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FLOW NETS

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Techniques for Finding Solutions toGroundwater Flow

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Techniques for Finding Solutions toGroundwater Flow

Inspection (intuition) Graphical Techniques

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Techniques for Finding Solutions toGroundwater Flow

Inspection (intuition) Graphical Techniques Analog Models Analytical Mathematical Techniques

(Calculus)

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Techniques for Finding Solutions toGroundwater Flow

Inspection (intuition) Graphical Techniques

Analog Models Analytical Mathematical Techniques (Calculus) Numerical Mathematical Techniques

(Computers)

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I. Introduction A. Overview

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I. Introduction A. Overview one of the most powerful tools for the

analysis of groundwater flow.

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I. Introduction A. Overview one of the most powerful tools for the

analysis of groundwater flow.

provides a solution to LaPlacesEquation for 2-D, steady state,boundary value problem.

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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:

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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

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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

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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.

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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.

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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 + d 2h = 0 gives the rate of change ofdx 2 dy 2 h in 2 dimensions

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II. Assumptions Needed For Flow NetConstruction

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II. Assumptions Needed For Flow NetConstruction

Aquifer is homogeneous, isotropic Aquifer is saturated

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II. Assumptions Needed For Flow NetConstruction

Aquifer is homogeneous, isotropic Aquifer is saturated There is no change in head with time

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II. Assumptions Needed For Flow NetConstruction

Aquifer is homogeneous, isotropic Aquifer is saturated There is no change in head with time Soil and water are incompressible

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II. Assumptions Needed For Flow NetConstruction

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

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II. Assumptions Needed For Flow NetConstruction

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.

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III. Boundaries A. Types

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III. Boundaries A. Types

1. Impermeable2. Constant Head3. Water Table

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III. Boundaries A. Types

1. Impermeable2. Constant Head3. Water Table

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III. BoundariesB. Calculating Discharge Using Flow Nets

Q = Kphf

Where: Q = Discharge per unit depth of flow net (L3/t/L) K = Hydraulic Conductivity (L/t)p = number of flow tubesh = head loss (L)f = number of equipotential drops

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IV. Refraction of Flow Lines

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IV. Refraction of Flow Lines A. The derivation

B. The general relationshipsC. An example problem

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IV. Flow Nets: Isotropic, HeterogeneousTypes

A. Reminder of the conditions needed todraw a flow net for homogeneous,isotropic conditions

B. An Example of Iso, Hetero

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