Body Dimensions

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FIGURE 7.4.4 A graph on logarithmic coordinates of total head and body length against body mass for whales. (From Economos, A.C., J. Theor. Biol. 103,167, 1983. With permission.) 

FIGURE 7.4.5 Plot of primate chest circumference against body mass. (From Stahl, W. R., and Gummerson, J.Y., Growth 31, 21, 1967. With permission.) 

Measurements in 35 Animals Representing 5 Species of Adult Primates 

Source McMahon, T.A., Muscles, Reflexes, and Locomotion, Princeton University Press, Princeton, NJ, 1984. With permission. 

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It is seen that the diameters of bronchioles (averaged over generations 11 - 15) vary little with age. The increase in bronchial size is greater, but still less than might be expected if airways are simply scaled for overall body dimensions (illustrated by the dashed curves in Figure 9, which are functions of body weight W). Since bronchiolar diameter does not change much with age it is likely that the thickness of bronchiolar epithelium is also relatively constant. However, in the case of the bronchi, it is reasonable to assume that epithelial thickness is proportional to bronchial diameter. Thus, it is necessary to use age dependent conversion factors between the surface density of alpha-decays and dose to cells. 

For a given orifice area, there may be a number of different inlet and outlet connection sizes, as well as body dimensions such as centreline-to-face dimensions. Many competing products, particularly those of European origin, have different dimensions and capacities for the same nominal size, unlike the API valves which have strict dimensional and capacity standardizations. DIN valves are, therefore, not necessarily interchangeable. 

It can be shown that the error of the finite-difference approximation to dTIdx is of the order of (Ax/L)2 where L is some characteristic body dimension. 

In these parameters s designates some characteristic dimensions of the body for the plate it is the half-thickness, whereas for the cylinders and sphere it is the radius. The Biot number compares the relative magnitudes of surface-convection and internal-conduction resistances to heat transfer. The Fourier modulus compares a characteristic body dimension with an approximate temperature-wave penetration depth for a given time r. 

Three general flow regimes may be anticipated for the flow over a flat plate shown in Fig. 12 12. First, the continuum flow region is encountered when the mean free path A is very small in comparison with a characteristic body dimension. This is the convection heat-transfer situation analyzed in preceding chapters. At lo wer gas pressures, when A L, the flow seems to slip along the surface and u 4= 0 at y = 0. This situation is appropriately called slip flow. At still lower densities, all momentum and energy exchange is the result of... 

Evidently, the parameter which is of principal interest is a ratio of the mean free path to a characteristic body dimension. This grouping is called the Knud-sen number,... 

We have already mentioned that the temperature-jump effect arises as a result of the failure of the molecules to accommodate to the surface temperature when the mean free path becomes of the order of a characteristic body dimension. The parameter which describes this behavior is called the accommodation coefficient a, defined by... 

For this purpose, a worm-like coil is represented by an extended body of revolution for which the central radius of gyration is related to the longitudinal, H, and transverse, Q, body dimensions by the general equation... 

In spite of this, we shall see that potential-flow theory plays an important role in the development of asymptotic solutions for Re i>> 1. Indeed, if we compare the assumptions and analysis leading to (10-9) and then to (10-12) with the early steps in analysis of heat transfer at high Peclet number, it is clear that the solution to = 0 is a valid first approximation lor Re y> 1 everywhere except in the immediate vicinity of the body surface. There the body dimension, a, that was used to nondimensionalize (10-1) is not a relevant characteristic length scale. In this region, we shall see that the flow develops a boundary layer in which viscous forces remain important even as Re i>> 1, and this allows the no-shp condition to be satisfied. 

The conclusion to be drawn from the preceding discussion is that the potential-flow theory (10-9) [or, equivalently, (10 12) and (10 13)] does not provide a uniformly valid first approximation to the solution of the Navier Stokes and continuity equations (10-1) and (10 2) for Re 1. Furthermore, our experience in Chap. 9 with the thermal boundary-layer structure for large Peclet number would lead us to believe that this is because the velocity field near the body surface is characterized by a length scale 0(aRe n), instead of the body dimension a that was used to nondimensionalize (10-2). As a consequence, the terms V2co and u V >, in (10 6), which are nondimensionalized by use of a, are not 0(1) and independent of Re everywhere in the domain, as was assumed in deriving (10-7), but instead are increasing fimctions of Re in the region very close to the body surface. Thus in... 

Approximate Relations of Surface Area and Weights of Individuals of Average Body Dimensions... 

This is just the Helmholtz-Smoluchowski equation, as might have been expected, since electrophoresis is just the complement of electroosmosis. Its derivation shows that the electrophoretic velocity of a nonconducting particle is independent of the particle size and shape for a constant surface potential when the Debye length is everywhere small compared with the characteristic body dimension. Note that Eq. (7.2.6) differs from the Huckel large Debye length result (Eq. 7.2.2) only by the factor. ... 

TABLE 1 US Civilian Body Dimensions (cm) for Ages 20-60 Years... 

Dependences of Body Dimensions on Body Mass for Bovids... 

Body dimensions for bovids (ruminants with paired nondeciduous hollow horns, including antelopes, cattle, sheep, and goats) are also related to body mass (Table 7.4.2). 

Make some measurements of body dimensions. Which appear to form values close to the golden ratio ... 

If the aortic diameter scales with body dimensions, which of these vessel groups would also be expected to scale with body mass ... 

Lee, S., Bro, R. (2008). Regional differences in world human body dimensions The multi-way analysis approach. Theoretical Issues in Ergonomics Science, 9(4), 325-345. 

For large bodies that are linear elastic, the version of Hooke s Law given as Eq. (2.2) is not very useful. Indeed, even the use of force and displacement to describe the deformation becomes inappropriate. Consider the atomic arrangements shown schematically in Fig. 2.7. For the four pairs of atoms in (b), one would need to apply four times the force to get the same displacement as a single pair of atoms in (a). For the string of three atoms in (c), one would apply only one-half the force to get the same displacement as the single pair. This implies Hooke s Law would involve body dimension terms as well as k. This is somewhat awkward as it would be preferable to describe the linear elastic response of bulk materials in the simplest way possible. This problem can be overcome by normal-... 

In a simulation, every single pedestrian is modelled individually with specific goal and behaviours, with his own velocity and body dimension. The software allows flexible and realistic simulation of normal as well as panic hehaviour of pedestrian in complex environments, evaluating the station layout during normal condition and emergency. 

Key words anthropometry, body dimensions, human variability, military... 

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