We report on the design of microchannels made of glass capillary coated with polymer brushes elaborated by the so-called "grafting-from" technique. We present measurements of velocity profiles for pressure-driven flows of water in such "hairy" capillaries. We show that the flow reduction induced by the presence of the brush is unexpectedly greater than what could be anticipated from simple geometric arguments on the reduction of the effective capillary diameter or from predictions by models describing the brush layer as a poro-elastic boundary.