# Similarity and Dimensional Methods in Mechanics by L. I. Sedov

By L. I. Sedov

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However, when the fluid motion involves cavitation phenomena resulting from vaporization in the lower pressure regions, it is necessary to include the quantity p0—p' among the characteristic parameters, where p' is the vapour pressure at a given temperature. The quantity pQ or an equivalent parameter must be included among the number of characteristic parameters for a compressible fluid. The nondimensional parameter κ = 2 — is also important in motions accompanied pv2 by cavitation. When studying the influence of the cavitation number κ in experiments, its value can be varied either by varying pQ,v or, artificially, by varying p''.

7) is Poiseuille's law which was established experimentally by Hagen in 1839 and by Poiseuille in 1840. The very good agreement of this law with experiment is one of the main confirmations of the validity of the law of viscous friction in fluids and of the initial survey of the phenomenon. 4 . , leads to the problem of forward uniform motion of a solid body in an infinite fluid. FIG. 5. Motion of a solid body in a fluid. If we regard the geometric shape of the boundary of the body as fixed, then it will be completely specified by a characteristic length d in order to give the surface of the body completely.

Using dimensional analysis, it is not difficult to find the form of this function. /sec. /sec. Consequently, the ratio Q is nondimensional. This ratio is a function of the quantities p, g, h from 28 SIMILARITY AND DIMENSIONAL METHODS IN MECHANICS which a nondimensional combination cannot possibly be formed. 1) where C is an absolute constant which is determined, most readily, by experiment. This formula determines the relation between the mass flow, the head A and the density p completely. We can extend this analysis to cover spillways with different included angles a.