Darcy's experiments and the deviation to nonlinear flow regime

Many important technological and natural processes involving flow through p orous media are characterized by large filtration velocity It is important to know when the transition from the linear flow regime to the quadratic fl ow regime actually occurs to obtain accurate models for these processes. By interpreting the quadratic extension of the original Darcy equation as a m odel of the macroscopic form drag, we suggest a physically consistent param eter to characterize the transition to quadratic flow regime in place of th e Reynolds number, Re. We demonstrate that an additional data set obtained by Darcy, and so far ignored by the community, indeed supports the Darc equ ation. Finally, we emphasize that the cubic extension proposed in the liter ature, proportional to Re-3 and mathematically valid only for Re much less than1, is irrelevant in practice. Hence, it should not be compared to the q uadratic extension experimentally observed when Re greater than or equal to O(1). [S0098-2202(00)01703-X].