Dimensional Analysis |
Other editions - View all
Common terms and phrases
a₁ absolute significance absolute temperature absolute units acceleration applied arbitrary function arguments atoms b₁ charge complete equation condition consider Const defined determined dielectric constant dimensional analysis dimensional constants dimensional formulas dimensionless product dimensions electron electrostatic empty space enter equa equal equations of motion example exponents expressed factor final result force fundamental units gas constant gravitational constant heat Hence independent involved kinds of quantity kinds of unit liquid Lord Rayleigh m₁ measurable quantities ments model experiments Name of Quantity nature number measuring number of fundamental numerical magnitude numerical value obtained obvious oscillation particular pendulum phenomena physical quantity physical variables possible primary quantities problem products of powers quantum ratio Rayleigh restriction rules of operation secondary quantity solution solve square root stants surface tension Symbol system of units theorem thermal conductivity thermodynamic tion unit of length unit of mass unity velocity of light viscosity write Y₁ Y₂
Popular passages
Page 11 - Fourier equation for the conduction of heat, in which heat and temperature are regarded as sui generis. It would indeed be a paradox if further knowledge of the nature of heat afforded by molecular theory put us in a worse position than before in dealing with a particular problem.
Page 29 - ... with, begins to get back at the specialists by expressing himself in an equally incomprehensible style. PW Bridgeman, the American physicist and philosopher, filled his books with lengthy descriptions and explanations and very few equations. I quote a passage from his book Dimensional Analysis. . . . we have treated the dimensional formula as if it expressed operations actually performed on physical entities, as if we took a certain number of feet and divided them by a certain number of seconds....
Page 80 - ... do. There seems a naturalness in this result that justifies the assumption that these inductive capacities are really of the nature of a slowness. It seems possible that they are related to the reciprocal of the square root of the mean energy of turbulence of the jether.
Page 101 - But it is evident that this length must be the key to some essential structure. It may not be an unattainable hope that some day a clearer knowledge of the processes of gravitation may be reached; and the extreme generality and detachment of the relativity theory may be illuminated by the particular study of a precise mechanism.
Page 26 - MA, FRS* IN the calculation of the dimensions of Physical quantities we not unfrequently arrive at indeterminate equations in which two or more unknowns are involved. In such cases an assumption has to be made, and in general that selected is that one of the quantities is an abstract number. In other words the dimensions of that quantity are suppressed. The dimensions of dependent units which are afterwards deduced from this assumption are evidently artificial, in the sense that they do not necessarily...
Page 11 - July 29, p. 105)* belongs rather to the logic than to the use of the principle of similitude, with which I was mainly concerned. It would be well worthy of further discussion. The conclusion that I gave follows on the basis of the usual Fourier equation for the conduction of heat, in which heat and temperature are regarded as sui generis.
Page 27 - For the general theory of Dimensions we shall refer the reader to Maxwell's Theory of Heat, Chap. iv. ; we shall in this chapter confine our attention to the dimensions of electrical quantities. It may be well to state at the outset that the 'dimensions' of electrical quantities are a matter of definition and depend entirely upon the system of units we adopt.
Page 10 - If we suppose only three of these quantities are "really independent, ' ' we obtain a different result. For example, if the temperature is defined as the mean kinetic energy of the molecules, the principle of similitude* allows us only to affirm that = ka0F /----, c a1 Y U a* / * Rayleigh and other English authors use this name for dimensional analysis.
Page 80 - ... suggestion seems to have escaped notice. The electrostatic system of units may be described as one in which electric inductive capacity is assumed to have zero dimensions and the electromagnetic system as one in which the magnetic inductive capacity is assumed to have zero dimensions. Now if we take a system in which the dimensions of both, these quantities are the same, and of the dimensions of a slowness, ie the inverse of a velocity...
Page 9 - This is a rather famous problem in heat transfer, treated before Rayleigh by Boussinesq. A solid body, of definite geometrical shape, but variable absolute dimensions, is fixed in a stream of liquid, and maintained at a definite temperature higher than the temperature of the liquid at points remote from the body. It is required to find the rate at which heat is transferred from the body to the liquid. As before, we make a list of the various quantities involved, and their dimensions. Name of Quantity....