THEORETICAL SOLUTION OF THE UNSTEADY UNSATURATED FLOW PROBLEMS IN SOILS

Synopsis The mathematical description of the state of a moving fluid is effected by means of functions which give the distribution of the fluid velocity v = v(x, y, z, t) and of any two thermodynamic quantities pertaining of the fluid. These two quantities can be taken to be the pressure p(x, y, z, t) and the density q(x, y, z, t). The above quantities v, p and q are functions of the coordinates x, y, z and of the time t. Dealing with flow of water through soils the following three general laws of mechanics but in hydrodynamic terms are applied to all kinds of water movement: 1) The dynamical equation of motion which specifies the dynamical reactions of the fluid to pressure gradients or external forces (Darcy's equation replacing the Navier-Stokes relations which are the hydrodynamical restatement of Newton's first law of motion), 2) The equation of continuity which is the analytical statement of the law of the conservation of matter taken from mechanics; and 3) The equation of state which defines thermo...