By R. A. Penfold
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Extra info for Practical electronic model railway projects
3-12). 3-15) that gives the larger scale for ys since we want to bound y ∗ to always be less than or equal to 1. 3-13) provides the axial length scale. 3-9) equal to 1 to determine the pressure scale. 3-11) equal to 1 since the two terms in the continuity equation have to balance for a developing ﬂow. 3-16) Note that the scale for the y-component of velocity is dependent on the aspect ratio; for long closely spaced plates, the scale factor for uy will be considerably smaller than that for ux . This is perfectly reasonable since uy arises from a need for the velocity proﬁle to be rearranged to accommodate the change in spacing between the two plates.
No attempt is made in this chapter or elsewhere in the book to provide a detailed derivation of the describing equations that are used in scaling analysis. However, the reader is referred to the appendices, which summarize the continuity equations and equations of motion along with the corresponding forms of Newton’s constitutive equation in generalized vector–tensor notation as well as in rectangular, cylindrical, and spherical coordinates. These equations serve as the starting point for each example problem.
The derivative of this same velocity component). The manner in which this step is implemented is best learned by example, which is why most of the book is devoted to applying scaling analysis to a variety of problems in ﬂuid dynamics, heat transfer, mass transfer, and reaction processes. Step 8 is the desired end result of the scaling analysis: the unique minimum parametric representation of the describing equations for the process that ensures ◦(1) scaling. Since all the dimensionless dependent and independent variables and their relevant derivatives are ◦(1), the magnitude of each term in the describing equations is determined by the magnitude of the dimensionless group that multiplies this term.
Practical electronic model railway projects by R. A. Penfold