Small moons (moonlets) embedded in the rings of Saturn cause S-shaped density structures in their close vicinity called propellers. These structures have been predicted by Spahn and Sremcevic (2000) and Sremcevic et al. (2002). N-body simulations later not only confirmed the formation of a propeller but additionally showed the appearance of wakes induced by the moonlet in the region adjacent to the S-shaped gaps (Seiss et al., 2005; Sremcevic et al., 2007; Lewis and Stewart, 2009). One of the biggest successes of the Cassini mission is the detection of propeller structures in images taken by the Imaging Science Subsystem (ISS) of the spacecraft (Tiscareno et al., 2006). Here, we present isothermal hydrodynamic simulations of moonlet induced propellers in the A ring of Saturn. These allow for a combined treatment of gravitational scattering and diffusion and denote a further development of the original model (Spahn and Sremcevic, 2000; Sremcevic et al., 2002) where gravitational scattering of particles by the moonlet (creating the structure) and diffusion described by the hydrodynamic equations (smearing out the structure) had to be treated separately. We find excellent agreement between these new hydrodynamic and corresponding N-body simulations. Furthermore, the hydrodynamic simulations confirmed the scaling laws predicted by Spahn and Sremcevic (2000) and an analytical solution derived by Sremcevic et al. (2002). Finally, we match results from hydrodynamic simulations of the giant propeller Bleriot to two stellar occultation observations by the Cassini Ultraviolet Imaging Spectrometer (UVIS). Best fits of the optical depth profiles are achieved using a Hill radius of 600 m and a kinematic shear viscosity of the surrounding ring material of 350cm$^2$/s. The results imply a moonlet diameter of about 900 m.