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While compressible flow theory has relied on the perfect gas model as its workhorse for the past century, compressible dynamics in dense gases, solids and liquids have relied on many complex equations of state, yielding limited insight on the hydrodynamic aspect of the problems solved. Recently, Le Métayer and Saurel studied a simple yet promising equation of state owing to its ability to model both the thermal and compressibility aspects of the medium. It is a hybrid of the Noble-Abel equation of state and the stiffened gas model, labeled the Noble-Able Stiffened Gas (NASG) equation of state. In the present work, we derive the closed form analytical framework for modelling compressible flow in a medium approximated by the NASG equations of state. We derive the expressions for the isentrope, sound speed, the isentropic exponent, Riemann variables in the characteristic description, and jump conditions for shocks, deflagrations and detonations. We also illustrate the usefulness by addressing the Riemann problem. The closed form solutions generalize in a transparent way the well-established models for a perfect gas, highlighting the role of the medium's compressibility.