ESS 454 Hydrogeology Module 3 Principles of Groundwater Flow • Point water Head, Validity of Darcy’s Law • Diffusion Equation • Flow in Unconfined Aquifers & Refraction of Flow lines • Flownets Instructor: Michael Brown [email protected] .edu
ESS 454 Hydrogeology
Feb 21, 2016
ESS 454 Hydrogeology. Module 3 Principles of Groundwater Flow Point water Head, Validity of Darcy’s Law Diffusion Equation Flow in Unconfined Aquifers & Refraction of Flow lines Flownets. Instructor: Michael Brown [email protected]. Outline and Learning Goals. - PowerPoint PPT Presentation
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ESS 454 Hydrogeology
Module 3Principles of Groundwater Flow
• Point water Head, Validity of Darcy’s Law• Diffusion Equation• Flow in Unconfined Aquifers & Refraction
of Flow lines• Flownets
Instructor: Michael [email protected]
Outline and Learning Goals
• Understand how to quantitatively calculate heads and water fluxes in unconfined aquifers
• Be able to qualitatively and quantitatively estimate how flow lines are bent at interfaces between materials having different hydraulic conductivities
x=0
h1
h2
q’in=Qin/y q’out=q’in
Unconfined AquiferWater Table 1. Hydraulic gradient is
slope of water table2. Flow is horizontal
Jules Dupuit’s Contribution:Assume
x=L
h
x
y
dxdy
h1
h2
w=Infiltration (inches/year)
qinqout
Vertical Flux:Qinfiltration=w dx dy
Qin
Qout
Horizontal Flux
Unconfined AquiferWater Table
Unconfined Aquifer
Consider change in storage caused by flow in x-direction
Contribution from flow in y-direction
Consider unconfined aquifer with infiltration
Quantity change
Over distance dx
Unconfined Aquifer
A trick
Align water table gradient in x-direction
The steady-state behavior of an unconfined aquifer
Unconfined Aquifer
This is easy to solve:Just integrate twice
Two integrations, two integration constants
The value of the head a two points (usually the two boundaries) gives enough information to solve this
h1
h2
x=0 L
w
Unconfined Aquifer
x=0 -> h=h1
x=L -> h=h2
At divide q’=0
xw.t.divide
flowflow
You can solve for h at water table divide
w=0
Diffusion Equation for Unconfined Aquifer
• Valid for – small draw-down (small ∆h)– Nearly horizontal water table
b is average thickness of saturated zone
K1
K2
i
Refraction of Flow Lines
r
tan(r)=K2/K1 tan(i)
Bent away if K2<K1
Bent towards if K2>K1
Derivation given in book
Apply Darcy’s Law at interfaceConserve water through boundary
Use standard trig. relationships
Imagine flux tube intersecting boundary
End of Flow in unconfined Aquifers and Refraction of flow lines
Coming up: The creation of “Flownets”
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