The reaction kinetic rate and mass transport play an important role in the sizing and scale-up of reactors. The Damköhler's dimensionless number ( Da ) is the quotient of these effects. A new interpretation of Da as a local property is introduced Da(x,y,z,t) . A new graphical methodology is proposed for the sizing and scale-up of unidirectional flow reactors and CSTRs. The partial differential equation (PDE) and algebraic that describe the continuity within these reactors transform into dimensionless variables, and the conversion at the output is expressed as a function of the conditions at the input Da0 . The operating conditions as volumetric flow, residence time; design variables as reactor volume; and intrinsic reaction rate are involved in Da0 . The equations are solved numerically to develop the design charts Da0 vs X. The design volume is linear with Da0 , and the conversion is obtained from the charts ( Da0 vs X) or vice versa. Using these charts avoids the analytical or numerical solution of the PDE that governs the unidirectional flow reactors becoming an easy tool for scale-up. The article portrays how to use these diagrams. Reactors with Da0 < 0.1 have a low conversion per pass, the charts also allow estimating the number of recirculations required as a function of the overall conversion. Reactors with the same conversion have the same Da0 , both laboratory and industrial scale. Then, the Da number is presented as a fundamental parameter for design and scaling-up these reactors.