Flow leaks renormalization

Flow leaks are small devices that generate a well-determined flow when subject to a pressure differential (feed pressure). Such devices are widely used in the industry for the easy generation of flows, which can be used for several applications. In order to be correctly included in a Quality Management System (QMS), they need to be calibrated against a reference flow. Such calibration depends on the feed pressure and on the fluid density through a complex relation which can be derived from the modified Darcy law, therefore results of a calibration performed in a given condition are not necessarily valid when the leak is used in different conditions (e.g. different atmospheric pressure, ambient temperature). In the present paper we will show how to obtain a correct renormalization of the calibration results, which, if applied in use, allows to compute precisely the actual flow rate generated by the leak. The renormalization is based on the modified Darcy law, and therefore requires the determination of the leak permeability. A mathematical description of the renormalization will be presented. Additionally, a method for the experimental determination of the permeability will be discussed The effect of the renormalization on the output of the leak will be demonstrated through a set of example cases, obtained in various environmental conditions within our laboratory. It will be shown that, first the calibration uncertainty can be reduced dramatically by applying the correct normalization, and second that the in-use uncertainty can be brought to be of the same order of magnitude as the calibration uncertainty