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Groundwater Flow Equations

Groundwater Flow Equations. Groundwater Hydraulics Daene C. McKinney. Summary. General Groundwater Flow Control Volume Analysis General Continuity Equation Confined Aquifer Flow Continuity Equation Integrate over vertical dimension Transmissivity Continuity Examples

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Groundwater Flow Equations

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  1. Groundwater Flow Equations Groundwater Hydraulics Daene C. McKinney

  2. Summary • General Groundwater Flow • Control Volume Analysis • General Continuity Equation • Confined Aquifer Flow • Continuity Equation • Integrate over vertical dimension • Transmissivity • Continuity • Examples • Unconfined Aquifer Flow • Darcy Law • Continuity Equation • Examples

  3. Control Volume • Control volume of dimensions Dx, Dy, Dz • Completely saturated with a fluid of density r Mass flux in Mass flux out Control volume z y x

  4. Mass Flux mass flux out mass flux in • Mass flux = Mass in - Mass out: • Fluid mass in the volume: • Continuity:Mass flux = change of mass

  5. Aquifer Storage

  6. Continuity Equation

  7. Confined Aquifer Flow

  8. Horizontal Aquifer Flow • Most aquifers are thin compared to horizontal extent • Flow is horizontal, qx and qy • No vertical flow, qz = 0 • Average properties over aquifer thickness (b) Ground surface Head in confined aquifer Confining Layer h Qx Confined aquifer b z y K x Bedrock

  9. Aquifer Transmissivity • Transmissivity (T) • Discharge through thickness of aquifer per unit width per unit head gradient • Product of conductivity and thickness Hydraulic gradient = 1 m/m Potentiometric Surface Confining Bed Transmissivity, T, volume of water flowing an area 1 m x b under hydraulic gradient of 1 m/m 1 m b 1 m Confined Aquifer 1 m Conductivity, K, volume of water flowing an area 1 m x 1 m under hydraulic gradient of 1 m/m

  10. Continuity Equation • Continuity equation • Darcy’s Law • Continuity Ground surface Head in confined aquifer Confining Layer h Qx Confined aquifer b z y K x Radial Coordinates Bedrock

  11. Example – Horizontal Flow • Consider steady flow from left to right in a confined aquifer • Find: Head in the aquifer, h(x) Ground surface steady flow Confining Layer Confined aquifer hA hB Qx b z y K x Head in the aquifer Bedrock L

  12. Example – Horizontal Flow • L = 1000 m, hA = 100 m, hB = 80 m, K = 20 m/d, f = 0.35 • Find: head, specific discharge, and average velocity Ground surface Confining Layer Confined aquifer hA=100m hB=80m Qx b z y K=2-m/d x Bedrock L=1000m

  13. Unconfined Aquifer Flow

  14. Flow in an Unconfined Aquifer • Dupuit approximations • Slope of the water table is small • Velocities are horizontal Ground surface Water table Unconfined aquifer h Qx K z y x Bedrock Dx

  15. Steady Flow in an Unconfined Aquifer • 1-D flow • Steady State • K = constant Ground Surface Water Table Flow hA h hB Bedrock L x

  16. Steady Flow in an Unconfined Aquifer • K = 10-1 cm/sec • L = 150 m • hA = 6.5 m • hB = 4 m • x = 150 m • Find Q Ground Surface Water Table Flow hA=6.5m h hB=4m K=0.1cm/s Bedrock L=150m x

  17. Summary • General Groundwater Flow • Control Volume Analysis • General Continuity Equation • Confined Aquifer Flow • Continuity Equation • Integrate over vertical dimension • Transmissivity • Continuity • Examples • Unconfined Aquifer Flow • Darcy Law • Continuity Equation • Examples

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