow Lines
  • The derivation
  • The general relationships
  • An example problem
slide29
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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