We have investigated the flow of liquids through anodic alumina membranes with cylindrical nanopores bearing asymmetric polystyrene (PS)−polyethylene oxide (PEO) block copolymer brushes, where the short PEO block acts as an anchor on the alumina surface. The flow is well described by Poiseuille's law, which allows determination of the hydrodynamic brush height within the nanopores. The height of the brushes in good solvent is found to vary systematically with the PS molecular weight, M w , consistent with a power law of the form M w 3/5 . Dramatic changes in the flow rate are observed as a function of solvent quality, which is tuned by varying the ratio of good to poor solvent (toluene to cyclohexane, respectively) in the solvent mixture. Flow control is achieved via the regulating effect triggered by the spontaneous and reversible response of the brush height to the quality of the solvent flowing through the membrane nanopores.