The new mathematical model of the fluid flow in T-part with adjacent branch of the arbitrary angle is introduced in this article. This paper relates to the previous author's research. The previous work was focused only on the case with the angle of the adjacent branch 90°. The aim of this work is to explain main ideas applied during the derivation of the mathematical model of T-part. This mathematical model can be used as a tool for solution of steady and unsteady flow in pipeline systems. The coefficients describing fluid flow in the T-part are specified in this model. They can be used in the designing of the optimal shape of the pipe bifurcation as a criterion for the different T-part designs comparison. This research is in the process now therefore only theory of extended mathematical model is presented in this paper. The measurements and the numerical modeling of the fluid flow in this T-part are going to be done soon.