We investigate the flow-induced linear and ring polymer translocation through nanopores using a hybrid simulation method that combines a lattice-Boltzmann approach for the fluid with a molecular dynamics model for the polymer chain. Our results illustrate that the critical velocity flux for the linear and ring chain exhibits characteristic differences: for the linear chain, the critical velocity flux is independent of the chain length, which is in agreement with previous work; whereas, for the ring chain, the critical velocity flux decreases slowly with the increase of the chain length and gets closer to the critical velocity flux of the linear chain. In addition, we find that the ring chain shows much faster translocation compared to the linear chain with the same chain length. Moreover, the ring chain and the folded linear chain display the similar configurational deformation during the translocation. These results above indicate that with the increase of the chain length, the separation between the linear and ring polymers in the flow-induced translocation through nanopores becomes increasingly difficult.