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Aerodynamic Theory: A General Review of Progress Under a by William Frederick Durand

By William Frederick Durand

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer publication documents mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

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Extra info for Aerodynamic Theory: A General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics

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1), and must be of zero dimension. 3) are also of zero dimension. 25 SECTION 3 Again let the exponents of L, M, T, in the dimensional expressions for Qv Q2 , x, y, z, be as follows: T _Jf L Qt m3 m2 ml Q2 n3 n2 nl X P3 P2 Pt y q3 q2 ql z r3 r2 r1 That is, the dimensions of Q1 are Lm Mm, Tm, and similarly for the others. he final dimensional form shall each independently be zero. 6) In each of these sets of equations, the first is formed for the fu:udamental dimension L, the second forM and the third for T.

5), the quantities on the right will be known and we shall have a set of three simultaneous equations with a 1 , {31 and y1 as the unknowns. 2). 3). We may therefore conclude that it is always possible to write such expressions with four variables and with exponents such that the dimensions of the expression will be zero. 3) are of zero dimension. 7) 26 A IV. 4). 4). 3), the first affected by the exponent af~. 1), as representing any given term in the general equation of zero dimension. 7). These properties are either self evident, or the interested reader will readily supply a proof.

Such a line has two specifications-length and direction. The length of the line may represent magnitude to any arbitrary scale and the direction of the line may represent the direction of the line of action of the physical quantity, in space or in y a plane, as the case may require. A ·A line used in this F manner and for this purpose is known as a vector. From the geometrical viewpoint, therefore, we may Fig. 10. simply consider a vector as a line characterized by the two specifications, length and direction.

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