Using Parsons-type scaling, the Onsager theory for the isotropic-nematic (I-N) transition of rigid-rod lyotropic polymer liquid crystals is combined with the equation of state for hard-sphere-chain fluids of Chapman et al. and that of Hu et al. The equation of Hu et al. gives the I-N transition pressure and density in good agreement with computer simulation by Wilson and Alien for a semi-flexible hard-sphere chain consisting of seven segments. For real semi-flexible polymers, we follow the Khokhlov-Semenov theory of persistent chains that introduces chain flexibility into the Onsager theory. Using a consistent procedure to regress the equation-of-state parameters, the equations of Chapman et al. and Hu et al. are also compared with the theory of DuPre and Yang that uses the equation of Lee for hard spherocylinders. These models are compared with experiment for two binary polymer solutions containing poly(hexyl isocyanate) and another solution containing polysaccharide schizophyllan. The concentration of polymer at the I-N transition is predicted as a function of the molecular weight of polymer. All models perform similarly and show semi-quantitative agreement with experiment.