By William Frederick Durand
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Additional resources for Aerodynamic Theory: A General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics
37 SECTION 3 This equivalence expressed in algebraic form will serve the purpose of complete vector representation. 1) The symbol i is to be here understood simply as an operator or as an indicator of direction. As an operator it implies a rotation through + 90°. Any letter used as a scalar, that is, simply as a measure of length, is understood to be laid off in the direction of the scalar axis which we here take as the axis of X. A vector expressed as x + i y is therefore to be understood as directing that a length x be laid off along the direction of X followed by a length y laid off at + 90° to the same axis.
Or otherwise, any value of the coefficient corresponding to a given value of the Reynolds number will apply to all cases which have the same number, regardless of the individual values of L, v, e. and fl· Still otherwise, the application of these coefficients may be stated as follows. Given a particular case with specified values of L, v, e. and fl. l, we have at hand the values of the coefficient for the latter case, the same coefficient may be employed for the case in hand. , to all quantities representing the values of functions of non-dimensional or II I groups of variables as developed in 3.
1 ....... - 2 ....... - 2 D ................ 1 1 ....... - 1 v .... ' ........... e ....... 1 ....... 5) 30 A IV. THEORY OF DIMENSIONS It may be of interest to note results in the case of another selection of variables as basic. Thus assume the group, G p,, v. _] = 0 Gp nza _ (ez'lfl) ---;;v-- - I1 Gp. 2) we remember that since p,fDve is of zero dinlension, so also will be Dvelt-t and likewise any function of either of these. 7) standing as a factor in an equation in which it must be of zero dinlension in m:der to render the equation homogeneous as to dimensions, is known as a "non-dimensional coefficient".
Aerodynamic Theory: A General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics by William Frederick Durand