Two hydraulic losses take effect at the junction point of three cylindrical conduits. These two quantities are considered to be functions of the three signed flow rates and two geometrical parameters: the cross-sectional area ratio and the angle between the main conduit and branch tube. A new design of experiment is developed for exploring the parameter space with continuous response surfaces, which cover both dividing and combining flow regimes with a general trigonometric formula. The loss coefficients are determined by using a steady-state, single-phase, three-dimensional (3D) computational fluid dynamics (CFD) model. To help the analytical treatment, a new reference velocity formulation is introduced. The new loss coefficient formula is validated against known empirical correlations for different junction types and flow directions. The obtained continuous solution promotes the applicability of the resistance model in hydraulic network models.