The mathematical model of a 3-element centripetal-turbine hydrodynamic torque converter and analytic description of fluid flow inside the hydrodynamic torque converter are investigated.A new torus coordinate system is proposed so as to quantitatively describe fluid movement inside the hydrodynamic torque converter.The particle movement inside the hydrodynamic torque converter is decomposed into meridional component movement and torus component movement, and a universal meridional streamline equation is derived.According to the relationship between the converter wheel velocity polygon and its blade angle, a torus streamline differential equation is established.The universal meridional streamline equation is approximated with square polynomials.The approximation error curve is given and the percentage error is not greater than 0.86%.Considered as a function of polar angle, the blade angle cotangent of each converter wheel varies linearly with polar angle.By using integral calculus, torus streamline equations are obtained.As a result, the problem of difficult flow description of the hydrodynamic torque converter is solved and a new analytic research system is established. The mathematical model of a 3-element centripetal-turbine hydrodynamic torque converter and analytic description of fluid flow inside the hydrodynamic torque converters are investigated. A new torus coordinate system is proposed so to as quantitatively describe fluid movement inside the hydrodynamic torque converter. movement inside the hydrodynamic torque converter is decomposed into meridional component movement and torus component movement, and a universal meridional streamline equation is derived. According to the relationship between the converter wheel velocity polygon and its blade angle, a torus streamline differential equation is established. universal meridional streamline equation is approximated with square polynomials.The approximation error curve is given and the percentage error is not greater than 0.86% .Considered as a function of polar angle, the blade angle cotangent of each converter wheel varies linearly with polar angle.By using integral calculus, torus streamline equations are obtained. As a result, the problem of difficult flow description of the hydrodynamic torque converter is solved and a new analytic research system is established.