Various technological fluids, such as drilling muds, drill-in fluids, fracturing fluids, spacers, washes and cement slurries are used in the wellbore drilling process. The fundamental issue, which needs to be addressed in order to become acquainted with the phenomena occurring during fluids flow through a circulatory system, is to establish mutual dependencies between a stream of fluid being pumped and flow resistances. The awareness of these dependencies enables the optimisation of hydraulic parameters in order to minimise costs and maximise drilling works safety. This article presents rheological models of drilling fluids and proposes the application of a new rheological model, not used in the drilling industry so far, namely the Vom Berg model. The model has been presented in other publications; however, there is an unsolved and unpublished problem of determining the effect of rheological parameters of the model on the value of resistance to laminar and turbulent flow. In this article, algorithms and Cloud-Native application enabling numerical determination of rheological properties of the Vom Berg fluid are presented. What is more, an algorithm for calculating pressure losses during the laminar flow of fluid in a pipe is provided. Taking an example from the industry, a practical application of the proposed calculation methodology is presented.