Equation for one‐dimensional vertical flow of groundwater: 1. The Rigorous Theory

摘要: A new mathematical derivation of the one-dimensional flow equation in an elastic, saturated, porous medium is presented. The approach involving consideration a fixed elemental volume coordinates developed by starting from both Lagrangian and Eulerian definitions position vector. confusion existing about these two fundamental points view has so far led to theoretically erroneous results. formulations prove be equivalent provide same outcome if they are correctly interpreted consistently applied. rigorous equation, compared with Cooper's (1966) turns out contain additional nonlinearity resulting correct expansion partial spatial derivative grain velocity. It also shown that based on deforming element simple straightforward, since it does not introduce velocity into development. However, needs particular definition for compressibility different classical one. proved compressibilities equal; their link derived.