With over 30 million people worldwide in need of assistive devices, there is a great need for low-cost, high performance prosthetic technologies in the developing world. A majority of the hydraulic dampers used in prosthetic knee designs are highly specialized, expensive, require regular maintenance, and are incompatible for use with low-cost, single-axis prosthetic knees popular in developing countries. In this study, optimal damping coefficients were computed based on a theoretical analysis of gait, specifically during the transition from the stance to swing phase of human walking when a large damping torque is needed at the knee. A novel rotary hydraulic damper prototype was designed using high-viscosity silicone oil and a concentric meshing of fins for shearing the oil. The prototype was validated experimentally to provide the desired damping torque profile. For preliminary, user-centric validation of the prototype, a gait study on one above-knee amputee in India was conducted with four different damping magnitudes. Feedback from the subject validated the optimal damping torque magnitude predicted for minimizing gait deviations and for enabling able-bodied knee kinematics. The new rotary hydraulic damper design is novel, passive, and compatible with low-cost, single-axis knee prostheses.