This study shows that the thermo-hydraulic behavior of several supercritical fluids are nearly identical when their thermophysical properties are non-dimensionalized with adequate fluid-dependent scaling constants. Hence, the transport equations are shown to be solvable as a function of dimensionless numbers (e.g., supercritical Reynolds number), from which the solution to other fluids can be scaled, a possibility only available for constant-property fluids thus far. The fluid-specific scaling coefficients are determined by squared-error minimization for triatomic fluids for various thermodynamic states near the critical point. The proposed non-dimensionalization is demonstrated by showing that the temperature and velocity fields, and their respective gradients, of supercritical CO2 flowing inside a heated-wall channel are nearly identical whether the transport equations are solved with the actual equation of state of CO2 or with dimensionless properties scaled from water. Finally, the fluid-specific scaling constants are shown to be determinable by closed-form expressions.