The solution viscosity of neutral polyacrylamide (PAM), the partially hydrolyzed polyacrylamide (70% HPAM), and polyacrylic acid (PAA) were measured concurrently with the apparent diffusion coefficient in the dilute and semidilute concentration regimes. We identified the scaling relation eta - eta(s) = A/D in the semidilute regime, where eta is the solution viscosity, eta(s) is the solvent viscosity, D is the coefficient of the slow diffusion mode obtained from dynamic light scattering, and A is a prefactor found to have a unique value of similar to 1.0 x 10(-8) cP cm(2)/s. The scaling relation as well as the prefactor are independent of the the ionic strength, the solvent quality, the molecular weight, the charge density, the polyelectrolyte, and salt concentrations. For the neutral PAM, the product [eta - eta(s)]D is proportional to the polyelectrolyte concentration c(p), consistent with Rouse theory and previous experimental findings.