We measure velocity profiles in water flowing through thin microchannels, using particle image velocimetry combined with a nanopositioning system. From the velocity profiles, we determine the slip lengths in two cases: Smooth hydrophilic glass surfaces, and smooth hydrophobic glass surfaces, grafted with a monolayer of silane. The slip length is determined within (+/- 100 nm), i.e., five times more accurately than previous work. In all cases, we find that the slip length is below 100 nm.
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