The equation for filtration at constant rate, while building a cake, enabled to model data from two experimental units of drastically different sizes. Both units used an ultrafiltration hollow-fibre membrane, operated at slight vacuum, and continuously cleaned by air injection. They filtered biologically treated urban wastewater or preflocculated and settled effluent. The transmembrane pressure against time curves were straight lines in all the cases with or without gas sparging. The straight-line gradient divided by the turbidity of the suspension to be filtered provided a precise measurement of fouling. Without gas sparging, this quantity was of the same order of magnitude in both units. With gas sparging, this quantity, linked to the energy dissipation in the vessel, showed that air injection was much more effective in the larger unit. (C) 2003 Elsevier B.V. All rights reserved.