In this work a dimensionless form of the equations of motion used for dynamic simulation of turbomachine components is presented. The dimensionless equations are obtained from the governing equations of unsteady compressible viscous one-dimensional flow by defining three variables of state that have a direct link with the variables measured in the experimental investigations: total pressure, total temperature and the Mach number. The new dimensionless form of equations presents the characteristics of generality that makes it easy to apply to many fluid dynamic problems. The application of dimensionless equations to more complex systems can be simplified and made easier by using the lumped parameter discretization method. Another important feature of the dimensionless system of equations is that it can be solved explicitly without any iterative process within each step of integration, thus making it easier and faster during dynamic simulations. The equations can be further simplified in the case of stationary flows for which some examples of application are given in order to highlight the generality of the method and its ease of application.