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Darcy s Law 1856

Units. Hydraulic Conductivity (K)

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Darcy s Law 1856

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    2. Units Hydraulic Conductivity (K)[L/T] Specific Storage (S) . [1/L] Hydraulic Head Elevation (h) [L] Pressure head (P/?g) .[L] Velocity head (v2/2g) [L] negligible 2

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    4. 4 DARCYS LAW q = Darcy flux or hydraulic flux (L/T) K = Saturated hydraulic conductivity (L/T) dH = difference in total head (L) dl = distance increment (L) dH/dl = I = hydraulic gradient (unitless)

    5. 5 Darcy Law

    6. 6 Darcy Law

    7. 7 DARCYS LAW Q = total flow (L3/T) A = total cross-sectional area (L2) Q = qA

    8. 8 DARCYS LAW Actual water velocity is higher than q and called the pore water velocity, v. v = q/n n = porosity

    9. 9 Example Consider measurements taken at two monitoring wells in an unconfined aquifer. The wells are located 200 m apart. The average K of the aquifer is 3.5 m/day. The observed values are 23.1 m and 24.2 m. Find the total flow across the aquifer and the transmissivity.

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    11. 11 Example q = -K dh/dx Using consistent units of meters and days, h1 = 23.1, h2=24.2, K=3.5 q = -K . (h2-h1)/(x2-x1) = -3.5 . (24.2-23.1)/(200-0) = - 0.01925 m/day

    12. 12 Since q is negative, flow is opposite to the direction of x. This is correct because flow occurs from high potential to low potential. Q = qA = 0.01925 x 0.5(24.2+23.1)x1 = 0.455 m3/m-day T = KD D = 0.5(24.2+23.1) = 23.65 m T = 3.5x23.65 = 82.8 m2/day

    13. Deriving flow equations 13

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