Flow in Aquifers 2 Unconfined Aquifer Flow Groundwater Hydraulics Daene C McKinney 1 Summary Unconfined Aquifer Flow Continuity Equation Steady Horizontal Flow Steady Horizontal Flow with Infiltration ID: 768494
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Flow in Aquifers – 2 Unconfined Aquifer Flow Groundwater HydraulicsDaene C. McKinney 1
SummaryUnconfined Aquifer Flow Continuity EquationSteady Horizontal FlowSteady Horizontal Flow with Infiltration Drains 2
Unconfined AquiferFlows bounded above by a water table occur in unconfined aquifers Thickness of capillary fringe above the water table is assumed to be much smaller than the saturated domain below the water tableThe water table is a nonlinear boundary and makes the exact solution of the governing equations almost impossibleApproximate solutions can be obtained based on a linearization of the boundary conditions or the nonlinear continuity equation. 3
Flow in an Unconfined Aquifer Dupuit approximations Slope of the water table is smallVelocities are horizontalConsiders a streamtube bounded by two streamlines: water table and impervious bottom 4 Ground surface Bedrock Unconfined aquifer Water table Q x K h ( x ) x y z w
5 h Water table Continuity Equation in an Unconfined Aquifer N (accretion, infiltration)
Continuity Equation in an Unconfined Aquifer Divide by and take limit as 6
Continuity Equation in an Unconfined AquiferHomogeneous aquifer (K = constant) Steady flowNo accretion (infiltration)One-dimensional flow 7
1-D Steady Flow in an Unconfined Aquifer Find the head in a homogeneous, unconfined aquifer with steady flow from left to right Head in the aquifer 8 Governing equation Simplifications: steady, 1-D flow, K = Constant, No accretion h Flow h A h B Water Table Ground Surface Bedrock L x
Steady Flow in an Unconfined Aquifer K = 10-1 cm/sec L = 150 m h A = 6.5 mhB = 4 mx = 150 mFind Q h Flow h A =6.5m h B =4m Water Table Ground Surface Bedrock L =150m x K =0.1cm/s 9
1-D Steady Flow in an Unconfined Aquifer with Infiltration Find the head in a homogeneous, unconfined aquifer with steady flow from left to right 10 Governing equation Simplifications: steady, 1-D flow, K = Constant, With accretion h h Max Flow h A h B Water Table Ground Surface Bedrock N, Infiltration L x
h h Max Flow h A h B Water Table Ground Surface Bedrock N, Infiltration L x Steady flow in an unconfined aquifer with infiltration 11
Example (Embankment)Given L = 3000 mK = 20 m/dayhA = 30 m h B = 20 m N = 500 mm/yrFind: Flow to the streams and shape of water table h h Max Flow h A h B Water Table Ground Surface Bedrock N, Infiltration L x 12
Example (Cont.) h h Max Flow h A h B Water Table Ground Surface Bedrock N, Infiltration L x 13
Unconfined Flow in an Aquifer with Horizontal Stratification 14 h A h B Water Table Ground Surface Bedrock L x Observation Well A Observation Well B a K 2 K 1
Example 15 h A h B Water Table Ground Surface Bedrock L x Observation Well A Observation Well B a K 2 K 1
Example (Drains)Subsurface drains are often used to prevent the water table elevation from increasing to an elevation where it would waterlog the roots of crops or bring unwanted salts and other chemicals in to the root zone. Steady, 1-D flow , homogeneous, isotropic aquifer, w/infiltration h d h Max Water Table Ground Surface Lower Confining Layer N, Infiltration L x 16
SummaryUnconfined Aquifer Flow Continuity EquationSteady Horizontal FlowSteady Horizontal Flow with Infiltration Drains 17