A transport equation for a solution flow increasing due to osmosis inside a hollow cylindrical fibre is derived. The equation can be applied for either direct, pressure-retarded or reverse osmosis, when the membrane is highly selective. This transport equation is used to study theoretically the net power delivered, and the entropy generated by two different concepts of a pressure-retarded osmosis power production system. As a result, the system can be optimized either by maximizing the net power or maximizing the ratio (Psi) between the net power and entropy generation. In both cases the optimal values of the initial hydrostatic pressure difference between the inner and the outer sides of the fibre, the initial velocity of the solution and the fibre length could be specified. However, in some cases these two methods of optimization result in remarkably different optimal values. The resulting net power, when Psi was maximized, was found to drop to less than half the maximum net power. The local entropy generation was found always to result in a minimum value at a certain longitudinal position inside the fibre.