Kriging, a technique originating from geostatistics, is employed to build black-box models to be used to predict a quantity of interest based on the values taken by some experimental factors. This attractive alternative to more popular techniques such as neural networks is first presented. It is then applied to the measurement of the flow in a water pipe from the observation of speed at given points of a cross section. A pure black-box model turns out not to be satisfactory, and two approaches are suggested for incorporating prior knowledge. The second one, which is more systematic also turns out to provide much better performance.