In this study, we consider the ideal aggregate with quadratically increasing permeability κ=k₂r² and derive the analytical expression of the stream function within the porous aggregate by incorporating the Brinkman and continuity equations. The hydrodynamic properties of the aggregate are investigated by taking account of the hydrodynamic radius, settling velocity, and fluid collection efficiency, which are found to be solely dependent on the permeability prefactor k₂. The fractal dimension D_f and prefactor k₂ of the ideal aggregate are found to be 5/3 (=1.67) and 0.20, respectively, and well describe the hydrodynamics of aggregates formed in the diffusion-limited-cluster-aggregation (DLCA) regime. More important, hydrodynamic similarity between the ideal aggregate and impermeable solid sphere is discovered in terms of variations of the hydrodynamic radius, settling velocity, and fluid collection efficiency with respect to the aggregate radius.