Tesla valves are passive hydraulic devices capable of producing directional flow resistance without moving components, making them attractive for applications in microfluidics, thermal systems, and high-reliability hydraulic circuits. Despite extensive experimental and numerical studies, an analytical formulation capable of describing the hydrodynamic behavior of Tesla valves under varying operating and geometric conditions remains limited. In this work, a comprehensive analytical model is developed to describe the pressure losses, flow redistribution, and diodicity behavior of Tesla valves through a physics-based formulation derived from conservation laws, dimensional analysis, and inertial scaling principles. The proposed model incorporates the influence of Reynolds number, flow partition, geometric ratios, branch inclination angle, and number of diode stages within a unified nonlinear framework. A closed structural equation is obtained that relates hydraulic losses and directional asymmetry to the internal geometry of the valve. The formulation reveals the existence of geometric and energetic constraints governing rectification efficiency, including bounds associated with stage number, channel scaling, and angular momentum exchange. The results show that Tesla valve performance emerges from a delicate balance between inertial amplification and dissipative mechanisms, providing an analytical framework for the design and optimization of Tesla-type hydraulic systems across multiple scales.
