|
41-2 PRINCIPLES S 2 1
<br /> where v = Q/A = fluid flux or macroscopic flow velocity, Q = volume flow
<br /> rate,A = cross sectional area normal to the flow direction and 41
<br /> Air-to-Water Permeability Ratio _ (k'/,?)(p + pgz)' [2]
<br /> where k' = permeability of the medium, ,7 = fluid viscosity, p = fluid pres-
<br /> sure, p = fluid density, g = acceleration of gravity and z = distance from
<br /> some reference elevation along the z coordinate which is oriented in the
<br /> R. C. REEVE ; direction of the gravity force field. The negative sign of equation [1] is
<br /> U. S. Salinity Laboratory, ARS, USDA used to indicate that the velocity vector increases in the direction of the
<br /> Rntierside,California 1 negative potential gradient. Assuming isotropic media and isothermal flow,
<br /> Darcy's law,from equations[1]and [2],may be written as
<br /> —(k'/n)(d/ds)(p + pgz) [3]
<br /> 3
<br /> where v, = volume flow rate or volume flux in the direction s.
<br /> 41-1 INTRODUCTION For all practical cases for liquids, p and g may be considered constant.
<br /> Equation [3]then becomes
<br /> The ratio of the permeability of soil to air and to water is an index of sta-
<br /> bility of soil structure. The permeability of a soil is first measured by using v, _ —(k'pg/,txdh/ds). [4]
<br /> Solving fork'
<br /> air, a fluid that has little effect on structure, followed by a measurement of j
<br /> permeability using water. Water, being a polar liquid, reacts with soil to ! k' _ (Qn/Apg)[1/(dh/ds)] [5]
<br /> cause a change in structure, resulting usually in a decrease of permeability. where h = p/pg + z = hydraulic head, where p/pg = pressure head and
<br /> This decrease results from swelling, slaking, deflocculation, dispersion, and z= position head. Hydraulic head has the dimensions of length (L) and
<br /> other structure-disrupting processes. The ratio of air-to-water permeability represents energy per unit weight of fluid (see section I I).The permeability
<br /> is a dimensionless number which reflects the magnitude of the breakdown k'is a property of the medium, independent of the fluid, and has the dimen-
<br /> of structure as a result of wetting. A value of one, which is rarely, if ever, sions of length squared (U).
<br /> obtained with soils, indicates no change in structure. Values greater than It is sometimes helpful and convenient to combine the permeability con-
<br /> one signify a deterioration of soil structure. stant with the properties of the fluid into a single proportionality constant
<br /> A knowledge of the stability of structure is useful in predicting the irriga- as follows:
<br /> bility of soils and assessing the effects of management practices and various
<br /> treatments on the physical condition of soil. The wet-sieving method of where v= _ —k dh/ds [6]
<br /> Yoder has been used extensively for evaluating soil structure. It involves
<br /> the determination of size distribution of water-stable aggregates after agita-
<br /> tion in water, whereas the air-water permeability method involves flow For water, this proportionality factor k between the flow velocity and the
<br /> through the pore openings of the soil. The latter method is perhaps more hydraulic gradient is termed "hydraulic conductivity" and has the dimen-
<br /> directly related to the physical problems that involve the movement of sions of velocity (LIT). Methods for measuring the hydraulic conductivity
<br /> gases and water into and through soils. are given in sections 13, 14, 15,and 16.
<br /> In the case of viscous flow of gases through a permeable medium, equa-
<br /> tion[3]must be modified to take into account gas compressibility.
<br /> 41-2 PRINCIPLES In all practical gas-flow cases, the gravitational term is negligible com-
<br /> pared to the pressure term. The gas-flow equation may, therefore, be writ-
<br /> Darcy's law forms the basis for permeability measurements of permeable ten as
<br /> media using viscous fluids. In the generalized vector form, it may be written 'The kinetic energy term, p0/2, which relates to the inertial forces in fluid-flow
<br /> as systems as treated in classical hydrodynamics, is negligible for viscous flow in
<br /> permeable media.
<br /> 520
<br />
|