The hypothesis starts from considering the physical vacuum as a superfluid quantum medium, that we call superfluid quantum space (SQS), close to the previous concepts of quantum vacuum, quantum foam, superfluid vacuum etc. We usually believe that quantum vacuum is populated by an enormous amount of particle-antiparticle pairs whose life is extremely short, in a continuous foaming of formation and annihilation. Here we move further and we hypothesize that these particles are superfluid symmetric vortices of those quanta constituting the cosmic superfluid (probably dark energy). Because of superfluidity, these vortices can have an indeterminately long life. Vorticity is interpreted as spin (a particle's internal motion). Due to non-zero, positive viscosity of the SQS, and to Bernoulli pressure, these vortices attract the surrounding quanta, pressure decreases and the consequent incoming flow of quanta lets arise a gravitational potential. This is called superfluid quantum gravity. In this model we don't resort to gravitons. Once comparing superfluid quantum gravity with general relativity, it is evident how a hydrodynamic gravity could fully account for the relativistic effects attributed to spacetime distortion, where the space curvature is substituted by flows of quanta. Also special relativity can be merged in the hydrodynamics of a SQS and we obtain a general simplification of Einstein's relativity under the single effect of superfluid quantum gravity.