The equilibrium behavior of dilute polyelectrolyte solutions has previously been successfully described by scaling theories based on the electrostatic blob model of de Gennes et al. in terms of just two scaling variables: the number of blobs X, and the Debye screening length relative to the size of the blob Y, where both X and Y are determined from the properties of the polyelectrolyte, and the solvent. We show, in the context of Brownian dynamics simulations, that (i) the scaling picture at equilibrium can be accurately reproduced by a bead-spring chain model and that, (ii) with the inclusion of the characteristic shear rate beta as the additional scaling variable in shear flow, the equilibrium blob model provides a framework to obtain parameter free data collapse, even for theological properties. As a result, regardless of the degree of coarse-graining, i.e., the number of beads N in the bead spring chain model (provided N >= X), identical results for the shear rate dependence of viscosity are obtained, so long as X, Y, and beta are the same.