The transport properties of fluids are significant quantities needed in engineering application. In this research, transport of water/dimethyl sulfoxide (DMSO) and water/acetone mixtures through armchair boron nitride nanotubes (BNNTs) was investigated using molecular dynamics simulations technique. The studied systems were composed of (6,6) BNNTs, water/DMSO or water/acetone mixtures. External pressures were applied in these systems along the x axis of the simulation cell. These simulations allow us to explore the mechanisms of transport and separation of solvents as organic contaminants. Without an applied pressure, DMSO or acetone molecules enter and occupy inside the BNNT, but their passing was not significant. For complete analysis of the systems, we calculated the density profiles of species, the radial distribution function of molecules, the retention time of solvents and their hydrogen bonds. The results showed that the transport of solvents through the BNNT was dependent on the amount of applied pressure.