APPENDIX A: HYDRAULIC CONDUCTIVITY AND PERMEABILITY ESTIMATION

186

APPENDIX A: HYDRAULIC CONDUCTIVITY AND

PERMEABILITY ESTIMATION

187 Using Darcy’s Law

𝑸 = 𝑲𝑰𝑨

where: Q = flowrate (volume/time) (mL/s) K = hydraulic conductivity (cm/s) I = hydraulic head (h/L)

A = cross-sectional area of the membrane (cm²)

solving K,

𝐾 =

_𝐼𝐴^𝑄

=

^{(0.3 𝑚𝐿𝑠 )(1 𝑐𝑚31 𝑚𝐿)}

(^{80 𝑚𝑚}_{6 𝑚𝑚})(6400 𝑚𝑚²)(_{10 𝑚𝑚}^{1 𝑐𝑚} )²

𝑲 (𝒉𝒚𝒅𝒓𝒂𝒖𝒍𝒊𝒄 𝒄𝒐𝒏𝒅𝒖𝒄𝒕𝒊𝒗𝒊𝒕𝒚) = 𝟑. 𝟓𝟏𝟔 𝒙 𝟏𝟎^!𝟒𝒄𝒎

𝒔 𝒐𝒓 𝟑. 𝟓𝟏𝟔 𝒙 𝟏𝟎^!𝟔𝒎 𝒔 IN

OUT

L = 6 mm

(membrane thickness) 80 mm

80 mm

membrane active surface area = 6400 mm ² h

188

Relationship between hydraulic conductivity and permeability

𝑲 = 𝒌 𝜸 𝝁

where: K = hydraulic conductivity (cm/s) k = permeability (m²)

𝛾 = unit weight (Pa/m) 𝜇 = dynamic viscosity (Pa-s)

K = 3.516 x 10^-4 cm/s (computed)

𝛾 0.5M NaCl at T = 25.0oC = 𝜌 𝑔 = @2160_&^$%_!E @9.81_'^&_"E = 21,189.6⁽⁾_&

𝜇 0.5M NaCl at T = 25.0oC = 928.6 𝜇𝑃𝑎 ∙ 𝑠 = 0.9286 𝑃𝑎 ∙ 𝑠

solving k,

𝑘 = 𝐾

^!_"

=

3.516 𝑥 10^{!* +&}_' (,../01 ()∙' /4,40..1^#$_%)

𝒌 = 𝟏. 𝟓𝟑𝟖 𝒙 𝟏𝟎

^#𝟏𝟎

𝒎

^𝟐

Based on the calculations, the estimated value of permeability is quite low and will NOT fall within the limits for pervious concrete.