An efficient and simple method to compute one-dimensional steady-state and transient turbulent single-phase flows across singularities (e.g., sudden contractions or expansions in ducted flows) is presented. This method accounts for the effective inertia of a fluid at a constriction and the irreversible pressure losses caused by recirculation zones generated near a singularity. For selected singularities of technical interest, algebraic expressions for the equivalent inertia lengths and the hydraulic resistance coefficients are presented. The implementation of the method into one-, two-, and three-dimensional numerical fluid dynamics codes is explained and the limitations of the method are discussed. The method is also extended to two-phase flow where additional flow parameters characterizing the momentum exchange between the phases play a role.