Varying inversely

Spreading velocities v are on the order of 15-30 cm/sec on water [39], and v for a homologous series tends to vary linearly with the equilibrium film pressure, it", although in the case of alcohols a minimum seemed to be required for v to be appreciable. Also, as illustrated in Fig. IV-3, substrate water is entrained to some depth (0.5 mm in the case of oleic acid), a compensating counterflow being present at greater depths [40]. Related to this is the observation that v tends to vary inversely with substrate viscosity [41-43]. An analysis of the stress-strain situation led to the equation... 

This orientation interaction thus varies inversely with the sixth power of the distance between dipoles. Remember, however, that the derivation has assumed separations large compared with d. 

In this model of electrostatic in teraction s, two atoms (i and j) have poin t charges tq and qj. The magnitude of the electrostatic energy (V[. , [ ) varies inversely with the distance between the atoms, Rjj. fh e effective dielectric constant is . For in vacuo simulations or simulation s with explicit water rn olecules, the den om in a tor equals uRjj, In some force fields, a distance-dependent dielectric, where the denominator is uRjj Rjj, represen is solvent implicitly. 

Boyle s law states that the volume of a given quantity of a gas varies inversely as the pressure, the temperature remaining constant. That is. 

The Wien displacement law states that the wavelength of maximum emission, A , of a blackbody varies inversely with absolute temperature the product A T remains constant. When A is expressed in micrometers, the law becomes... 

In a free jet the absence of a pressure gradient makes the momentum flux at any cross section equal to the momentum flux at the inlet, ie, equations 16 and 17 define jet velocity at all points. For a cylindrical jet this leads to a center-line velocity that varies inversely with (x — aig), whereas for slot jets it varies inversely with the square root of (x — Xq As the jet proceeds still further downstream the turbulent entrainment initiated by the jet is gradually subordinated to the turbulence level in the surrounding stream and the jet, as such, disappears. 

Scratch Te.st. The scratch microhardness test is a refinement of the Mohs test. The corner of a cubic diamond is drawn across the surface of a metaHographicaHy poHshed sample under a constant load, usuaHy 29.4 N (3 kgf). The width of the resultant Vee groove scratch varies inversely with the hardness of the material displaced where H = scratch hardness number and A = groove width in micrometers. 

The quantity of resin appHed to the reinforcing ply to achieve a state of full densification varies inversely with the laminating pressure. Therefore, high pressure laminates pressed at about 7 MPa (1000 psi) need only about 25—30% phenoHc resin in kraft paper, whereas low pressure (1 MPa = 145 psi) laminates need 50—60% resin in the reinforcing ply if all voids are to be filled in the final product. 

X 20 cm, 2.5 x 5 cm, 1.3 x 0.6 cm, etc, or even narrower ranges, are more conducive to uniform calcination. As an example, if the size ranges between 1.25—15 cm, the small size would tend to be severely over-burned, or the large size would be incompletely calcined if the small size was properly burned. At constant temperature, the rate of calcination varies inversely with the size of the stone, increasing with smaller fractions. 

The devitrification rate is extremely sensitive to both surface and bulk impurities, especially alkah. Increased alkah levels tend to increase the devitrification rate and lower the temperature at which the maximum rate occurs. For example, a bulk level of 0.32 wt % soda increases the maximum devitrification rate 20—30 times and lowers the temperature of maximum devitrification to approximately 1400°C (101). The impurity effect is present even at trace levels (<50 ppm) and can be enhanced with the addition of alumina. The devitrification rate varies inversely with the ratio of alumina-to-alkah metal oxide. The effect is a consequence of the fact that these impurities lower glass viscosity (102). 

Based on the above equilibria, the concentration of HOCl in the normal pH range varies inversely with the total concentration of cyanurate. Increased concentration of cyanuric acid, therefore, should decrease the biocidal effectiveness of FAC. This has been confirmed by laboratory studies in buffered distilled water which showed 99% kill times of S.faecalis at 20°C increasing linearly with increasing cyanuric acid concentration at constant av. Cl at pH 7 and 9 (45). Other studies in distilled water have found a similar effect of cyanuric acid on kill times of bacteria (46—48). Calculations based on the data from Ref. 45 show that the kill times are highly correlated to the HOCl concentration and poorly to the concentration of the various chloroisocyanurates, indicating that HOCl is the active bactericide in stabilized pools (49). 

To provide for suitable timing of the pH reduction over the wide range of temperatures that may be encountered, the instant films may use polymeric timing layers in which permeabiUty to alkaU varies inversely with temperature. In the integral films, where all components are retained within the film unit after processing and the moisture content remains high for several days, care must be taken to avoid materials that could migrate or initiate unwanted reactions even at reduced pH. 

However, the steady-state process gain described by this derivative varies inversely with liquid flow Adding a given increment of heat flow to a smaller flow of liquid produces a greater temperature rise. 

FIG. 8-48 Temperature leaving a heat exchanger responds as a distributed lag, the gain and time constant of which vary inversely with flow. 

If a straight line such as curve B of Fig. 12-43 represents the experimental data and if it has been established that the drying time varies inversely as the square of the thickness, the average hquid diffusivity can be obtained as follows. At a given value of (W — W )/ W — W ), read the corresponding value of DS/d from cui ve A, Eq. (12-32), Fig. 12-43. At the same value of (W - WJ/(W - WJ, read the corresponding experimental value of 0 from cui ve B (upper scale). Then... 

Mobility is affected by the dielectric constant and viscosity of the suspending fluid, as indicated in Eq. (22-28). The ionic strength of the fluid has a strong effect on the thickness of the double layer and hence on As a rule, mobility varies inversely as the square root of ionic strength [Overbeek, Adv. Colloid Sci., 3, 97 (1950)b... 

The torque of the motor would approximately vary inversely as the square of the frequency. 

These equations combine Boyle s law, which states that when temperature is held constant the volume varies inversely with the pressure, and the law of Guy-Lussac, which states that when pressure is held constant the volume varies in proportion to the absolute temperature. 

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