Masses, ratio

By assumption, the mass ratio = m/M is a small parameter. Thus, rescaling the Schrbdinger equation properly in time and potential transforms it into the singularly perturbed equation... 

In the following we devise, following [14], an efficiently implementable scheme which leads to favorable error bounds independently of the highest frequencies under the mere assumption that the system has bounded energy. The scheme will be time-reversible, and robust in the singular limit of the mass ratio m/M tending to 0. 

Parts per million (ppm) and parts per billion (ppb) are mass ratios of grams of solute to one million or one billion grams of sample, respectively. For example, a steel that is 450 ppm in Mn contains 450 pg of Mn for every gram of steel. If we approximate the density of an aqueous solution as 1.00 g/mL, then solution concentrations can be expressed in parts per million or parts per billion using the following relationships. 

By convention, the components C and D are assigned so that the ratio exceeds unity. The greater the selectivity, the easier is the separation of C and D using solvents A and B. Selectivity can be defined in terms of mass ratio, mole ratio, or concentration. 

A specially designed water induction system was used in the Provo-Orem bus to increase the water induction mass ratio when operating at or near full power setting. Engine performance data as a function of the equivalence ratio and water injection mass ratio are shown in Figure 7. 

Fig. 7. NO formation for the Provo-Orem bus mn at a compression ratio of 12 1 at 30°C, 3000 rpm, where A is brake mean effective pressure B, brake thermal efficiency and C, oxides of nitrogen, (a) Effect of equivalence ratio, ( ), at a water/H2 mass ratio of 6.0 and spark = 17° before top-dead (BTC) and (b), effect of water injection where (j) = 0.60 and spark = 14°BTC. To convert MPa to psi, multiply by 14.

The more penetrating P-rays were easily studied. In 1899 their direction of deflection in a magnetic field was observed, indicating the negative charge. Then Becquerel was able to deflect P-rays in electric and magnetic fields and thereby deterrnined the charge-to-mass ratio. This ratio showed that the mass was much smaller than that of any atom and corresponded to that of electrons. 

In 1903, Rutherford and associates were finally able to deflect the a-rays by electric and magnetic fields, showing that these are positively charged. Measurement of the charge-to-mass ratio indicated that a-rays were of atomic dimensions. In 1908 definitive experiments showed a-rays to be doubly chaiged helium atoms, ie, helium nuclei. 

Table 3. Mass Ratio of Crystalline Chloride and Chlorate Salts in Equilibrium with an Aqueous Solution...

Solubility data can be found ia a variety of units, and conversion from one set of units to another often is requited before computation of yield can be performed. Guides to such conversions are available. It is often most convenient, however, to express solubiUty and compositions ia mixed streams ia terms of mass ratios, ie, mass of solute per mass of solvent. 

Particle size distribution determines surface-to-mass ratios and the distance internal moisture must travel to reach the surface. Large pieces thus have higher critical moisture contents than fine particles of the same material dried under the same conditions. Pneumatic-conveyor flash dryers work because very fine particles are produced during initial dispersion and these have low critical moisture contents. 

The former usually involves process temperature or isolation. Sohds surface characteristics are important in that they control the extent to which an operation is diffusion-limited, i.e., diffusion into and out of the pores of a given sohds particle, not through the voids among separate particles. The size of the solids parti(des, the surface-to-mass ratio, is also important in the evaluation of surface characteristics and the diffusion problem. 

L/G = mass ratio of hquid flow to gas flow nozzle = diameter of the air discharge... 

Inasmuch as only mass ratios are involved in these calculations, kilograms or any other unit of mass maybe substituted for pounds without affecting the validity of the example. 

Misunderstandings arise when membrane users assume that MWCO means what it seems to say. The definition implies that a 50 kD membrane will separate a 25 kD material from a 75 kD material. The rule of thumb is that the molecular mass must differ by a factor of ten for a good separation. Special techniques are used to permit the separation of proteins with much smaller mass ratio. 

Test Piece The size and the shape of specimens will vaiy with the purpose of the test, nature of the material, and apparatus used. A large surlace-to-mass ratio and a small ratio of edge area to total area are desirable. These ratios can be achieved through the use of rectangular or circular specimens of minimum thickness. Circular specimens should be cut preferably from sheet and not bar stock to minimize the exposed end grain. 

There is no single standard size or shape for corrosion-test coupons. They usually weigh from 10 to 50 g and preferably have a large sur-face-to-mass ratio. Disks 40 mm (IV2 in) in diameter by 3.2 mm Vh in) thick and similarly dimensioned square and rectangular coupons are... 

Fig. 28.22. Sandwich-type sectional composites give a much-improved stiffness-to-mass ratio.

In one sueeessful offshore installation, the turboexpander reeeives rieh natural gas at 80 bar and produees an 80/20 gas-to-liquid mass ratio at the diseharge. The integral eompressor reeompresses expander diseharge gases from 25-37 bar after the liquid is removed. The magnetie bearings operate in envu onments where namral gas is at 25 bar. 

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