By L. Salvadori
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Additional info for Bifurcation theory and applications
The internal cylinder is contained in an external one, coaxial with it, with C2 of radius r2, a bit larger than r1. Hence, we have Dr r2 À r1 ( r1 . The external cylinder is ﬁxed to an axis that can be put into rotation by an engine (not shown in the ﬁgure). The interspace between the cylinders is ﬁlled with the liquid under study up to the level AA. Let h be the height of the immersed part of the internal cylinder. We now put in rotation C2 with a certain angular velocity ω, corresponding to the velocity υ = ωr of its wall.
31 The drag coefﬁcient for a smooth sphere versus a Reynolds number. Letters mark the different flow regimes with reference to Fig. 32 We shall now examine, in a qualitative way, how the flow pattern around the sphere changes as the Reynolds number increases. These changes can be subdivided into several flow regimes . The changes from one regime to the next are gradual and cannot be sharply deﬁned. 32 shows a series of cartoon flow patterns with increasing Re. The corresponding positions on the drag coefﬁcient curve are marked with the same letters in Fig.
This, indeed, happens for equal values of the Reynolds number, for completely immersed bodies. This is an important conclusion that has relevant practical applications. For example, we can determine the behavior of an airplane wing without having to build the airplane. Rather, we can test a model of reduced dimensions at a velocity that gives the same Reynolds number. For this purpose, wind tunnels are used to test small-scale airplanes and cars. The method works as long as the compressibility of the fluid can be neglected.