Polyelectrolytes (PEs) are charged polymers in polar solvents. Classical scaling theories suggest that the viscosity η for semidilute unentangled PE solutions in θ solvents obeys the empirical Fuoss law η∝n_{p}^{1/2} in the "salt-free" regime, and η∝n_{p}^{5/4} in the regime affected by added salt, where the polymer concentration n_{p} is defined as the number of monomers per volume. However, recent experiments have also reported η∝n_{p}^{0.68} and η∝n_{p}^{0.91}, which are at odds with the classical scaling theories. To rationalize the four distinct scaling laws, we probe the electrostatic energy per monomer under the influence of salt and their contributions to the viscosity of PE solutions. We identify four consecutive regimes dependent on the magnitude of the ratio of the polymer concentration n_{p} to the salt concentration n_{s}, which capture the unexplained observations, and provide physical insights for the influence of salt contamination and added salt on the properties of both weakly and strongly charged semidilute unentangled PE solutions.