As this text is not intended to be a treatise on fluid mechanics or hydraulics, only the essentials of these disciplines necessary as a background to further discussion of the main theme, i.e. modelling in hydraulics, will be dealt with here; furthermore, a basic knowledge and understanding of fluid mechanics and hydraulics and of their principles are assumed throughout. In most cases the equations presented are given without formal proofs in their derivation – for further details and references, see, for example, Batchelor (2000), Chadwick et al. (2004), Daily and Harleman (1966), Douglas et al. (2005), Fox (1977), Goldstein (1965), Rouse (1961), Tritton (1988) and Vardy (1990). Some parts of (applied) hydraulics developed from statements in this section and used in the formulation and application of scaling laws, in mathematical modelling of various types of flow or engineering applications, are best dealt with immediately before discussing the modelling procedure and problems, and therefore have mainly been placed in the relevant ‘applied’ Chapters (7–13).