HYDRAULIC CONDUCTIVITY, K m/s
Darcy's Law:
qv = - Kh
HYDRAULIC CONDUCTIVITY, K m/s
K
= kg/?
= kg/ units of velocity
Proportionality constant in Darcy's Law
Property of both fluid and medium
see D&S, p. 62
HYDRAULIC POTENTIAL ():
= g h = gz + P/w
energy/unit mass
cf. h = energy/unit weight
Consider incompressible fluid element @ elevation zi= 0 pressure Pi i and velocity v = 0
Move to new position z, P, , v
Energy difference: lift mass + accelerate + compress (= VdP)
= mg(z- zi) + mv2/2 + m V/m) dP
latter term = m (1/)dP
Energy/unit mass = g z + v2/2 + (1/)dP
For incompressible fluid ( = const) & slow flow (v2/2 0), zi=0, Pi = 0
Energy/unit mass: = g z + P/ = g h
Force/unit mass = = g - P/
Force/unit weight = h = 1 - P/g
Rewrite Darcy's Law: Hubbert (1940, J. Geol. 48, p. 785-944)
qm = qv =
k
g
-
P
=
k
[force/unit
mass]
qm
Fluid flux mass vector (g/cm2-sec)
k rock (matrix) permeability (cm2)
fluid density (g/cm3)
[.....] Force/unit mass acting on fluid element
1/
where Kinematic Viscosity
= ?/ cm2/sec
Rewrite Darcy's Law: Hubbert (1940; J. Geol. 48, p. 785-944)
qv
=
k [g - P]
= k [ force/unit vol]
q
v Fluid volumetric flux vector (cm3/cm2-sec) = qm /
k rock (matrix) permeability (cm2)
[.....] Force/unit vol. acting on fluid element
1/
where Kinematic Viscosity
= ?/ cm2/sec
Rewrite Darcy's Law: Hubbert (1940; J. Geol. 48, p. 785-944)
qv
=
k [g - P]
= k [gh]
[force/unit vol]
= kg h
= Kh
................
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