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Figure from Hornberger et al. (1998)

Darcy’s data for two different sands. Figure from Hornberger et al. (1998). Range in hydraulic conductivity, K 13 orders of magnitude. Figure from Hornberger et al. (1998). Figure from Hornberger et al. (1998). Generalization of Darcy’s column.  h/L = hydraulic gradient.

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Figure from Hornberger et al. (1998)

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  1. Darcy’s data for two different sands Figure from Hornberger et al. (1998)

  2. Range in hydraulic conductivity, K 13 orders of magnitude Figure from Hornberger et al. (1998)

  3. Figure from Hornberger et al. (1998)

  4. Generalization of Darcy’s column h/L = hydraulic gradient Q is proportional to h/L q = Q/A Figure from Hornberger et al. (1998)

  5. qz 2 qx 1 q = Q/A q is a vector z q z x x In general: Kz < Kx, Ky

  6. q = - Kgrad h

  7. Vector Form of Darcy’s Law q = - K grad h q = specific discharge (L/T) K = hydraulic conductivity (L/T) grad h = hydraulic gradient (L/L) h = head (L)

  8. q = - Kgrad h q is a vector with 3 components h is a scalar K is a tensor with 9 components (three of which are Kx, Ky, Kz)

  9. Darcy’s law q = - Kgrad h q equipotential line grad h q grad h Isotropic Kx = Ky = Kz = K Anisotropic Kx, Ky, Kz

  10. True flow paths Linear flow paths assumed in Darcy’s law Average linear velocity v = Q/An= q/n n = effective porosity Specific discharge q = Q/A Figure from Hornberger et al. (1998)

  11. q = - Kgrad h Equivalent Porous Medium (epm) Representative Elementary Volume (REV) REV

  12. Water balance equation Law of Mass Balance + Darcy’s Law = Governing Equation for Groundwater Flow --------------------------------------------------------------- div q = - Ss (h t) +R* (Law of Mass Balance) q = - Kgrad h (Darcy’s Law) div (K grad h) = Ss (h t)–R*

  13. Transient Water Balance Equation Inflow = Outflow +/- Change in Storage Steady State Water Balance Equation Inflow = Outflow Recharge Discharge Outflow - Inflow = Change in Storage

  14. S =  V / A  h S = Ss b Ss = specific storage Storage Terms h h b Unconfinedaquifer Confinedaquifer Specific yield = Sy Storativity = S Figures from Hornberger et al. (1998)

  15. V = Ssh (x y z) t t W OUT – IN = x y z REV = change in storage = -V/ t S =  V / A  h Ss = S/b here b =  z Ss = V / (x y z h)

  16. OUT – IN =

  17. Law of Mass Balance + Darcy’s Law = Governing Equation for Groundwater Flow --------------------------------------------------------------- div q = - Ss (h t) +W (Law of Mass Balance) q = - Kgrad h (Darcy’s Law) div (K grad h) = Ss (h t)–W

  18. 2D confined: (S = Ss b & T = K b) 2D unconfined:

  19. Figures from: Hornberger et al., 1998. Elements of Physical Hydrology, The Johns Hopkins Press, Baltimore, 302 p.

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