Density variations

Projection radiography is widely used for pipe inspection and corrosion monitoring. Film digitisation allows a direct access to the local density variations by computer software. Following to a calibration step an interactive estimation of local wall thickness change based on the obtained density variation is possible. The theoretical model is discussed, the limitations of the application range are shown and examples of the practical use are given. The accuracy of this method is compared to results from wall thickness measurements with ultrasonic devices. 

Basically it is only possible to determine a wall thickness change in penetration direction from a density variation of a radiographic film. No absolute wall thickness values can be obtained in this way contrary to the tangential method. 

Fig.3 User interfaee for wall thickness evaluation based on density variations on a step wedge, the nominal wall thickness was set to 15 mm...

Moduli and Poisson s Ratio. The Young s modulus of vitreous sihca at 25°C is 73 GPa (<1.06 x 10 psi), the shear modulus is 31 GPa (<4.5 X 10 psi), and the Poisson s ratio is 0.17. Minor differences in values can arise owing to density variations. The elastic modulus decreases with increasing density and Poisson s ratio increases (26). 

The physics and modeling of turbulent flows are affected by combustion through the production of density variations, buoyancy effects, dilation due to heat release, molecular transport, and instabiUty (1,2,3,5,8). Consequently, the conservation equations need to be modified to take these effects into account. This modification is achieved by the use of statistical quantities in the conservation equations. For example, because of the variations and fluctuations in the density that occur in turbulent combustion flows, density weighted mean values, or Favre mean values, are used for velocity components, mass fractions, enthalpy, and temperature. The turbulent diffusion flame can also be treated in terms of a probabiUty distribution function (pdf), the shape of which is assumed to be known a priori (1). 

Flows are typically considered compressible when the density varies by more than 5 to 10 percent. In practice compressible flows are normally limited to gases, supercritical fluids, and multiphase flows containing gases. Liquid flows are normally considerea incompressible, except for certain calculations involved in hydraulie transient analysis (see following) where compressibility effects are important even for nearly incompressible hquids with extremely small density variations. Textbooks on compressible gas flow include Shapiro Dynamics and Thermodynamics of Compre.ssible Fluid Flow, vol. 1 and 11, Ronald Press, New York [1953]) and Zucrow and Hofmann (G .s Dynamics, vol. 1 and 11, Wiley, New York [1976]). 

FIQURE 5-3.5. Schematic charge density variation in tanker loading circuit. (Adapted from API RP 2003.)... 

A compressible fluid is a fluid in which significant density variations that occur during its flow have to be considered, as is usually the case with vapors and gases. 

If the flow is isothermal, there is no need to solve for the temperature equation (Eq. (11.6)). In this case the last term in Eq. (11.5) is also dropped. If, however, the thermal comfort is simulated, then the temperature equation must be solved. In ventilation the temperature variations are normally small, which means that it is sufficient to account for density variation only in the gravitation term (the last term in Eq. (11.5)). The gravitation term acts in the vertical direction, and in Eq. (11.5) it is assumed that the xj coordinate is directed vertically upward. denotes a reference temperature, which should be constant. It does not influence the predicted results, except that the pressure level is changed. It could, however, affect convergence rate (i.e., increase the number of required iterations required to reach a converged solution), and it should be chosen to a reasonable value, such as the inlet temperature. 

Air exfiltration The uncontrolled rate of air interchange from a space to outdoors due to density variations, or by space pressurization by means of a fan. 

The molecular structure and dynamics of the ice/water interface are of interest, for example, in understanding phenomena like frost heaving, freezing (and the inhibition of freezing) in biological systems, and the growth mechanisms of ice crystals. In a series of simulations, Haymet and coworkers (see Refs. 193-196) studied the density variation, the orientational order and the layer-dependence of the mobilitity of water molecules. The ice/water basal interface is found to be a relatively broad interface of about... 

Statistical methods are used to measure the density variation as the tool rotates, the stand-off can be estimated and the density corrected. A density caliper can be computed that works for cavings of 2 in. (5 cm) or less when the tool rotates at a speed ranging from 6 to 150 rpm. 

Convection is classified according to the motivating flow. When the flow takes place because of density variations caused by temperature gradients, the motion is called natural convection. When it is caused by an external agency such as a pump or a fan the process is called forced convection. 

Incompressible Limit In order to obtain the more familiar form of the Navier-Stokes equations (9.16), we take the low-velocity (i,e. low Mach number M = u I /cs) limit of equation 9,104, We also take a cue from the continuous case, where, if the incompressible Navier-Stokes equations are derived via a Mach-number expansion of the full compressible equations, density variations become negligible everywhere except in the pressure term [frisch87]. Thus setting p = peq + p and allowing density fluctuations only in the pressure term, the low-velocity limit of equation 9,104 becomes... 

Other methods for estimating the volume percentage of the interphases in a composition have been proposed, too, for example, measurements of density variations [76, 77], volume of compressed sample [78], the dielectric constant [77], etc. The important thing is that the interphase thickness determined in one way or another is an effective value dependent upon the conditions and type of the experiment by which it was determined [51]. 

Distribution and Octol Density Variation in Shaped Charge Warheads (Shillelagh, TOW, DRAGON) , FATM 2134 (April 1974)... 

Density Variation Gravimetric HYDROMETER METHOD Ths suspension of a powder is prepd as for other sedimentation... 

For an incompressible fluid, the density variation with temperature is negligible compared to the viscosity variation. Hence, the viscosity variation is a function of temperature only and can be a cause of radical transformation of flow and transition from stable flow to the oscillatory regime. The critical Reynolds number also depends significantly on the specific heat, Prandtl number and micro-channel radius. For flow of high-viscosity fluids in micro-channels of tq < 10 m the critical Reynolds number is less than 2,300. In this case the oscillatory regime occurs at values of Re < 2,300. 

Here the extraction is carried out continuously in a single, perfectly mixed, extraction stage as shown in Fig. 3.34. It is assumed that the outlet flow concentrations, Xi and Yi, achieve equilibrium and that density variations are negligible. 

Nonideal volumetric density variation versus pressure. 

Why temperatures and rainfall near Chesapeake Bay should be affected by variations of the tidal forces is not so clear. However the atmosphere and stratosphere are pulled away from the earth by tidal forces just as are the waters of the earth. These forces vary by as much as 10 percent during the tidal periods [67] resulting in density variations in the stratosphere with the same periods the consequent density variations may affect the relative rates of stratospheric chemical reactions, causing disturbances of temperature and rainfall on the ground with the tidal periodicities. 

As a blast wave passes through the air or interacts with and loads a structure or target, rapid variations in pressure, density, temperature and particle velocity occur. The properties of blast waves which are usually defined are related both to the properties which can be easily measured or observed and to properties which can be correlated with blast damage patterns. It is relatively easy to measure shock front arrival times and velocities and entire time histories of overpressures. Measurement of density variations and time histories of particle velocity are more difficult, and few reliable measurements of temperature variations exist. 

---