How fast can fluids squeeze through micro-pores?

We use a one dimensional symmetric exclusion model to study pressure and osmosis driven flows through molecular-sized channels, such as biological membrane channels and zeolite pores. Analytic expressions are found for the steady-state flow which show rich nonlinear behavior. We find a maximum in the flow rates depending upon pore radius, pore energetics, reservoir temperature, and driving force. We also present exact mean-field results of transport through pores with internal defects. The interesting nonlinear dependences suggest numerous diagnostic experiments in biological and zeolitic systems which may reveal the features presented.