The definitions of hydraulic head and soil water potential in chapter 1 assumed equilibrium. However, the primary motivation was to develop a background useful to describe dynamic systems. If a system is in equilibrium, no flow will occur; otherwise, flow will occur from regions of high to low hydraulic head. The primary flow equation will be Darcy’s law. When Darcy’s law is combined with conservation of mass, the result is a continuity equation that can have several different forms. We will refer to all of those forms generically as soil water flow equations. Generally, for unsaturated conditions, the soil water flow equation is called the Richards equation. A starting point is to examine two classical relationships from fluid dynamics, the Bernoulli and the Poiseuille laws. Bernoulli’s law relates the total potential for ideal fluids and is commonly derived in introductory physics and fluid mechanics texts (see Serway, 1990). Assumptions include an ideal fluid (non-viscous), which is one that is incompressible and which exhibits steady and irrotational flow. For these conditions, the sum of gravitational, pressure, and inertial energy at positions S1and S2 are the same along any streamline For a real fluid, viscosity causes a loss of energy as friction that must be overcome. Additionally, for most problems of interest in soils, the velocity head will be negligible compared with the pressure and gravitational terms.
Towards new soil water flow equations using physics‐constrained machine learning
