Variable-curvature part

The phenomenon of Dean vortices was first observed by Dean in a curved tube. The fluid in the central part is driven toward the external wall by the centrifugal force, which gives rise to a secondary flow. This results in the inward movement of the fluid near the wall and the outward movement of the fluid near the center (Fig. 3A,B). Curved tubes may be classified as torus, bends, helical coils (with a constant curvature), and spirals (with a variable curvature). Fig. 4 shows the helical coiled, spiral, and bend tubes. The hydrodynamics in a coiled tube can be characterized by a dimensionless number named after Dean and is defined as ... 

F.2.3.6. Comparison with Experimental Results. The experimental results for which the measurement parameters are controlled, which permits only the derivation of the various parameters included in the formulas and a checking of the models, were until now very limited. They concern Fe particles in Al Oj matrix and y-FCjOj particles We show an example in Figure F.2.8 for y-FCjOs particles. We can see from the figure that a weak curvature is observed for 1/x when H pp is parallel to the sample plane. It is also clear that the value of the intercept (the d p value) of the quasi-linear part of 1 ix with the temperature axis is strongly dependent of the thermal correction M ,(r)/M (0). That raises the problem of the determination of this variable. In fact, it is only directly measurable from neutron diffraction experiments (see Section F.8). It can be deduced from magnetization under high-field experiment (see Section F.3) on the condition that does not vary much with H pp. If this is not fulfilled, only approximate values are obtained, which leads to difficulties for a precise determination of the intercept. We shall discuss the A/ p(r)/A/ r(0) determination in Section F.3. 

For the experiment array, I prefer an orthogonal central-composite design (2), (3), which consists of three main parts, as shown in Table I. The first is a conventional 16-experiment fractional factorial design for five variables at two levels. The second comprises three identical experiments at the average, or center-point, conditions for the first 16 experiments. The final part comprises two out-lier experiments for each variable. These augment the basic two level design to provide an estimate of curvature for the response to each variable. The overall effect of the design is to saturate effectively the multi-dimensional variable space. It is more effective than the conventional "one-variable-at-a-time" approa.ch. 

The flexural stiffness matrix can be set up using the principle of virtual work for the case of members with variable cross section. The current rigidities are calculated from the moment versus curvature relationship at each member end. Models with more than three parts have been proposed but are not deemed appropriate for practical application. 

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