Fluid flow in tube

Laminar fluid flow in tubes has been described by Levich [ 3 ]. An entry length, le, is necessary to establish Poiseuille flow, given approximately by... 

Ujhidy, A., Nemeth, J., Szepvolgyi, J., Fluid flow in tubes with helical elements, Chem. Eng. Proc. 2003, 42,1-7. 

Laminar steady-state fluid flows in tubes of various cross-sections were studied by many authors (e.g., see [179,276, 427]). Such flows are often encountered in practice (water-, gas- and oil pipelines, heat exchangers, etc.). It is worth noting that in these cases the corresponding hydrodynamic equations admit an exact closed-form solution. In what follows we describe the most important results in that direction. 

For surfaces in unbounded convection, such as plates, tubes, bodies of revolution, etc., immersed in a large body of fluid, it is customary to define h in Eq. (1.12) with 7 as the temperature of the fluid far away from the surface, often identified as T. (Fig. 1.2). For bounded convection, including such cases as fluids flowing in tubes or channels, across tubes in bundles, etc., Tf is usually taken as the enthalpy-mixed-mean temperature, customarily identified as T . 

Plug flow in a tube is an ideal-flow assumption in which the fluid is well mixed in the radial and angular directions. The fluid velocity is assumed to be a function of only the axial position in the tube. Plug flow is often used to approximate fluid flow in tubes at high Reynolds number. The turbulent flow mixes the fluid in the radial and angular directions. Also in turbulent flow, the velocity profile is expected to be reasonably flat in the radial direction except near the tube wall. 

Reynolds no Re inertial forces/ pipe Fluid flow in tubes ... 

When hoi fluid flows in tubes, intei-change subscripts c and h. 

Thus, the change in the rate of fluid flows in tube W devices and relation dp/d is almost the only, but very effective way to affect the nature of the dispersion and the quality of the emulsion. These patterns of relationships allow under optimal conditions and without nontechnical or technical problems create thin homogeneous dispersion systems liquid-liquid with a minimum residence time of the reactants in the mixing zone, and use simple apparatus to design small confusor-diffuser design. 

S. Yoshida and H. Mori, Heat Transfer to Supercritical Pressure Fluids Flowing in Tubes, Proc. 1st Int. Symp. on SCWR, Tokyo, Japan, November 6-8, 2000, Paper No. 106 (2000)... 

Circular Tubes Numerous relationships have been proposed for predicting turbulent flow in tubes. For high-Prandtl-number fluids, relationships derived from the equations of motion and energy through the momentum-heat-transfer analogy are more complicated and no more accurate than many of the empirical relationships that have been developed. 

Fluid-Elastic Coupling Fluid flowing over tubes causes them to vibrate with a whirling motion. The mechanism of fluid-elastic coupling occurs when a critical velocity is exceeded and the vibration then becomes self-excited and grows in amplitude. This mechanism frequently occurs in process heat exchangers which suffer vibration damage. 

Nr = Rows of tubes per shell pass (Nr is always equal to the number of minimum clearances through which the fluid flows in series. For square staggered pitch the maximum velocity, Umax, which is required for evaluating Re may occur in the transverse clearances a or the diagonal clearances c. In the latter case Nr is one less than the number of tube rows.)... 

The influences these factors have on fluid flow in the tubes are as follows ... 

ISO 3966. Measurements of fluid flow in closed conduits—Velocity area method using Pitot static tube. 1977, p. 39. 

ISO Standard 3966. Measurement of Fluid Flow in Closed Conduits—Velocity Area Method Using Pitot Static Tubes. International Organisation fot Standardisation, 1977. 

Normally the vortex finder should extend down into the conical portion of the cyclone. It is thought that the vortex finder plays an important role in the maintenance of a stable spiraling fluid flow in the cyclone, and this makes it more difficult for the particles to leak through the boundary layer on the roof of the lid of the cyclone to the overflow tube.- Without a vortex finder, the efficiency may be reduced by 4-5%. However, an excessive long vortex finder may hinder the high spin velocity in the fluid flow and thus reduce the efficiency of the cyclone. 

Some gas processes use direct fired furnaces. Process fluid flows inside tubes that are exposed to a direct fire. In this case radiant energy is important. Furnaces are not as common as other devices used in production facilities because of the potential fire hazard they represent. Therefore, they are not discussed in this volume. 

For heat exchangers in true counter-current (fluids flowing in opposite directions inside or outside a tube) or true co-current (fluids flowing inside and outside of a tube, parallel to each other in direction), with essentially constant heat capacities of the respective fluids and constant heat transfer coefficients, the log mean temperature difference may be appropriately applied, see Figure 10-33. ... 

This unit consists of two pipes or tubes, the smaller centered inside the larger as shown in Figure 10-92. One fluid flows in the annulus between the tubes the other flows inside the smaller tube. The heat transfer surface is considered as the outside surface of the inner pipe. The fluid film coefficient for the fluid inside the inner tube is determined the same as for any straight tube using Figures 10-46-10-52 or by the applicable relations correcting to the O.D. of the inner tube. For the fluid in the annulus, the same relations apply (Equation 10-47), except that the diameter, D, must be the equivalent diameter, D,.. The value of h obtained is applicable directly to the point desired — that is, the outer surface of the inner tube. ... 

Figure 10-142. Pressure drop in fluid flowing across tube banks with segmental baffles. (Used by permission Buthod, A. P. Oil Gas Journal, V. 58, No. 3, 1960. PennWell Publishing Company. All rights reserved.)...

Celata GP, Cumo M, Marcom V, McPhail SJ, Zummo Z (2005) Micro-tube heat transfer scaling effects an experimental validation. In Proceedings of ECI International Conference on Heat Transfer and Fluid Flow in Microchannels, Caste/Vecchio PascoU, Italy, 25-30 September 2005... 

Stream C is the bundle-to-shell bypass stream. The fluid flowing in the clearance area between the outer tubes in the bundle (bundle diameter) and the shell. 

RG Cox, SG Mason. Suspended particles in fluid flow through tubes. Annu Rev Fluid Mech 3 291-315, 1971. 

Figure 18 illustrates the difference between normal hydrodynamic flow and slip flow when a gas sample is confined between two surfaces in motion relative to each other. In each case, the top surface moves with speed ua relative to the bottom surface. The circles represent gas molecules, and the length of an arrow is proportional to the drift velocity for that molecule. The drift velocity variation with distance is illustrated by the plots on the right. When the ratio of the mean free path to the separation distance between surfaces is much less than unity (Fig. 18a), collisions between gas molecules are much more frequent than collisions of the gas molecules with the surfaces. Here, we have classical fluid flow or viscous flow. If the flow were flow in tubes, Poiseuille s law would be obeyed. The velocity of gas molecules at the surface is the same as the velocity of the surface, and in the case of the stationary surface the mean tangential velocity of the gas at the surface is zero. 

Heat is to be transferred from one process stream to another by means of a double pipe heat exchanger. The hot fluid flows in a 1 in. sch 40 tube, which is inside (concentric with) a 2 in. sch 40 tube, with the cold fluid flowing in the annulus between the tubes. If both fluids are to flow at a velocity of 8 ft/s and the total equivalent length of the tubes is 1300 ft, what pump power is required to circulate the colder fluid Properties at average temperature p = 55 lbm/ft3, p = 8 cP. 

In nonadiabatic operation, heat transfer for control of T is accomplished within the bed itself. This means that the reactor is essentially a shell-and-tube exchanger, with catalyst particles either inside or outside the tubes, and with a heating or cooling fluid flowing in the shell or in the tubes accordingly. 

In the common case of cylindrical vessels with radial symmetry, the coordinates are the radius of the vessel and the axial position. Major pertinent physical properties are thermal conductivity and mass diffusivity or dispersivity. Certain approximations for simplifying the PDEs may be justifiable. When the steady state is of primary interest, time is ruled out. In the axial direction, transfer by conduction and diffusion may be negligible in comparison with that by bulk flow. In tubes of only a few centimeters in diameter, radial variations may be small. Such a reactor may consist of an assembly of tubes surrounded by a heat transfer fluid in a shell. Conditions then will change only axially (and with time if unsteady). The dispersion model of Section P5.8 is of this type. 

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