The equation of groundwater flow in fixed and deforming coordinates


  • Hilton H. Cooper Jr.


Two forms of the equation of flow of a compressible liquid in an elastic porous medium are derived by considering mass conservation in (1) a control volume whose boundaries are fixed in space and (2) a control volume that deforms and moves through space when the material deforms. The first method yields a form of the equation that necessarily involves the velocity of the grains of the medium. The second yields a form that does not involve the grain velocity. Jacob's equation is found to be correct when negligible terms are omitted.