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A thermodynamic method is employed to analyse the slip length of hydrophobic nanopatteed surface.The maximal slip lengths with respect to the hydrophobicity of the nanopatteed surface are computed.It is found that the slip length reaches more than 50μm if the nanopatteed surfaces have a contact angle larger than 160°.Such results are expected to find extensive applications in micro-channels and helpful to understand recent experimental observations of the slippage of nanopatteed surfaces.