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FLOW NETS

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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

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

II. Assumptions Needed For Flow Net Construction

- 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

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

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