Fiber length correction factor

Note the similarity of this relationship to the equation of mixing given at the beginning of this section by Eq. (5.82). The factor /Si is called the fiber length correction factor, and it corrects the fiber modulus for the shortness of the fibers. It is plotted in Figure 5.95 as a function of the product na. When na becomes very large, fii approaches one, as is expected since this limit is the case of continuous fibers, and Eq. (5.110) reduces to Eq. (5.82). When na falls below about 10, Pi is significantly less than one. 

Figure 5.95 Fiber length correction factor for modulus, /3i, as a function of the geometric factor, na. Adapted from N. G. McCrum, C. P. Buckley, and C. B. Bucknall, Principles of Polymer Engineering, 2nd ed., p. 211. Copyright 1997 by Oxford University Press.

In many practical cases Leith s approach to the definition of the aerosol shape factor has greatly simplified the understanding of this correction to Stokes law. For example, consider again the aerodynamic diameter of a fiber having a cross-sectional diameter df, length L, and density p. This can be approximated by using Eqs. 5.17 and 5.18 for the case of long axis motion parallel to the flow as... 

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