696 PLANT GROWTH AND PLANT COMMUNITIES 



sures, and the intrinsic properties of the fluid and of the material com- 

 prising the tube. Such analytical description becomes more difficult if 

 the flow is turbulent, if the flux is time-dependent, or if the medium 

 through which the flow occurs is geometrically complex or only partly 

 filled by the flowing fluid. Complexity of the flow equation thus may 

 arise because of the nature of the function needed to describe either 

 the F, the k, or the P in the General Transport Law. In arriving at an 

 adequate analytical expression for many of the flow phenomena en- 

 countered in the soil-plant system, complex functions are frequently 

 encountered for each .of the three terms of the General Transport Law. 

 As a consequence, only elementary progress has been made to date in 

 the quantitative study of such phenomena. 



In addition to the three parameters appearing in the General 

 Transport Law, the analysis of flow also involves some expression for 

 the volume-concentration of the material being transported. In the case 

 of water flow in soil this parameter is the volume-fraction of water, 

 designated herein as C. For non-steady-state flow through unsaturated 

 porus media such as soil, C may change with time at various points 

 along the flow path; i.e., the porous medium may be acting as a source 

 or a sink for the fluid being transmitted. In such cases the dependence 

 of C on location and time as well as on the potential must be specified. 

 Inasmuch as k, P, and C are interdependent, it is useful to examine the 

 functional relations that may exist among them. In the study of soil- 

 moisture behavior, the system can be most usefully described in terms 

 of the C ^ f(P) and the k = f(P) relationships. A derived parameter, 

 S = dc/dp, is called the specific yield. The S =z f(P) function is a 

 third useful relation for describing soil-moisture behavior. The flow 

 equation may be written with the potential gradient replaced by a 

 concentration gradient. In this form the transmission constant, k, is re- 

 placed by the diffusivity, D, which is defined as D ^ pk/p^S, where p 

 and ps are the density of the fluid and the bulk density of the porous 

 medium, respectively. The selection of the concentration-dependent or 

 the potential-dependent form of the flow equation is largely determined 

 by the type of data available. 



Considerable progress in the study of flow phenomena has been 

 made by investigators studying the flow of fluids in saturated porous 

 media. In porous media such as soil or oil-bearing rocks it is necessary 

 to determine k experimentally because of the geometric complexity of 

 the voids. The classic work of Darcy, conducted 100 years ago, was the 

 straightforward application of the General Transport Law to the flow 

 of water through a saturated porous medium. Darcy s Law continues 

 to serve as the basic principle for the study of steady-state laminar 

 flow through saturated porous media. Numerous attempts to determine 

 the transmission coefficient analytically from such media parameters as 



