Pressure-velocity determination

In molecular distillation, the permanent gas pressure is so low (less than 0 001 mm. of mercury) that it has very little influence upon the speed of the distillation. The distillation velocity at such low pressures is determined by the speed at which the vapour from the liquid being distilled can flow through the enclosed space connecting the still and condenser under the driving force of its own saturation pressure. If the distance from the surface of the evaporating liquid to the condenser is less than (or of the order of) the mean free path of a molecule of distillate vapour in the residual gas at the same density and pressure, most of the molecules which leave the surface will not return. The mean free path of air at various pressures is as follows —... 

Fan Rating. Axial fans have the capabiUty to do work, ie, static pressure capabiUty, based on their diameter, tip speed, number of blades, and width of blades. A typical fan used in the petrochemical industry has four blades, operates neat 61 m/s tip speed, and can operate against 248.8 Pa (1 in. H2O). A typical performance curve is shown in Figure 11 where both total pressure and velocity pressure are shown, but not static pressure. However, total pressure minus velocity pressure equals static pressure. Velocity pressure is the work done just to collect the air in front of the fan inlet and propel it into the fan throat. No useflil work is done but work is expended. This is called a parasitic loss and must be accounted for when determining power requirements. Some manufacturers fan curves only show pressure capabiUty in terms of static pressure vs flow rate, ignoring the velocity pressure requirement. This can lead to grossly underestimating power requirements. 

Maximum linear velocities and operating pressures were determined in 2.5-cm-diameter columns packed to a bed height of ca. 30 cm. 

Maximum operating linear velocities and pressures were determined in 2.5 X 30-cm beds for Sepharose and Sepharose CL media and with 5 X 15-cm beds for Sepharose fast flow gels, assuming pure/water as mobile phase. 

Thus in all corrosion reactions one (or more) of the reaction products will be an oxidised form of the metal, aquo cations (e.g. Fe (aq.), Fe (aq.)), aquo anions (e.g. HFeO aq.), Fe04"(aq.)), or solid compounds (e.g. Fe(OH)2, Fej04, Fe3 04-H2 0, Fe203-H20), while the other reaction product (or products) will be the reduced form of the non-metal. Corrosion may be regarded, therefore, as a heterogeneous redox reaction at a metal/non-metal interface in which the metal is oxidised and the non-metal is reduced. In the interaction of a metal with a specific non-metal (or non-metals) under specific environmental conditions, the chemical nature of the non-metal, the chemical and physical properties of the reaction products, and the environmental conditions (temperature, pressure, velocity, viscosity, etc.) will clearly be important in determining the form, extent and rate of the reaction. 

In a recent study of the transport of coarse solids in a horizontal pipeline of 38 mrrt diameter, pressure drop, as a function not only of mixture velocity (determined by an electromagnetic flowmeter) but also of in-line concentration of solids and liquid velocity. The solids concentration was determined using a y-ray absorption technique, which depends on the difference in the attenuation of y-rays by solid and liquid. The liquid velocity was determined by a sail injection method,1"1 in which a pulse of salt solution was injected into the flowing mixture, and the time taken for the pulse to travel between two electrode pairs a fixed distance apart was measured, It was then possible, using equation 5.17, to calculate the relative velocity of the liquid to the solids. This relative velocity was found to increase with particle size and to be of the same order as the terminal falling velocity of the particles in the liquid. 

The velocity-determining streamline. is always the axial one, since the wave will travel at the speed determined by the maximum values of Pj (pressure) and W2 (particle velocity) on the C-J plane... 

Jaffe et al (Ref 3), in the course of determination of the shock pressure required to initiate detonation of an acceptor in the shock sensitivity test, found that the velocity of the front as sensed by the pressure probe method, falls behind the true velocity of the shock front as the shock is attenuated. It has also been found that the maximum transmitted shock velocity generated by the two Tetryl pellets and measured in Lucite is 4.6mm/frsec. Shock velocities determined by optical method, shown in Table 3, p 25, run between 2.701... 

Taylor (Ref 23) stated that ignition of TNT chge at some point inside the expl, results in a very rapid drop in pressure velocity behind the deton front. A fixed proportion of the whole vol of burnt gas is at rest and the radial rat e of change of the variables velocity, pressure density become finite at the deton front. The fact that the velocity drops to ze ro at some point between the deton surface the center shows that a spherical deton wave can maintain itself in the case of TNT. It is not known whether this is true in all cases Lutzky (Ref 86) determined the "Flow ... 

Cooke, 1979 Wu, 1981). In this range transfer velocities determined from natural systems are possibly distorted by an additional effect called wind pumping. In this situation, bubbles are injected deep below the water surface and experience pressures in excess of atmospheric. As a result, larger quantities of the chemicals contained in the bubbles are dissolved in the water than are required for equilibrium at the water surface. This leads to supersaturation of 02, N2, and C02 of up to 15% (Smith and Jones, 1985). Note that this process not only influences the deduced sizes of viW and v a/w, but it may also invalidate the general form of Eq. 20-1 according to which the sign of the net air-water flux is determined by the sign of the concentration difference (C, w - ). In order to produce supersaturation, F a/w must... 

SFC is complementary to other classical techniques of liquid or gas chromatography. The migration of the analyte is explained by a dissolution-precipitation mechanism that depends on the solvation power of the mobile phase. Thus, it is governed by the pressure that determines the density of the supercritical phase. Resistance to mass transfer between the stationary and mobile phases is less than that found in HPLC because diffusion is faster. The C factor in Van Deemter s equation is smaller so the velocity of the mobile phase can be increased (see Fig. 6.3). Moreover, because the viscosity of the mobile phase is similar to that of a gas, it is possible to use capillary columns like those used in capillary GC. However, the... 

Evaluation of the density at the front, together with the Rankine-Hugoniot relations and the measured front velocity, determines the pressure and particle velocity there. In practice, this requires an additional assumption, which will be made throughout. Since the reaction zone is much smaller than the foil spacing, the reaction is treated as instantaneously complete within the shock transition, and the final state to which the Rankine-Hugoniot equations apply is taken to be the equilibrium state at the end of the reaction zone. No evidence of a reaction zone can be detected either in the analysis of the foil data or on the radiographs. 

Fluid-dynamic operating conditions, such as axial or angular velocity (i.e., shear stress that determines drag force value) and transmembrane pressure (that determines disperse-phase flux, for a given disperse-phase viscosity and membrane... 

Figure 12.33 gives velocity profiles for the PP/PS system, which were obtained with the aid of Eqs. 12.3-21 and 12.3-22, using volumetric flow rates and pressure gradients determined experimentally in a rectangular channel. Figure 12.34 gives plots of viscosity versus shear stress for the PP and PS employed. It is seen that the polymer melts obey a Power Law model for y > 10s 1. 

In order to determine the distributions of pressure, velocity, and temperature the principles of conservation of mass, conservation of momentum (Newton s Law) and conservation of energy (first law of Thermodynamics) are applied. These conservation principles represent empirical models of the behavior of the physical world. They do not, of course, always apply, e.g., there can be a conversion of mass into energy in some circumstances, but they are adequate for the analysis of the vast majority of engineering problems. These conservation principles lead to the so-called Continuity, Navier-Stokes and Energy equations respectively. These equations involve, beside the basic variables mentioned above, certain fluid properties, e.g., density, p viscosity, p conductivity, k and specific heat, cp. Therefore, to obtain the solution to the equations, the relations between these properties and the pressure and temperature have to be known. (Non-Newtonian fluids in which p depends on the velocity field are not considered here.) As discussed in the previous chapter, there are, however, many practical problems in which the variation of these properties across the flow field can be ignored, i.e., in which the fluid properties can be assumed to be constant in obtaining fire solution. Such solutions are termed constant... 

Microfiltration is a unit operation for the separation of small particles. The separation limits are between 0.02 and 10 (jum particle dimensions. Microfiltration can be carried out in a dead-end mode and a cross-flow mode. In downstream processing, the cross-flow filtration is carried out continuously or discontinuously. The most important parameters that determine the productivity of cross-flow microfiltration are transmembrane pressure, velocity, particle size and surface, viscosity of the liquid and additives such as surfactants, and changing the surface and surface tension. 

In Chapter 4.2.2 we already discussed methods for the theoretical calculation of the detonation velocity and detonation pressure. In this chapter we now want to focus on the experimental determination of the detonation velocity. Bearing in mind that detonation velocities of known high explosives may reach up to 10,000 m s the experimental determination of the detonation velocity is not easily achieved. There are several methods which are suitable to measure the detonation velocity [38], Most of these methods are based on the fact that the detonation process is accompanied by the emission of light (autoluminous process). Depending on the measuring equipment selected, the methods for the detonation velocity determination can be divided into,... 

Effect of Flow Velocity. The flow velocity determines the shear rate and the pressure gradient. Therefore, the magnitude of a viscous force acting on a water droplet is directly related to flow velocity. This viscous force determines whether droplets can pass through pore throats smaller than themselves. It is also a factor in breakup of droplets into smaller droplets. 

The steady gas flow in a long macroscopic channel with impermeable walls is basically a Poiseuille flow with the constant velocity determined by the pressure gradient. However, the velocity of the flow in the fuel cell channel varies since there is mass and momentum transfer through the channel/backing layer interface. 

First of all, the density and all the thermodynamic coefficients are constants. Secondly, when the density and the transport properties are constants, the continuity and momentum equations are decoupled from the energy equation. This result is important, as it means that we may solve for the three velocities and the pressure without regard for the energy equation or the temperature. Third, for incompressible flows the pressure is determined by the momentum equation. The pressure thus plays the role of a mechanical force and not a thermodynamic variable. Fourth, another important fact about incompressible flow is that only two parameters, the Reynolds number and the Froude number occur in the equations. The Froude number, Fr, expresses the importance of buoyancy compared to the other terms in the equation. The Reynolds number indicates the size of the viscous force term relative to the other terms. It is mentioned that compressible flows are often high Re flows, thus they are often computed using the inviscid Euler (momentum) equations. 

In an effort to understand the formidable-appearing output of many computations for a wide variety of C-H-N-O explosives at various initial loading densities, we have investigated interrelationships between such properties as pressure, velocity, density, heat of reaction, etc. These studies have led to a number of interesting observations, important among which were the facts that much simpler semiempirical formulas could be written for desk calculation of detonation velocities and detonation pressures, with about the same reliance on their answers as one could attach to the more complex computer output. These equations require as input information only the explosive s composition and loading density and an estimate of its heat of formation, and, in their comparative simplicity, seem to throw light on the relative importance of the quantities which determine the detonation pressure in particular, and other properties as well. 

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