4.4 Methods of superposition and images 4.4.1 Method of superposition 44.2 Method of images 4.5 Flow net…… 4.5.1 Potential function and equipotential lines 4.5.2 Stream function and stream lines 4.5.3 Flow net 5. Non-Steady Groundwater Flow in Aquifers 5.1 Basic equations for non-steady flow in aquifers. 5.1.1 Confined aquifer 5.2 Non-steady Groundwater Flow in a confined aquifer. 5.2.1 Conceptual hydrogeological model 5.2.2 Mathematical model 5.2.3 Analytical solution 76 5.2. 4 Analysis of the resul .3 Non-steady Groundwater Flow in an unconfined aquifer 5.3.1 Conceptual hydrogeological model 78 5.3.2 Mathematical model 78 5.3.3 Analytical solutions 5.3.4 Analysis of results 6. Non-steady Groundwater Flow to wells 6.1 Groundwater flow to a well in a confined aquifer 6.1.1 Conceptual hydrogeological model 6.1.2 Mathematical model 6.1.3 Analytical Solution: Theis formula(1935) 6. 1. 4 Analysis of the solution 86 6. 1. 5 Simplification of Theis formula: Jacob's formula 6.1.6 Applications 6.2 Non-steady groundwater to a well in an unconfined aquifer. 6.2.1 Conceptual hydrogeological model 6.2.2 Mathematical model 6.2.3 Analytical Solution 96 6.2.5 Application of the solution 3 Non-steady groundwater flow to a well in a semi-confined aquifer 6.3.1 Conceptual hydrogeological model 6.3.2 Mathematical model 6.3.3 Analytical solution 6.3.4 Analysis of the results 6.3.5 Application of the solution 7. Refe 8. Anneres T1 Well function of confined aquifers T2 Well function of semi-confined aquifers 12 T3 Function e Ko(x)…., T 4 Function Io(x),I, (x), Ko(x), K(x) 114 9. Exercise4.4.4 Analysis of results ................................................................................................................... 52 4.4 Methods of superposition and images.......................................................................................... 55 4.4.1 Method of superposition.......................................................................................................... 55 4.4.2 Method of images.................................................................................................................... 61 4.5 Flow net .......................................................................................................................................... 65 4.5.1 Potential function and equipotential lines................................................................................ 65 4.5.2 Stream function and stream lines............................................................................................. 66 4.5.3 Flow net................................................................................................................................... 66 5. Non-steady Groundwater Flow in Aquifers........................................................................................... 71 5.1 Basic equations for non-steady flow in aquifers.......................................................................... 71 5.1.1 Confined aquifer...................................................................................................................... 71 5.1.2 Unconfined aquifer.................................................................................................................. 72 5.2 Non-steady Groundwater Flow in a confined aquifer ................................................................ 75 5.2.1 Conceptual hydrogeological model ......................................................................................... 75 5.2.2 Mathematical model ................................................................................................................ 75 5.2.3 Analytical solution................................................................................................................... 76 5.2.4 Analysis of the result ............................................................................................................... 77 5.3 Non-steady Groundwater Flow in an unconfined aquifer ......................................................... 78 5.3.1 Conceptual hydrogeological model ......................................................................................... 78 5.3.2 Mathematical model ................................................................................................................ 78 5.3.3 Analytical solutions................................................................................................................. 79 5.3.4 Analysis of results ................................................................................................................... 81 6. Non-steady Groundwater Flow to Wells................................................................................................ 83 6.1 Groundwater flow to a well in a confined aquifer ...................................................................... 83 6.1.1 Conceptual hydrogeological model ......................................................................................... 83 6.1.2 Mathematical model ................................................................................................................ 84 6.1.3 Analytical Solution: Theis formula (1935).............................................................................. 85 6.1.4 Analysis of the solution ........................................................................................................... 86 6.1.5 Simplification of Theis formula: Jacob's formula.................................................................... 87 6.1.6 Applications............................................................................................................................. 87 6.2 Non-steady groundwater to a well in an unconfined aquifer..................................................... 94 6.2.1 Conceptual hydrogeological model ......................................................................................... 94 6.2.2 Mathematical model ................................................................................................................ 94 6.2.3 Analytical Solution.................................................................................................................. 96 6.2.4 Analysis of results ................................................................................................................... 97 6.2.5 Application of the solution ...................................................................................................... 98 6.3 Non-steady groundwater flow to a well in a semi-confined aquifer .......................................... 99 6.3.1 Conceptual hydrogeological model ......................................................................................... 99 6.3.2 Mathematical model .............................................................................................................. 100 6.3.3 Analytical solution................................................................................................................. 101 6.3.4 Analysis of the results............................................................................................................ 102 6.3.5 Application of the solution .................................................................................................... 104 7. References............................................................................................................................................. 110 8. Annexes................................................................................................................................................. 111 T.1 Well function of confined aquifers............................................................................................. 111 T.2 Well function of semi-confined aquifers.................................................................................... 112 T.3 Function e K (x) 0 x ..................................................................................................................... 113 T.4 Function I (x), I (x) 0 1 , K (x), K (x) 0 1 ...................................................................................... 114 9. Exercises............................................................................................................................................... 116 2