Understanding the hydrodynamic properties of polymeric coatings is crucial for the rational design of molecular transport involving polymeric surfaces and is relevant to drug delivery, sieving, molecular separations, etc. It has been found that the hydrodynamic radius of a polymer segment is an order of magnitude smaller than its physical size, but the origin of this effect does not seem to be well understood. Herein, we study the hydrodynamic properties of polymeric coatings by using molecular dynamics simulations, navigated by the continuous Navier-Stokes-Brinkman model. We confirm that the averaged hydrodynamic radius of a polymer bead is about one order of magnitude smaller than its physical radius, and, in addition, we show that it exhibits a strong dependence on the degree of polymerization. We relate this variation of the hydrodynamic radius to the structural properties and hydrodynamic shielding by surrounding polymer beads. This is done by separating the effects originating from near and far beads. For the near beads, shielding is mainly due to the two nearest beads (of the same polymer) and leads to about a 5-fold reduction in the hydrodynamic radius. Assuming the additivity of the hydrodynamic shielding by far beads, we suggest a simple model, which captures correctly the qualitative behaviour of the hydrodynamic radius with the degree of polymerization. The revealed shielding effects provide important insights relevant to the advanced modelling of hydrodynamic properties of polymeric coatings.