Besides the state equation there exists another cubic algebraic equation about μf in the form of${\mu }_f^3$ + pμf + q = 0, which relates parameters, temperature T, chemical potential μf, and net quark number nff (flavor f) for a baryon-rich quark-gluon plasma (QGP). A criterion may be acquired simply according to Cardan formula of the solution of the above equation, which gives naturally a condition: if n$\ll 2\pi T^3/3\sqrt{3}$, one may approximately use the conservation of specific entropy, and then the set of hydrodynamic equation of baryon-rich QGP may be reduced to the set of hydrodynamic equation for baryon-free QGP.