Total internal pressure

For some moist materials, the Lu number increases with the moisture content following a slow linear dependence. From Eq. (6.184), we can appreciate that, for Lu>l, the propagation velocity of the mass transfer potential is greater than the propagation velocity of the temperature field potential. The value of the diffusive filtration number of moisture LUp is normally much higher than one. The total internal pressure relaxation of the vapour-gas mixture in a capillary porous body is 2-3 orders of magnitude higher than the relaxation of the temperature field. The relationships between Fourier numbers may be expressed in terms of Lu and LUpi... 

Under steady-state conditions, total internal pressure (P) approaches atmospheric pressure (PJ plus the saturated water vapor pressure, as described by the following equation ... 

By adding the osmotic pressure, 77, the electrostatic stress, Pe, and the capillary pressure, 77 (eigenstresses), in the ion cluster, which are induced by the redistribution of the ions and water, the total internal pressure, p, of the ion cluster can be calculated (Zhu et al. 2013a, b) ... 

Most of the steel pipes in use can be categorized as operating under moderate to high pressure. Corrosion of steel results in the reduction of wall thickness whereby the strength and pressure rating of the pipe are compromised. FRP can be used to create a pressure vessel inside the pipe that can resist all or a portion of the total internal pressure of the pipe. 

The internal pressure is a differential quantity that measures some of the forces of interaction between solvent molecules. A related quantity, the cohesive energy density (ced), defined by Eq. (8-35), is an integral quantity that measures the total molecular cohesion per unit volume. - p... 

Scope, 52 Basis, 52 Compressible Flow Vapors and Gases, 54 Factors of Safety for Design Basis, 56 Pipe, Fittings, and Valves, 56 Pipe, 56 Usual Industry Pipe Sizes and Classes Practice, 59 Total Line Pressure Drop, 64 Background Information, 64 Reynolds Number, R,. (Sometimes used Nr ), 67 Friction Factor, f, 68 Pipe—Relative Roughness, 68 Pressure Drop in Fittings, Valves, Connections Incompressible Fluid, 71 Common Denominator for Use of K Factors in a System of Varying Sizes of Internal Dimensions, 72 Validity of K Values,... 

Fans are classified according to the discharge pressure. Reprinted per written permission from the Air Movement and Control Association International, Inc., the AMCA Standard 99-1401-66 from Standards Handbook 99-56 1986, the total static pressure classification for operating limits for central station units is as follows ... 

Total static pressure includes the internal static pressure losses. ... 

Performance of a rotary positive-displacement compressor can be evaluated using the same criteria as a positive-displacement pump. As constant-volume machines, performance is determined by rotation speed, internal slip, and total back-pressure on the compressor. 

Figure 7. Total internal reflection sum frequency generation (TIR-SFG) vibrational spectroscopy of high-pressure room temperature adsorption of carbon monoxide on PVP-protected Pt cube monolayers and calcined (373 K, 3h) monolayers [27], The infrared spectra demonstrate CO is adsorbed at atop sites, but is considerably red-shifted on the PVP-protected Pt cubes. After calcination, the atop frequency blueshifts to 2085 cm in good agreement with CO adsorption on Pt(l 0 0) at high coverages [28], (Reprinted from Ref [27], 2006, with permission from American Chemical Society.)...

Since mercury has a contact angle with most solids of about 140°, it follows that its cosine is negative (i.e., it takes applied pressure to introduce mercury into a pore). In a mercury porosimeter, a solids sample is evacuated in a cell, mercury is then intruded, and the volume, V, is noted (it actually reads out), and the pressure, P, is then increased stepwise. In this fashion it is possible to deduce the pore volume of a particular radius [corresponding to P by Eq. (21)]. A pore size distribution will give the total internal pore area as well, which can be of importance in dissolution. 

A pole barn with thin metal walls must be fitted with a vent to safely vent a hydrocarbon deflagration from the combustion of a hydrocarbon similar to propane. The maximum pressure that this building can withstand is estimated at 0.5 psi. Determine the vent area required for this structure if the total internal surface area of the structure (including floor and roof) is 24,672 ft2. 

The total reinforcement area = 0.527 in.2 This is more than 0.343 in.2, so that no additional reinforcement is required to sustain the internal pressure. 

Chemists define the total internal energy of a substance at a constant pressure as its enthalpy, H. Chemists do not work with the absolute enthalpy of the reactants and products in a physical or chemical process. Instead, they study the enthalpy change, AH, that accompanies a process. That is, they study the relative enthalpy of the reactants and products in a system. This is like saying that the distance between your home and your school is 2 km. You do not usually talk about the absolute position of your home and school in terms of their latitude, longitude, and elevation. You talk about their relative position, in relation to each other. 

More recently, cells using total internal reflectance (TIR) probes have become readily available. The spectrum in Figure 5.3 was obtained, again at temperature and pressure, from an Ir catalysed carbonylation of methanol in a Parr autoclave modified to take a Sentinel IR probe. 

Johannes van der Waals developed his famous equation of state by the introduction of both the attractive and the repulsive forces between the molecules. First he postulated that the gas behaves as if there is an additional internal pressure to augment the external applied pressure, which is based on the mutual attraction of molecules since the density of molecules is proportional to 1/V, the intensity of the binary attractive force would be proportional to 1/V. Then he postulated that when the measured total volume begins to approach the volume occupied by the real gaseous molecules, the free volume is obtained by subtracting the molecular volume from the measured volume. Then he introduced the parameter a, which represents an attractive force responsible for the internal pressure, and the parameter b, which represents the volume taken by the molecules. He arrived at... 

The thicknesses of free soap films and liquid films adsorbed on surfaces (Figs. 1.26d and 1.26e), which can be measured using optical techniques such as reflected intensity, total internal reflection spectroscopy, or ellipsometry as functions of salt concentration or vapor pressure, can provide information on the long-range repulsive forces stabilizing thick wetting films. We see an example of this in Chapter 11. 

A similar situation exists for the isomer shift, and to some extent for the quadrupole interaction. For both interactions, the problem is theoretical in nature that is, for a particular catalytic system, it is not a priori known whether the particle size-dependent isomer shift or quadrupole interaction should be interpreted in terms of a shell model or an internal pressure effect. In the shell model, the Mossbauer parameters of the surface atoms are considered to be different from the corresponding parameters of the bulk atoms, and thus the total spectrum is a sum of these two contributions... 

Another important factor is the volume of unfilled headspace designed into the bottle. Typically, this is not less than 5% of the total volume for an IPP carbonated product and ideally it is more like 7%. This is because as the product expands during pasteurising, the headspace becomes squeezed, and the smaller the headspace volume, the higher the internal pressure becomes. This could blow the closure off the bottle or, more typically, cause leakage of carbon dioxide or product or both. The loss of product gives rise to uneven fill levels, which could cause consumer concern over apparent low fills or, more seriously, draw attention from trading standards officers because of short volume fills. 

There were disturbances due to the liquefaction of the gas. P. Isambert found that the coeff. of compressibility of aq. soln. of ammonia is less than that of water alone and the more cone, the soln., the smaller the compressibility. For a litre of liquid at 21-5° containing 330 litres of dissolved gas, the coeff. was 0-0000376, and at 20-4° with 140 litres of dissolved gas, 0-0000387. Observations were also made by G. M. Maverick, and E. L. Nichols and A. W. Wheeler. 0. Maass and D. M. Morrison studied the effect of molecular attraction on the total press, of ammonia and E. Lurie and L. J. Gillespie, the equilibrium press, of mixtures of ammonia and nitrogen. F. Schuster calculated 4512 atm. for the internal pressure of the liquid and J. H. Hildebrand, 3900 atm. 

The high-pressure device is a microautoclave made of tantalum and located in a thermo-regulated oven as shown in Figure 2. It is a closed reactor with a constant volume of 140 cm3. The total expected pressure is about 80 bars for a temperature close to 280°C. Tantalum has been chosen as the reference material for the internal part of the reactor in order to avoid corrosion from the products under study. 

Two particles of radii f and r% are each enveloped by a fluid whose surface tension is external pressure on each is pa and the internal pressure pi and pi, respectively, show that when the two particles coalesce, there is a decrease in the total surface. 

The total pore volume, Vp, sometimes called specific pore volume when referred to unit mass, is the total internal volume per unit mass of catalysts. Some of this pore volume may be completely enclosed and thus inaccessible to molecules participating in a catalytic reaction. The total accessible pore volume is often derived from the amount of vapour adsorbed at a relative pressure close to unity, by assuming that the pores are then filled with liquid adsorptive. The accessible pore volume may be different for molecules of different sizes. It may be useful to determine the dead space by means of a nonsorbable gas (normally helium) in conjuction with the determination of the bulk volume of the catalyst by means of a non-wetting liquid (mercury). 

Thermodynamic principles arise from a statistical treatment of matter by studying different idealized ensembles of particles that represent different thermodynamic systems. The first ensemble that we study is that of an isolated system a collection of N particles confined to a volume V, with total internal energy E. A system of this sort is referred to as an NVE system or ensemble, as N, V, and E are the three thermodynamic variables that are held constant. N, V, and E are extensive variables. That is, their values are proportional to the size of the system. If we combine NVE subsystems into a larger system, then the total N, V, and E are computed as the sums of N, V, and E of the subsystems. Temperature, pressure, and chemical potential are intensive variables, for which values do not depend on the size of the system. 

P = maximum allowable internal pressure, psig, or total pressure AP means pressure-difference driving force across filter Pi refers to vacuum-pump intake pressure P2 refers to vacuum-pump delivery pressure, lbf/ft 2 Pb = bursting pressure, psig Ps = safe working pressure, psig... 

---