By G. K. Batchelor
First released in 1967, Professor Batchelor's vintage paintings remains to be one of many premiere texts on fluid dynamics. His cautious presentation of the underlying theories of fluids continues to be well timed and appropriate, even at present of just about unlimited computing device strength. This reissue guarantees new iteration of graduate scholars reports the splendor of Professor Batchelor's writing.
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Extra info for An Introduction to Fluid Dynamics
At temperature o°C and a pressure of one atmosphere, the number of molecules in one cubic centimetre of gas is 2·69 x 1019 (known as Loschmidt's number, and the same for all gases, as stated by Avogadro's law), so that if the molecules were placed at the corners of a cubical lattice the distance between neighbours would be 3·3 x 10-7 em. 1). For many simple molecules this effective diameter do lies in the range 3-4 x 10-8 em, so that the average separation of molecules in the above sense is something like lodo• At this distance apart the cohesive force between molecules is completely negligible, so that for most of their life molecules move freely, in straight lines with constant speed (provided they are electrically neutral, as we shall assume).
7) It is also necessary, as found earlier, that the level-surfaces of 'Y, p and p coincide. 4] Mechanical equilibrium of a fluid 19 of p coincide with one set of parametric surfaces, we see that the kinds of solution are severely restricted. Rigorous enumeration of the solutions is difficult, but the only possibilities seem to be solutions in which p and p are functions only of (i) one co-ordinate of a rectilinear system, or (ii) the radial co-ordinate ofa cylindrical polar system, or (iii) the radial co-ordinate r of a spherical polar system, corresponding to symmetrical' stars' in one, two or three dimensions.
4. 8) and further progress cannot be made without information about the distribution of density. 8) corresponding to an assumed simple relationship between p and p are sometimes useful for comparison with more complicated models. 8) numerically for any value of n. Two analytical and representative solutions are also available. When n = 0, corresponding to a fluid of uniform density, Po say, we have p = f1TGpg( aa - ra), where r = a may be interpreted as the outer boundary of the star. I. 27aset p = Cpa = (21TG)f(a 2+r2)S; the pressure and density here are non-zero for all r and there is no definite outer boundary, but the total mass of the star is finite.