Modelling the fill height gradient in Archimedes screw pumps

State-of-the-art design for Archimedes screw pumps (ASP) remains rooted in heuristic models established by Muysken in 1932. While functionally robust for nominal conditions, these historical standards do not account for the ‘fill height gradient’ (FHG) – a dynamic hydraulic phenomenon where bucket water levels decrease during axial transport. This paper presents the first quantified performance prediction model, the FHG model, to explicitly document and model these bucket transport gradients. Leveraging a comprehensive dataset from 21 laboratory-scale screws, a novel optical differential volume method to experimentally isolate gap leakage, and a 33.7-fold geometric scaling analysis (Do = 0.15 m to 5.00 m), we demonstrate that the FHG model provides significant accuracy gains over current constant fill height (CFH) assumptions. This work represents the first modernization of ASP design standards since the early twentieth century, providing a validated framework for twenty-first-century industrial and wastewater applications.