Pressure horizontal flow

Total pressure drop for vertical upflow of gases and solids includes acceleration and fric tional affec ts also found in horizontal flow, plus potential energy or hydrostatic effects. Govier and Aziz review many of the pressure drop calculation methods and provide recommendations for their use. See also Yang AIChE J., 24, 548-552 [1978]). 

At all points in a system, the static pressure is always equal to the original static pressure less any velocity head at a specific point in the system and less the friction head required to reach that point. Since both the velocity head and friction head represent energy and energy cannot be destroyed, the sum of the static head, the velocity head, and the friction head at any point in the system must add up to the original static head. This is known as Bernoulli s principal, which states For the horizontal flow of fluids through a tube, the sum of the pressure and the kinetic energy per unit volume of the fluid is constant. This principle governs the relationship of the static and dynamic factors in hydraulic systems. 

There are several possible explanations of the apparent conflict between Figs. 34 and 35. One possible explanation, for example, would be that the vertical upflow curve drawn in Fig. 34 may not be a straight line, but should perhaps curve upwards (the data itself shows some signs of this) toward the uppermost point of the horizontal flow line, which corresponds to the rod bundle in question. It will be seen later, however, that this would not appear to be the explanation. In addition, there is the fact that all the horizontal flow data in Fig. 34, as well as the new data in Fig. 35, are for a test pressure of 1215 psia, whereas the vertical upflow data in Fig. 34 refer to 1000 psia. Although there is no evidence to indicate the effect of pressure in the case of rod-bundle systems with round tubes, it is found that increasing pressure from... 

Farooqi, S. 1. and Richardson, J. F. Trans. Inst. Chem. Eng. 60 (1982) 323. Horizontal flow of air and liquid (Newtonian and non-Newtonian) in a smooth pipe Part II Average pressure drop. 

Figure 3.8 Comparison of theory and experiments (water-air horizontal flow at 25°C and 1 atm pressure with diameter of 2.5 cm). Solid lines theory. (From Dukler, 1978. Copyright 1978 by National Council of Canada. Reprinted with permission.) Fuzzy lines experimental data. (From Mand-hane et al., 1974. Copyright 1974 by Elsevier Science Ltd., Kidlington, UK. Reprinted with permission.)...

The frictional pressure gradient is obtained by different correlations described in following sections. In a horizontal flow, (dp/dz)elev = 0, it is an ideal case to perform experiments excluding the term of elevation pressure drop. Because of nonhomogeneity of the slug flow, the acceleration pressure gradient term is different from that shown above it is given in Section 3.5.2.2. 

Two major effects contribute to the pressure drop in horizontal flow acceleration and friction loss. Initially the inertia of the particles must be overcome as they are accelerated up to speed, and then the friction loss in the mixture must be overcome. If Vs is the solid particle velocity and ms = ps I7s( l — ) is the solids mass flow rate, the acceleration component of the pressure drop is... 

Wirth, K. E., and Molerus, O., Critical Velocity and Pressure Drop for Horizontal Flow, 9 156-166 (1986)... 

Pressure filters, 76 658-659 horizontal belt, 77 379 thickening, 77 382-388 Pressure gauge, 20 645 Pressure gradients, flow caused by, 9 110 Pressure infiltration, of metal-matrix composites, 76 167-169 Pressure injection, moldings, 10 11 Pressure-jump method, 73 427-428... 

Consider the case of incompressible, horizontal flow. Equation 1.11 shows that if a flowing element of fluid is brought to rest (v2 — 0), the pressure P2 is given by... 

The experimental work on which the correlation is based was done for horizontal flow of air-liquid mixtures at near-atmospheric pressures and with no change of phase. It is inadvisable to use the correlation for other conditions. For the conditions employed, the accelerative component of the pressure gradient was assumed to be negligible, while the static head... 

These empirical correlations were originally based mainly on data obtained for isothermal horizontal flow at pressures close to atmospheric (to 50 psi), normal temperatures, and pipe diameters to one inch using air and eight different liquids. In order to apply these equations to singlecomponent two-phase flow with mass transfer between phases, Martinelli... 

This correlation (C3) is intended to apply for turbulent-turbulent horizontal flow in pipes, and was developed to give better pressure-drop prediction for higher pressures and larger-diameter pipes. On an entirely empirical basis, the quantity APtp/aPl is given as a function of liquid volume-fraction of the feed, with a quantity >Pq pl/ l po as a parameter. For this correlation aP l is evaluated as the pressure-drop based on the total mass-flow using the liquid-phase properties. The parameter po ph/ Lpo is defined as... 

For mass transfer in two-component cocurrent two-phase flow, very little work seems to have been carried on in systems analogous to those for which pressure-drops have been measured, that is, in tubes, pipes, or rectangular channels. Only two publications dealing with vertical flow (V2, V3), and two concerned with horizontal flow (A5, S6), have appeared. 

Fig. 5 SEM images of ordered GaN nanopillars grown at a substrate temperature of 950 °C. a Reactor pressure of 8 bar with N2 as carrier gas (100 seem) using SMP 1 in a horizontal flow reactor and b at a reactor pressure of 4 bar with N2 as carrier gas (100 seem) in a vertical flow reactor. Inset-, side view of nanopillars...

The numerical solutions necessary to solve the practical three-dimensional problems agree well with the closed-form analytical solutions for simpler one- and two-dimensional cases with constant material properties. The resin pressure gradient in the thickness (vertical) direction for a well-dammed laminate (no horizontal flow) is nonlinear. 

Resin flow models are capable of determining the flow of resin through a porous medium (prepreg and bleeder), accounting for both vertical and horizontal flow. Flow models treat a number of variables, including fiber compaction, resin viscosity, resin pressure, number and orientation of plies, ply drop-off effects, and part size and shape. An important flow model output is the resin hydrostatic pressure, which is critical for determining void formation and growth. 

The pressure curves for both laminates (Fig. 10.8) showed the existence of a horizontal pressure gradient and that the magnitude of the gradient depends on the amount of horizontal flow (i.e., the larger gap distance between the laminate edges and the dams resulted in more horizontal flow). 

The pressure curves also illustrate the horizontal flow process. The resin pressure initially approaches the applied autoclave pressure and then decreases as bleeding occurs. The opposite occurs in the bleeder. The applied vacuum is measured initially, and the pressure increases as resin begins to fill the bleeder. Note that the horizontal pressure gradient is very small for a majority of the laminate but becomes large near the edges. 

A method for predicting pressure drop and volume fraction for non-Newtonian fluids in annular flow has been proposed by Eisen-berg and Weinberger (AlChE J., 25, 240-245 [1979]). Das, Biswas, and Matra (Can. J. Chem. Eng., 70, 431—437 [1993]) studied holdup in both horizontal and vertical gas/liquid flow with non-Newtonian liquids. Farooqi and Richardson Trans. Inst. Chem. Engrs., 60, 292-305, 323-333 [1982]) developed correlations for holdup and pressure drop for gas/non-Newtonian liquid horizontal flow. They used a modified Lockhart-Martinelli parameter for non-Newtonian... 

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