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Recent researches suggest an analogy between the theory of general relativity (GR) and fluid dynamics. As a result of this analogy, the Navier-Stokes equations and Einstein field equations are the same, and it is possible to study the properties of space-time by using fluid mechanics. In this paper, we present a new model to describe gravitational phenomena by an inviscid and compressible fluid called space-time fluid (STF). The analogy method is used to obtain the gravity field of both static and rotating masses from the flow field of STF around static and rotating point sinks. In addition, event horizons and the ergosphere of stationary black holes are defined based on our STF model. Then, we compare hydrodynamic forces exerted on a test particle with gravitational forces in the gravitoelectromagnetic approximation of the GR. As a natural consequence, it is shown that inertial and gravitational masses are equivalent in this analogy. Finally, using the aspect of fluid dynamics, Mach's principle, weak equivalence principle, and information discontinuity on the event horizon are discussed.