Viscosity, dimensions

For direct measurement from core samples, the samples are mounted in a holder and gas is flowed through the core. The pressure drop across the core and the flowrate are measured. Providing the gas viscosity (ji) and sample dimensions are known the permeability can be calculated using the Darcy equation shown below. 

The shear viscosity is an important property of a Newtonian fluid, defined in terms of the force required to shear or produce relative motion between parallel planes [97]. An analogous two-dimensional surface shear viscosity ij is defined as follows. If two line elements in a surface (corresponding to two area elements in three dimensions) are to be moved relative to each other with a velocity gradient dvfdx, the required force is... 

Nonfractionating continuous inlet. An inlet in which gas flows from a gas stream being analyzed to the mass spectrometer ion source without any change in the conditions of flow through the inlet or by the conditions of flow through the ion source. This flow is usually viscous flow, such that the mean free path is very small in comparison with the smallest dimension of a traverse section of the channel. The flow characteristics are determined mainly by collisions between gas molecules, i.e., the viscosity of the gas. The flow can be laminar or turbulent. 

Strauss and Williamst have studied coil dimensions of derivatives of poly(4-vinylpyridine) by light-scattering and viscosity measurements. The derivatives studied were poly(pyridinium) ions quaternized y% with n-dodecyl groups and (1 - y)% with ethyl groups. Experimental coil dimensions extrapolated to 0 conditions and expressed relative to the length of a freely rotating repeat unit are presented here for the molecules in two different environments ... 

In all of these derivations concerning rigid bodies, no other walls are considered except the particle surfaces. Before we turn to the question of the intrinsic viscosity of flexible polymers, let us consider the relationship between the viscosity of a fluid and the geometry and dimensions of the container in which it is measured. 

The wedge restriction has no critical surface dimensions or sharp edges and tends to retain accuracy despite visible corrosive or erosive wear. It is commonly appHed to high viscosity Hquids, slurries, and hot multiphase mixtures. A similar device is also available using a cone, positioned so that its large diameter is upstream, mounted on the meter centerline. 

Effect of Uncertainties in Thermal Design Parameters. The parameters that are used ia the basic siting calculations of a heat exchanger iaclude heat-transfer coefficients tube dimensions, eg, tube diameter and wall thickness and physical properties, eg, thermal conductivity, density, viscosity, and specific heat. Nominal or mean values of these parameters are used ia the basic siting calculations. In reaUty, there are uncertainties ia these nominal values. For example, heat-transfer correlations from which one computes convective heat-transfer coefficients have data spreads around the mean values. Because heat-transfer tubes caimot be produced ia precise dimensions, tube wall thickness varies over a range of the mean value. In addition, the thermal conductivity of tube wall material cannot be measured exactiy, a dding to the uncertainty ia the design and performance calculations. 

Fiber dimensions have been studied for hemodialysis. When blood is circulated through the fiber lumen (m vivo), a significant reduction in apparent blood viscosity may occur if the flow-path diameter is below 100 p.m (11). Therefore, current dialy2ers use fibers with internal diameters of 180—250 p.m to obtain the maximum surface area within a safe range (see Dialysis). The relationship between the fiber cross section and the blood cells is shown in Figure 5. In many industrial appUcations, where the bore fluid is dialy2ed under elevated pressure (>200 kPa or 2 atm), fibers may burst at points of imperfection. Failure of this nature is especially likely for asymmetric fibers that display a large number of macro voids within the walls. 

Capillary Viscometers. Capillary flow measurement is a popular method for measuring viscosity (21,145,146) it is also the oldest. A Hquid drains or is forced through a fine-bore tube, and the viscosity is determined from the measured flow, appHed pressure, and tube dimensions. The basic equation is the Hagen-Poiseuike expression (eq. 17), where Tj is the viscosity, r the radius of the capillary, /S.p the pressure drop through the capillary, IV the volume of hquid that flows in time /, and U the length of the capillary. 

The original Ostwald viscometer has been modified in many ways, and a number of different versions are on the market (Table 4) (21). Most are available with a wide choice of capillary diameters and therefore a number of viscosity ranges. A number of viscometers are described in ASTM D445, which also Hsts detailed recommendations on dimensions and methods of use. 

Spray Correlations. One of the most important aspects of spray characterization is the development of meaningful correlations between spray parameters and atomizer performance. The parameters can be presented as mathematical expressions that involve Hquid properties, physical dimensions of the atomizer, as well as operating and ambient conditions that are likely to affect the nature of the dispersion. Empirical correlations provide useful information for designing and assessing the performance of atomizers. Dimensional analysis has been widely used to determine nondimensional parameters that are useful in describing sprays. The most common variables affecting spray characteristics include a characteristic dimension of atomizer, d Hquid density, Pjj Hquid dynamic viscosity, ]ljj, surface tension. O pressure, AP Hquid velocity, V gas density, p and gas velocity, V. ... 

Viscosity. Although traditionally of Httle importance in the evaluation of vegetable and insect waxes, viscosity is an important test for mineral and synthetic waxes. One of the most frequently used tests, ASTM D88, is used to measure the time in seconds required for a specified quantity of wax at a specified temperature to flow by gravity through an orifice of specified dimensions. This viscosity is expressed in Saybolt Universal Seconds (SUS) at the temperature of the test. The SI unit for kinematic viscosity is mm /s (=cSt). 

Pxampk 2. A smooth spherical body of projected area Al moves through a fluid of density p and viscosity p with speed O. The total drag 8 encountered by the sphere is to be determined. Clearly, the total drag 8 is a function of O, Al, p, and p. As before, mass length /, and time t are chosen as the reference dimensions. From Table 1 the dimensional matrix is (eq. 23) ... 

When viscometric measurements of ECH homopolymer fractions were obtained in benzene, the nonperturbed dimensions and the steric hindrance parameter were calculated (24). Erom experimental data collected on polymer solubiUty in 39 solvents and intrinsic viscosity measurements in 19 solvents, Hansen (30) model parameters, 5 and 5 could be deterrnined (24). The notation 5 symbolizes the dispersion forces or nonpolar interactions 5 a representation of the sum of 8 (polar interactions) and 8 (hydrogen bonding interactions). The homopolymer is soluble in solvents that have solubility parameters 6 > 7.9, 6 > 5.5, and 0.2 < <5.0 (31). SolubiUty was also determined using a method (32) in which 8 represents the solubiUty parameter... 

The various models for predicting values of He and Hi are given in Sec. 5. The important parameters in the models include gas rate, liquid rate, gas and liquid properties (density, viscosity, siirrace tension, diffiisivity), packing type and size, and overall bed dimensions. 

The largest size that can be treated depends mostly on the dimensions of the separating vessel coal up to 0.3 m (12 in) has been successfully processed in a drum separator of the type illustrated in Fig. 19-32. Complete removal of fines is usually necessary to ensure proper viscosity of the media. Fines increase viscosity and slow the... 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

The narrow molecular weight distribution means that the melts are more Newtonian (see Section 8.2.5) and therefore have a higher melt viscosity at high shear rates than a more pseudoplastic material of similar molecular dimensions. In turn this may require more powerful extruders. They are also more subject to melt irregularities such as sharkskin and melt fracture. This is one of the factors that has led to current interest in metallocene-polymerised polypropylenes with a bimodal molecular weight distribution. 

Assuming the column dimensions are 320 pm I.D. (radius r=0.0160 cm), 30 m long, and it is operated at 120°C using nitrogen as the carrier gas which, at that temperature, has a viscosity of 129 x 10 Poises, then by using equation (3), the change in (y) can be calculated for different flow rates. The relationship between flow... 

It should be emphasized that the dimensions of the applied pressure (P) must be appropriate for the dimensions in which the viscosity (rj) is measured and also the... 

Equation (13) is the first important equation for open tubular column design. It is seen that the optimum radius, with which the column will operate at the optimum velocity for the given inlet pressure, increases rapidly as an inverse function of the separation ratio (cc-1) and inversely as the square root of the inlet pressure. Again it must be remembered that, when calculating (ropt)5 the dimensions of the applied pressure (P) must be appropriate for the dimensions in which the viscosity (r)) is measured. 

Example Determine the dimensions of a simple settling chamber required to remove 50 ft size particles under the following conditions Gas capacity, q = 2400 mVhr Particle density, Pp = 2400 kg/m Gas temperature, t = 20 °C Gas density, p = 1.2 kg/m Gas viscosity, ft = 1.8x 10 N-s/m. The solution is as follows. The settling regime for the particles must be determined first. Hence, the critical particle diameter is computed first ... 

The power consumed by an agitator depends on its dimensions and the physical properties of the fluids being mixed (i.e., density and viscosity). Since there is a possibility of a gas-liquid surface being... 

The kinematic viscosity of a gas is a function of the pressure, and its dimension is the square of length divided by the time, its unit being m s k... 

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