Linear mass density

Table I. Molecular weights, contour lengths, and linear mass densities...

The effect of dislocation line oscillations on the probability of its separation from the defect was accounted for by Natsik [211, 212], who has considered the following model A dislocation line moves in the slipping plane under the action of the one-axis stress. The dislocation is characterized by the linear mass density p and tension coefficient C. Pinning in A and B sites is considered to be rigid, and the dislocation detachment from the defect located in the zero point is considered (Figure 21). At a li, I2 < d [d is... 

Other techniques measure the volumetric concentration of solids and firom this infer a linear mass density through the mass density of the individual particles. Probably the most common example of this technique is the use of capacitance measurement [e.g, 18], In this case, the volumetric concentration is established by measuring the capacitance and therefore the dielectric constant of the solids/ gas mixture. The overall dielectric constant will increase in proportion to the dielectric constant of individual particles multiplied by the volumetric concentration. As in the case of y rays, the interaction with the field will depend on the chemical composition as the dielectric constant will be different. However unlike the y ray interaction the influence of water is significantly different to that of the solids - the dielectric constant of water is 81 whereas for a typical solid it will be in the range 2-4. This means that a varying moisture content can have a considerable influence on the uncertainty of the measurement,... 

With all volumetric techniques, the inferred linear mass density will depend on the mass density of the individual particles. This may be an additional factor in the measurement uncertainty if the solid phase contains particles of different mass density. 

Dealing with textile applications of fibers, one becomes familiar with the denier or tex units, which indicate the linear mass density. The denier is the mass expressed in grams and contained in a length, /, of 9,000 meters of fiber, or of fiber yarn. For example, a 9,000 meters length of a B. mori silk filament with a diameter (2r) of about 13 pm has a mass where the density, 6, is about... 

More than half of the late type galaxies exhibit non-axisymmetric deviations with large amplitudes, Smax/ mm 2, corresponding to Am > 0.35 (from Eq. 1). In particular, most late type (Sc) spirals e bit two and three arm spirals with a non-linear mass density contrast. 

Let Ap, Au and AT denote the deviations of the mass density, p, the velocity field, u, and the temperature, T, fiom their fiill equilibrium values. The fluctuating, linearized Navier-Stokes equations are... 

The usual measuring device for feed flow is a magnetic flowmeter, which is a volumetric device whose output F must be multiplied by density p to produce mass flowMo- For most aqueous solutions which are fed to evaporators, the product of density and the function of solid content appearing above is linear with density ... 

Assume, for lack of anything better, that the mass density varies linearly with the number of moles of A. Specifically, assume... 

The outlet density is calculated assuming the mass density varies linearly with conversion to polymer as in Example 2.8 pout =1012kg/m. The estimate for Qp based on the outlet density is... 

Let us briefly review the essential ingredients to this procedure (for more details of the method see [30] and for our model [42]). For a given system the hydrodynamic variables can be split up into two categories variables reflecting conserved quantities (e.g., the linear momentum density, the mass density, etc.) and variables due to spontaneously broken continuous symmetries (e.g., the nematic director or the layer displacements of the smectic layers). Additionally, in some cases non-hydrodynamic variables (e.g., the strength of the order parameter [48]) can show slow dynamics which can be described within this framework (see, e.g., [30,47]). 

All our arguments in the previous sections were based on the assumption that the undulations set in as a stationary instability. That is, that the oscillation rate co in our ansatz (35) vanishes at onset. In this section we will discuss the situation for non-zero co and find that our previous assumption was justified. In our linear analysis enters now (for the first time in this chapter) the mass density of the system, which we will choose to be equal to unity p = 1. 

To improve the accuracy of HTG systems, a third transmitter located at a fixed distance above the bottom transmitter can be used for density compensation (Figure 3.109). These tank expert packages, in addition to level, can also calculate mass, density, and volume on the basis of measurements from three or more d/p cells and one temperature transmitter. Most manufacturers offer optional digital communication and the ability for remote adjustments of suppression and linearization. "Smart" level transmitters can convert the level readings of spherical or cylindrical tanks into actual volume percentage readings (Figure 3.113). 

Velocity meters measure the velocity v of fluid flow in a pipe of known cross section, thus yielding a signal linearly proportional to the volume flow rate Q. Mass meters provide signals directly proportional to the mass flow rate m = pQ, where p is the mass density. Coriolis meters, which are true mass meters, can be used only for liquids. Thermal-type flow meters use a heating element and determine the rate of heat transfer, which is proportional to the mass flow rate. This type of device is used mostly for gas measurements, but liquid flow designs are also available. 

The electric resistance of a material is defined as the ratio of the voltage applied across a material to the current (measured in amperes) that flows as a result. The unit of resistance is fl (V/A). It is more convenient to use specific resistance r, defined as the resistance between opposite faces of a 1-m cube. However, as was the case for fibers, it is more convenient to base the measurement on the linear density rather than cross-sectional area. This leads to the mass specific resistance, = rd, where d is mass density. Rs is usually expressed in fl g/cm. Under standard conditions, Rs for raw cotton is approximately 0.5x 10 fl g/cm. As raw cotton is washed and otherwise purified, its resistance increases at least 50-fold [589]. Moisture content has even a greater role in resistance with Rs = lO" fl g/cm at 10% RH decreasing a millionfold to Rs= 10 H g/cm at 90% RH [590]. 

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