Dimensional analysis is a powerful tool used commonly to develop functional relations between variables affecting a physical system. Known for its versatility in incorporating several different energy domains, the method has allowed for dimensional manipulation of diverse parameters. However, the dimensional combinations developed have been, for the most part, strictly confined to static and time invariant systems. Expanding on the process we introduce a graphical approach to dimensionally model dynamic systems for design. Continuing this extension, we present a graphical and topological combination to illustrate the applicability of dimensional analysis as a state equation generation tool. This tool is comparable to conventional differential element analysis in system dynamics, but provides a systematic and visual approach to design modeling. Further, this exposition acts as a learning instrument where complex engineering equations are derived and interpreted through visual perception similar to a block diagram or flow chart. A dynamic system, in the form of a compressed air–water rocket, is also evaluated in this paper for elucidation.

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