Water purification membranes comprising aligned, dense arrays of carbon nanotubes (CNTs) have been investigated for more than 10 years. Water transport 2-5 orders of magnitude greater than Hagen-Poiseuille predictions has been observed in CNTs of diameters 0.8-10 nm in a small number of experiments. While the measured flow rates in different experiments substantially disagree with each other, there is a clear opportunity for these membranes to impact filtration technologies. We propose a multiscale computational flow method that combines molecular dynamics (MD) simulations in critical locations of the membrane with a continuum flow resistance model. This provides the flow resistances in a nanotube membrane configuration to enable, for the first time, computationally-efficient macroscopic predictions of flows through laboratory-scale membranes. Our multiscale simulation results of water flow through CNTs are also used to calibrate the Hagen-Poiseuille-Weissberg equation with slip. This study reveals that the slip length, density and viscosity can vary with CNT diameter at sub-2-nm diameters, which would otherwise be challenging to compute using MD alone. Previously published experimental results show either clear agreement or clear disagreement with our multiscale predictions; more work is required to understand this variance for similar flow cases.