We study pulsatile pressure-gradient driven flow through an annular confinement under the influence of streaming potential. Our study considers zeta potentials beyond the traditional DebyeHuckel limits, and takes care against aphysical predictions stemming from traditional Boltzmann statistics through modifications involving the finite size of the ionic species (steric effects). With these considerations, we demonstrate, rather non-intuitively, that an intrinsic asymmetry may be manifested in the velocity profile of the flow through the annulus, as a consequence of the streaming potential effects in presence of Steric interactions. Our findings are likely to provide a new design basis for micro- and nano-scale flow devices involving annular geometries.