“…where A, D, and f , are the area, diameter, and friction factor of the pipeline, respectively, ρ is the density of the fluid, and a v sin θ is the vehicle acceleration component along the line axis. The PDEs should be solved because the transient state fluid flow is unsteady in a pipe of CPSs, especially in the start-up process [37,141]. However, since there is no general solution for PDEs, the PDEs can be transformed by the method of characteristics, which is an application of a lagrangian multiplier method using the two PDEs, to two sets of two ordinary differential equations in a two-dimensional (pipeline and time axises) plane, as shown in Figure 9.…”