Gravitational effects

Gravitational Effects.—In one-component fluids, the existence of sizeable density gradients in equilibrium systems near the critical point are well known and their eflFect on the determination of critical exponents is recognized. An analogous situation involves composition gradients near the critical solution point in binary mixtures whenever the densities of the two pure liquids are appreciably different. 

Fannin and Knobler have recently presented an analysis of gravity-induced concentration gradients and their influence upon the experimental determination 

at the critical temperature phase separation will be observed at the bottom of the cell for a mixture for which x x , while at the top of the cell phase separation will be observed when x x . If these observations are recorded on a T, x diagram, they will produce not only a spurious flat top to the coexistence curve, but also changes in the shape of other regions. 

Using the scaled equation of state (21), Fannin and Knobler constructed an observed coexistence curve for CH4 + CF4 in a 2 cm cell, assuming a true  

Similar problems will arise in the analysis of other properties. For example, the observed heat capacity Cj, will not display an actual divergence. Only one layer in the cell is at the true critical point and the total enthalpy is averaged over all heights and will not show singular behaviour. The phenomenon is entirely analogous to the gravitational perturbation of the measurement of Cv for a pure fluid.  

Imagine that NASA has given you a ton of money to develop a mass sensor for the International Space Station. It will be used for monitoring the air quality inside the station. Which type of mass sensor could you NOT use QCM, SAW, cantilever (in bending), or cantilever (resonant mode)  

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There are a number of relatively simple experiments with soap films that illustrate beautifully some of the implications of the Young-Laplace equation. Two of these have already been mentioned. Neglecting gravitational effects, a film stretched across a frame as in Fig. II-1 will be planar because the pressure is the same as both sides of the film. The experiment depicted in Fig. II-2 illustrates the relation between the pressure inside a spherical soap bubble and its radius of curvature by attaching a manometer, AP could be measured directly. 

Small drops or bubbles will tend to be spherical because surface forces depend on the area, which decreases as the square of the linear dimension, whereas distortions due to gravitational effects depend on the volume, which decreases as the cube of the linear dimension. Likewise, too, a drop of liquid in a second liquid of equal density will be spherical. However, when gravitational and surface tensional effects are comparable, then one can determine in principle the surface tension from measurements of the shape of the drop or bubble. The variations situations to which Eq. 11-16 applies are shown in Fig. 11-16. 

As for any incompressible single-phase flow, the equivalent pressure P = p + pgz where g = acceleration of gravity z = elevation, may be used in place of p to account for gravitational effects in flows with vertical components. 

Emissions of gases or particles less than 20 microns (larger particles settle more quickly due to gravitational effects) disperse with an origin and plume centerline at the effective stack height. Pollutant concentrations are greatest within one standard deviation of the plume centerline. Thus, the determination of the value of these standard deviations is an important factor in calculating ambient concentrations. 

Apart from this gravitational effect, there are composition changes due to chemical reactions induced by light. These are caused by absorption of ultraviolet light in the upper atmosphere. For example, oxygen absorbs ultraviolet light and the energy taken up by the molecule exceeds the... 

The above conclusion must certainly be taken with a measure of reserve as regards the mass velocity, for at very low velocities it appears reasonable to expect that the relative motion between vapor and liquid in a boiling channel will be affected sufficiently to influence the burn-out flux. Barnett s conclusion also applies to simple channels, whereas Fig. 35 discussed in Section VIII,C shows that a rod-bundle system placed in a horizontal position is likely to incur a reduction in the burn-out flux at mass velocities less than 0.5 x 106 lb/hr-ft2, presumably on account of flow stratification. Furthermore, gravitational effects induced in a boiling channel by such means as swirlers placed inside a round tube can certainly increase the burn-out flux as shown by Bundy et al. (B23), Howard (H10), and Moeck et al. (Ml5). 

F. J. Miller, J. W. Easton, A. J. Marchese, and H. D. Ross, Gravitational effects on flame spread through non-homogeneous gas layers, Proc. Combust. Inst. 29(2) 2561-2567, 2002. 

As indicated in Figure 4.5.3, gravitational effects are especially significant in the system due to the horizontal orientation of the cylinders. Gravity acts in the plane x-y)... 

The physical significance of the first term is obvious. The second term is the inertia term. The third term accounts for gravitational effects it vanishes for horizontal pipelines. The last term represents the frictional losses. 

For the sake of simplicity the elevation (or gravitational effects) term will be omitted in the following development. Let Eq. (123) be multiplied by an unknown multiplier A and then added to Eq. (128),... 

The existence of dark matter (either baryonic or non-baryonic) is inferred from its gravitational effects on galactic rotation curves, the velocity dispersions and hydrostatic equilibrium of hot (X-ray) gas in clusters and groups of galaxies, gravitational lensing and departures from the smooth Hubble flow described by Eq. (4.1). This dark matter resides at least partly in the halos of galaxies such as our... 

In liquid mixing systems, baffles are used to suppress vortexing. Since vortexing is a gravitational effect, the Froude number is not required to describe baffled liquid mixing systems. In this case the exponent y in equations 5.17 and 5.18 is zero and FryM = 1. 

Two common types of one-dimensional flow regimes examined in interfacial studies Poiseuille and Couette flow [37]. Poiseuille flow is a pressure-driven process commonly used to model flow through pipes. It involves the flow of an incompressible fluid between two infinite stationary plates, where the pressure gradient, Sp/Sx, is constant. At steady state, ignoring gravitational effects, we have... 

However, these gravitational effects are very slight indeed, and astronomers must eliminate any interference due to imperfections in instrumental optics or atmospheric turbulence. 

Following one of the biggest inquiries ever held in modern astronomy, it transpires that their apparent luminosity is slightly less than would be found if space were Euclidean and expansion were merely slowed down by the gravitational effects of matter. In fact, the expansion is more vivacious than was previously thought. This means that distances to remote objects are slightly distended, so that the supernovas appear less luminous than expected. 

Inertial, Terrestrial and Celestial Guidance Systems for Missiles. An inertial guidance system is one which is independent of information, other than gravitational effects, obtd from outside the missile... 

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