The pressure-driven flow rate through individual carbon nanotubes is precisely determined from the hydrodynamics of emerging water jets, revealing unexpectedly large and radius-dependent surface slippage. Carbon nanotubes are of interest for applications such as desalination, because of the exceptional speed with which water moves through them. But the underlying mechanism for water transport has not been well characterized, reflecting the difficulty of unambiguously measuring the permeability of single nanotubes. Lydéric Bocquet and colleagues now show that permeability can be accurately determined by observing the hydrodynamics of water jets as they emerge from single nanotubes into a surrounding fluid. The results reveal large, radius-dependent surface slippage in carbon nanotubes and no slippage in boron nitride nanotubes. This contrast is attributed to subtle, atomic-scale differences between the solid–liquid interfaces of the two systems, illustrating that nanofluidics is the frontier at which the continuum picture of fluid mechanics meets the atomic nature of matter. Measurements and simulations have found that water moves through carbon nanotubes at exceptionally high rates owing to nearly frictionless interfaces1,2,3,4. These observations have stimulated interest in nanotube-based membranes for applications including desalination, nano-filtration and energy harvesting5,6,7,8,9,10, yet the exact mechanisms of water transport inside the nanotubes and at the water–carbon interface continue to be debated11,12 because existing theories do not provide a satisfactory explanation for the limited number of experimental results available so far13. This lack of experimental results arises because, even though controlled and systematic studies have explored transport through individual nanotubes7,8,9,14,15,16,17, none has met the considerable technical challenge of unambiguously measuring the permeability of a single nanotube11. Here we show that the pressure-driven flow rate through individual nanotubes can be determined with unprecedented sensitivity and without dyes from the hydrodynamics of water jets as they emerge from single nanotubes into a surrounding fluid. Our measurements reveal unexpectedly large and radius-dependent surface slippage in carbon nanotubes, and no slippage in boron nitride nanotubes that are crystallographically similar to carbon nanotubes, but electronically different. This pronounced contrast between the two systems must originate from subtle differences in the atomic-scale details of their solid–liquid interfaces, illustrating that nanofluidics is the frontier at which the continuum picture of fluid mechanics meets the atomic nature of matter.