It is a formidable challenge to understand water slippage through carbon nanotubes (CNTs), despite its great significance in fundamental research and technology. Herein, we propose an effective scheme to describe water slippage properties by extending two friction models - the phononic friction model and Einstein's diffusion model, both relying on the potential corrugation of water slippage. Our scheme effectively captures the tube-size effect on the viscosity and slippage of water molecules through CNTs. It also identifies the experimentally reported size-dependent transition from continuum to sub-continuum flow and further reveals that this transition is likely to be determined by the hydrogen bond instead of the structural transition or entropic change. Besides, the size-dependence of slip lengths is found to be controllable by temperature. Our methods are thus expected to be a useful basis for further studies on substance transport under confinement.