Deducing a Drain Spacing Formula by Applying Dimensional Analysis and Self-Similarity Theory

For designing a steady-state drainage system, a drain flow formula coupled with the Dupuit-Forcheimer form of the differential equation of groundwater flow is used. First, the most-applied drain flow formulas in steady-state conditions are reviewed and compared using as a dependent variable the ratio between the maximum water table height and the distance between two lines of parallel drains. These equation are also tested using experimental field data measured in three plots drained by surface pipe drains having different values of drain spacing. Then, applying the dimensional analysis and the self-similarity theory, a new drain spacing formula is theoretically deduced and compared with the solutions available in the literature. Finally, the analysis shows that the most-applied drain flow formulas have the general mathematical shape deduced by dimensional analysis and self-similarity condition.