Groundwater Flow Equations Groundwater Hydraulics Daene C. McKinney

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

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

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

Aquifer Storage

Continuity Equation

Confined Aquifer Flow

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 Bedrock Confined aquifer Qx K x y z h Head in confined aquifer Confining Layer b

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 Confined Aquifer b 1 m Transmissivity, T, volume of water flowing an area 1 m x b under hydraulic gradient of 1 m/m Conductivity, K, volume of water flowing an area 1 m x 1 m under hydraulic gradient of 1 m/m

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

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

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 Bedrock Confined aquifer Qx K=2-m/d x y z hB=80m Confining Layer b hA=100m L=1000m

Unconfined Aquifer Flow

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

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

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 h Flow hA=6.5m hB=4m Water Table Ground Surface Bedrock L=150m x K=0.1cm/s

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