Tube flow analogy

The tube-flow analogy viscous flow conditions... 

The viscous flow regime revised tube-flow analogy... 

Apparently no attempts have been made to prepare a complete chart for the prediction of flow patterns in vertical flow, analogous to Fig. 4. Kozlov (K5) has stated, on the basis of his experiments with air and water in a 1-in. diameter tube, that the flow pattern can be defined by plotting the volumetric gas fraction fed and the average Froude number, Vii /gD- He gives equations for the boundary lines between types of flow (assumed to be straight lines on a log-log plot of the type suggested). 

It turns out that Eq. (5-56) can also be applied to turbulent flow over a flat plate and in a modified way to turbulent flow in a tube. It does not apply to laminar tube flow. In general, a more rigorous treatment of the governing equations is necessary when embarking on new applications of the heat-trans-fer-fluid-friction analogy, and the results do not always take the simple form of Eq. (5-56). The interested reader may consult the references at the end of the chapter for more information on this important subject. At this point, the simple analogy developed above has served to amplify ouf understanding of the physical processes in convection and to reinforce the notion that heat-transfer and viscous-transport processes are related at both the microscopic and macroscopic levels. 

Equation (5-114) is called the Reynolds analogy for tube flow. It relates the heat-transfer rate to the frictional loss in tube flow and is in fair agreement with experiments when used with gases whose Prandtl numbers are close to unity. (Recall that Pr = 1 was one of the assumptions in the analysis.)... 

Metzner and Friend [73] measured turbulent heat transfer rates with aqueous solutions of Carbopol, corn syrup, and slurries of Attagel in circular-tube flow. They developed a semi-theoretical correlation to predict the Stanton number for purely viscous fluids as a function of the friction factor and Prandtl number, applying Reichardt s general formulation for the analogy between heat and momentum transfer in turbulent flow ... 

Horizontal Ducts. The topology of flow patterns in horizontal tubes with a circular cross section has different although analogous structure to that for the upward vertical two-phase flow. In Fig. 17.486, the major types of the horizontal tube flow patterns are presented. 

The most popular approach is the pipe flow analogy model, also called the capillary tube model or channel model, which approximates the flow through the packed bed by the flow through a bundle of straight capillaries of equal size. Further refinement produced the constricted tube model. In this model, an assembly of tortuous channels of varying cross sections simulates the varying dimensions and curvatures of pores in the packed bed. The major contributions following this approach include Blake (1922), Kozeny (1927),... 

Capillary Electrochromatography Another approach to separating neutral species is capillary electrochromatography (CEC). In this technique the capillary tubing is packed with 1.5-3-pm silica particles coated with a bonded, nonpolar stationary phase. Neutral species separate based on their ability to partition between the stationary phase and the buffer solution (which, due to electroosmotic flow, is the mobile phase). Separations are similar to the analogous HPLC separation, but without the need for high-pressure pumps, furthermore, efficiency in CEC is better than in HPLC, with shorter analysis times. 

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. 

Derive the Taylor-Prandtl modification of the Reynolds Analogy between momentum and heat transfer. In a shell and tube condenser, water flows through the tubes which are 10m long and 40 mm diameter. The... 

These filled tubes or capillaries hence are mini fixed beds with internal micro flow regions. Such approach is a link between real micro structured units and conventional equipment. The type of processing may be analogous to conventional processing, e.g. fixed-bed or trickle-bed operation. 

The stream flows can be arranged in series or parallel, or a combination of series and parallel, see Figure 12.61. Each stream can be sub-divided into a number of passes analogous to the passes used in shell and tube exchangers. 

Obviously, the nucleation is a randon process which is amplified by subsequent deposition of many thousands of silver atoms before the surface is completely covered (if integrated over the time interval of monolayer formation the current in each pulse corresponds to an identical charge). Such an amplification of random processes is the only way they can be observed. This situation is quite analogous, for example, to radioactive decay where a single disintegration is followed, in a Geiger tube, by the flow of millions of electrons. ... 

To identify the isomeric form of the product of the collisionally stabilized analog of reaction 44 experimentally, Scott et al.92 studied reactions of C3H30+ (C2Hj/CO) produced in that reaction and compared it with that produced directly from propynal in an electron impact ion source or by proton transfer from HCO+ to propynal in the flow tube (these latter two production methods yielded ions with... 

By analogy with laminar flow in a tube, the friction factor in laminar flow would be... 

---