Nanopores modified with stimuli-responsive polypeptide chains offer a smart flow-control mechanism. These unique materials have potential wide-ranging applications including smart drug delivery, bioimplants, and molecular machines. Here, we develop a continuum method to analyze flow control through nanopores grafted with polypeptide chains. The helix-coil transition of the polypeptide chains triggered by pH change enables flow regulation. The conformational transition is treated within the Zimm-Bragg model to determine the monomer density profile of the grafted layer inside a nanopore as a function of pH. The Brinkman equation for flow through porous materials is then used to calculate the flow rate. The results are compared with recent experiments in which pH-responsive water permeation through a poly(L-glutamic acid) grafted nanoporous membrane is achieved. The results establish that polymer statistical mechanics combined with a continuum porous layer treatment of flow through the polypeptide grafted nanopore can be used to successfully design smart flow control systems.