Trumpets

For a trumpet-shaped rounded entrance, with a radius of rounding greater than about 15 percent of the pipe diameter (Fig. 6-13Z ), the turbulent flow loss coefficient K is only about 0.1 (Vennard and Street, Elementary Fluid Meehanies, 5th ed., Wiley, New York, 1975, pp. 420-421). Rounding of the inlet prevents formation of the vena eontraeta, thereby reducing the resistance to flow. 

Trumpet-shaped enlargements for turbulent flow designed for constant decrease in velocity head per unit length were found by Gibson (ibid., p. 95) to give 20 to 60 percent less friclional loss than straight taper pipes of the same length. 

The shape of the converging section is a smooth trumpet shape similar to the simple converging nozzle. However, special shapes of the diverging section are required to produce the maximum supersonic-exit velocity. Shocks result if the divergence is too rapid and excessive boundary layer friction occurs if the divergence is too shallow. See Liepmann and Roshko (Elements of Gas Dynamic.s, Wiley, New York, 1957, p. 284). If the nozzle is to be used as a thrust device, the diverg-... 

Even the originator was hesitant to blow his own trumpet. In 1917, the elder Bragg published an essay on physical research and the way of its application , in a multiauthor book entitled Science and the Nation (Bragg 1917). Although he writes at some length on Rdntgen and the discovery of X-rays, he includes not a word on X-ray diffraction, five years after the discoveries by his son and himself. 

Miles Davis, the jazz trumpeter who seems to have a lock on cool-tone background music, played in the background one afternoon recently as I ordered an Adam and Eve. 

People drink to turn up the volume when they go out. A cocktail like the Kind of Blue turns it down. It is, at its best, a ballad. Played introspectively on a trumpet. Using a mute. 

The expression for Vy = Sy = Vres/ is true if a = Xmean however, if x is different from Xmean, an extrapolation penalty is paid that is proportional to the square of the deviation. [See Eq. (2.16).] This results in the characteristic trumpet shape observed in Figures 2.6 and 2.8. The influence of the calibration design is shown in Figure 2.8, where the corresponding individ-... 

Option (Valid) presents a graph of relative standard deviation (c.o.v.) versus concentration, with the relative residuals superimposed. This gives a clear overview of the performance to be expected from a linear calibration Signal = A + B Concentration, both in terms of (relative) precision and of accuracy, because only a well-behaved analytical method will show most of the residuals to be inside a narrow trumpet -like curve this trumpet is wide at low concentrations and should narrow down to c.o.v. = 5% and rel. CL = 10%, or thereabouts, at medium to high concentrations. Residuals that are not randomly distributed about the horizontal axis point either to the presence of outliers, nonlinearity, or errors in the preparation of standards. 

These days, sait iicks are for saie everywhere. Some are artificiai with added ingredients that contribute to "the horse s weii-being." Others are naturai biocks of sait taken from mines and marketed primariiy to deer hunters who want to attract deer to a spot where the hunter wiii be waiting. Apparentiy sait iicks do their job weii. As one advertisement trumpets, "The Bucks Stop Here." ... 

His words were heavy, like the tramp of troops, and quickening as if he heard again the trumpets and drums of an advance. Such men as we had were seasoned in France and the Scottish borders, and York s battles could not break through ours, not from the flank. Ours stood like rocks but we had too few of them. Then Warwick s archers came up past the Chequers Inn. They... 

All was as quiet as Sandwich ever is when I rode back through the deep cold of January to my own lodging. The news of wind and tide was proclaimed by trumpets even in the small hours, and the taverns did good business with ale and wine and whores, as taverns in a great port do. But my men and I agreed that we could hear nothing untoward, only the calls of the watches we had set on each ship. 

It was but a few minutes before the trumpets would sound. In our enclosure I looked over my horse, Belle Bete, and all our harness, as I have done a thousand times before and since. On such care for small things may a man s life rest, my father used to say in the stables, when I grew impatient as boys will with buckles and thongs, the proper care of leather and iron. Do not trust such care to any but yourself. When it was time to mount, I saw that the trappings over Belle Bete s chest hung crookedly, and the straps at his withers were differently fastened. Who has done this I asked. 

Kelly, Eric P. The trumpeter of Krakow. 1928 reprint, Aladdin Books, 1992. 

Fig. 6.8. Typical plots of residual deviations random scattering (a), systematic deviations indicating nonlinearity (b), and trumpet-like form of heteroscedasticity (c)...

Homoscedasticity. Unequal variances are recognizable from residual plots as in Fig. 6.8c where frequently ey is a function of x in the given trumpet-like form. In such a case, the test of homoscedasticity can be carried out in a simple way by means of the Hartley test (Fmax test), Fmax = smax/5min> see Sect. 4.3.4 (1). 

It is a well-known fact that the precision in trace analysis decreases with diminishing concentration in a similar way as it does with decreasing sample weight (Sect. 2.1). The dependency of the repeatability and reproducibility standard deviation on the concentration of analytes has been investigated systematically at first by Horwitz et al. [1980] on the basis of thousands of pieces of interlaboratory data (mostly from food analysis). The result of the study has been represented in form of the well-known Horwitz trumpet which is represented in Fig. 7.3. 

Fig. 7.3. The so-called Horwitz trumpet Dependency of the relative standard deviation, rsd(x) on the concentration (x)...

When the oxide is formed by anodizing in acid solutions and the sample is then left to rest at the OCP, some dissolution can occur. This process has been studied by a numbers of authors,70-75 especially in relation to porous oxides [cf. Section 111(4)]. It was found that pore walls are attacked, so that they are widened and tapered to a trumpet-like shape.70 71 Finally, the pore skeleton collapses and dissolves, at the outer oxide region. The outer regions of the oxide body dissolve at higher rates than the inner ones.9,19 The same is true for dissolution of other anodic oxides of valve metals.76 This thickness dependence is interpreted in terms of a depth-dependent vacancy concentration in the oxide75 or by acid permeation through cell walls by intercrystalline diffusion, disaggregating the microcrystallites of y-alumina.4... 

It has become one of the commonplaces in this area, however, that such behavioural genetic stories are regularly trumpeted in the popular press and almost always withdrawn without ceremony in the professional scientific literature a few weeks or months later. 

Limitations in Analytical Accuracy Part 1 - Horwitz s Trumpet... 

Figure 71-1 Relationship of Laboratory CV (as %) with analyte concentration as powers of 1C)—exp. (For example, 6 on the abscissa represents a concentration of 10-6 or 1 ppm.) Note the shape of the curves has been referred to as Florwitz s trumpet.

A paper published by Hall and Selinger [3] points out that an empirical formula relating the concentration (c) to the coefficient of variation (CV) is also known as the precision (cr). They derive the origin of the trumpet curve using a binomial distribution explanation. Their final derived relationship becomes equation 72-2 ... 

They further simplify the Horwitz trumpet relationship in two forms as ... 

Workman, J. and Mark, H., Chemometrics in Spectroscopy Limitations in Analytical Accuracy - Part 1 Horwitz s Trumpet, Spectroscopy 21(9), 18-24 (2006). 

Figure 2. Incensario form classes. Key a, cylindrical support b, trumpet-shaped receptacle c, pedestal d, bowl and e, ladle. Specimens not to scale. Also, b, base of specimen missing and a, after Rands 1969 (courtesy, Instituto Nacional de Antropologia e Historia), not analyzed.

Figure 8. Projection of incensario compositional profiles onto the first two discriminant axes defined for the seven reference units. Key (symbols have been assigned to the incensario form classes) S, cylindrical support P, pedestal T, trumpet-shaped B, bowl and X, miscellaneous.

The small class of trumpet-shaped receptacles (figure 2b) is divided between Palenque and Plains orientations. Specimens relating to the latter have low probabilities of group containment (SPSS) and are unassigned to any reference unit by ADCORR. 

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