By William Frederick Durand
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer ebook files 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
Of this we shall give here only a brief outline. We must first note the characteristics of a dimensionless quantity. Algebraically, when the expression of the dimensions reduces to unity, the quantity is dimensionless. Thus Length -:- Length = L -:- L Volume-:- Statical Moment of Area= £3-:- £3 Moment of force -:- Energy = M L 2 T-2 -:- M £2 T-2 Thus a ratio is always dimensionless and generally the quotient of two quantities each of which has the same dimensions. Again take the expression Lgv- 2 in which Lis a length, g is acceleration and vis velocity.
Thus we have: Quantity Length Mass Time Area: length X length Volume : length X length X length Statical Mom. of area: area X length Statical Mom. of volume: volume X length Density: mass -7- volume Dimension L }If T £Z La La L4 ~'If L-s 22 A IV. THEORY OF DIMENSIONS Quantity Velocity: length -7- time Angular Velocity Revolutions in unit time: number -7- time Acceleration: velocity -7- time Momentum: mass X velocity Force: mass X acceleration Moment of momentum: momentum X length Moment of force (Torque): force X length Energy, Work: force X length Power: Work per unit of time Pressure: force -7- area Pressure gradient along a length: pressure -7- length Viscosity: force per unit area -7- rate of shear Kinematic Viscosity: viscosity -7- density Vorticity: velocity X length Dimensians LT- 1 p-1 T-1 LT- 2 M LT- 1 MLT- 2 M £2 T-1 M £2 T-2 M £2 p-2 J:l £2 p-a ML- 1 T- 2 1J:l L-2 p-2 ML- 1 T- 1 £2T-1 PT-1 Of these various items, viscosity may require a word of further explanation.
A space vector is a length having a specified direction in space. A plane vector is a length having a specified direction in a plane. In contradistinction to the term vector, the term scalar is used to imply a number, or geometrically, a length, without reference to direction. The scalar value of a vector is simply its length measured in any convenient unit. Thus in Fig. 10 if the length of OP is 10 units, then as a scalar, OP is a line 10 units long and that is all; while as a vector, OP is a line 10 units long and inclined at an angle () with the XX direction.