By William Frederick Durand
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer booklet 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 resources for Aerodynamic Theory: A General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics
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. 3) to be of zero dimension. We must now show that it is always possible to write at will such expressions with dimensions zero.
6. First take the function represented by C ED, symmetrical about y. Evidently in such case, f (0) = f (- 0). Likewise we have sin nO=- sin(- nO). SECTION 2 19 Hence in the formula for a B coefficient, the elements in the integration will form pairs equal in value and opposite in sign and thus cancelling out in the summation. Hence each B coefficient will vanish. Again since cos nO= cos(- nO), the elements in the integration for an A coefficient will form pairs equal in value and of the same sign and thus combining in the summation.
The basic concept in velocity is a ratio of length to time. The relation of the unit of velocity to the basic units of length, mass and time is, therefore, L -;- T. This expression is said to give the "dimensions" of velocity. In a similar manner, by an expression of its basic concept or definition, we may write the dimensions of any and all quantities with which we have to deal in the problems of mechanics. Thus we have: Quantity Length Mass Time Area: length X length Volume : length X length X length Statical Mom.