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Gradient :

“del operator”. Gradient :. Divergence :. Laplacian :. Diffusion Equation :. “del operator”. Gradient :. Divergence :. Laplacian :. Diffusion Equation :. “Diffusion Equation”. Cartesian Coordinates. Cylindrical Coordinates. Cylindrical Coordinates, Radial Symmetry ∂h/∂ f = 0.

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Gradient :

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  1. “del operator” Gradient: Divergence: Laplacian: Diffusion Equation:

  2. “del operator” Gradient: Divergence: Laplacian: Diffusion Equation:

  3. “Diffusion Equation” Cartesian Coordinates Cylindrical Coordinates Cylindrical Coordinates, Radial Symmetry ∂h/∂f = 0 Cylindrical Coordinates, Purely Radial Flow ∂h/∂f = 0 ∂h/∂z = 0

  4. Flow beneath Dam Vertical x-section Flow toward Pumping Well, next to river = line source = constant head boundary Plan view River Channel Domenico & Schwartz (1990)

  5. Well Drawdown Case 1: Confined aquifier, Constant pumping rate Q, Steady radial flow where m=aquifer thickness “Equilibrium” eq., or “Theim” equation e.g., Fetter eq 7-38 D&S eq. 5.21 2x = Drawdown

  6. m Potentiometric Surface Q Confined Aquifer

  7. Well Drawdown Case 2: Unconfined aquifier, Constant pumping rate Q, Steady radial flow where m=aquifer thickness Unconfined “Theim” equation e.g., Fetter eq 7-39 D&S eq. 5.24 ≠ (Drawdown)2

  8. Swindle: 1) Singulatity at r = 0 2) Steady state flux impossible without source - this problem requires annular source term 3) Purely radial flow impossible for unconfined case

  9. Radial flow Transient flow, Confined Aquifer, No recharge Constant pumping rate Q Initial Condition & Boundary conditions:

  10. Radial flow Initial Condition & Boundary conditions: Solution: “Theis equation” or “Non-equilibrium Eq.” where and where

  11. Approximation for t >> 0 D&S p. 151

  12. Pumping of Confined Aquifer Not GW “level” Potetiometric sfc! USGS Circ 1186

  13. Pumping of Unconfined Aquifer USGS Circ 1186

  14. End L21: Now, Spring break!

  15. FLOW NETS Impermeble Boundary Constant Head Boundary Water Table Boundary after Freeze & Cherry

  16. Santa Cruz River near Tucson AZ 1942 USGS Circ 1186

  17. Santa Cruz River near Tucson AZ 1989 >100’ GW drop USGS Circ 1186

  18. Santa Cruz River Martinez Hill, South of Tucson AZ 1942 Cottonwoods, Mesquite 1989 >100’ GW drop USGS Circ 1186

  19. for unconfined flow

  20. Initial Condition Pumping @ rate Q1 (note divide) Pumping @ rate Q2 >Q1 USGS Circ 1186

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