Reynolds Number single phase fluids

For single-phase fluid flow in smooth micro-channels of hydraulic diameter from 15 to 4,010 pm, in the range of the Reynolds numbers Re < Recr, the Poiseuille number, Po, is independent of the Reynolds number. Re. 

For gas-liquid flows in Regime I, the Lockhart and Martinelli analysis described in Section I,B can be used to calculate the pressure drop, phase holdups, hydraulic diameters, and phase Reynolds numbers. Once these quantities are known, the liquid phase may be treated as a single-phase fluid flowing in an open channel, and the liquid-phase wall heat-transfer coefficient and Peclet number may be calculated in the same manner as in Section lI,B,l,a. The gas-phase Reynolds number is always larger than the liquid-phase Reynolds number, and it is probable that the gas phase is well mixed at any axial position therefore, Pei is assumed to be infinite. The dimensionless group M is easily evaluated from the operating conditions and physical properties. 

Evaluation of each term in Eq. (15-51) is straightforward, except for the friction factor. One approach is to treat the two-phase mixture as a pseudo-single phase fluid, with appropriate properties. The friction factor is then found from the usual Newtonian methods (Moody diagram, Churchill equation, etc.) using an appropriate Reynolds number ... 

Reynolds number, friction factor, and coefficient of resistance. The pressure drop per 100 feet of pipe is then computed. For a given volumetric rate and physical properties of a single-phase fluid, AP,oq for laminar and turbulent flows is laminar flow... 

In order to select the pipe size, the pressure loss is calculated and velocity limitations are estabHshed. The most important equations for calculation of pressure drop for single-phase (Hquid or vapor) Newtonian fluids (viscosity independent of the rate of shear) are those for the deterrnination of the Reynolds number, and the head loss, (16—18). 

The basis for single-phase and some two-phase friction loss (pressure drop) for fluid flow follows the Darcy and Fanning concepts. The exact transition from laminar or dscous flow to the turbulent condition is variously identified as between a Reynolds number of 2000 and 4000. 

The data presented in the previous chapters, as well as the data from investigations of single-phase forced convection heat transfer in micro-channels (e.g., Bailey et al. 1995 Guo and Li 2002, 2003 Celata et al. 2004) show that there exist a number of principal problems related to micro-channel flows. Among them there are (1) the dependence of pressure drop on Reynolds number, (2) value of the Poiseuille number and its consistency with prediction of conventional theory, and (3) the value of the critical Reynolds number and its dependence on roughness, fluid properties, etc. 

The Reynolds number for porous media is defined using an appropriate characteristic length, usually an average particle or pore diameter, so that Re = pvDp/jx. For single-phase flow at low Reynolds numbers Re < 1), the superficial velocity is linearly proportional to the applied force(s) driving the fluid flow. The most common equation for this linear relationship is Darcy s law ... 

The noncavitating pressure distribution for the Venturi is shown in Fig. 3. The data are plotted in terms of a pressure coefficient Cp as a function of the axial distance from the minimum pressure point. Cp is conventionally defined as the difference between the local wall and free-stream static-pressure head ijix — ho) divided by the velocity head F /2g. Free-stream conditions are measured in the approach section about 1 in. upstream from the quarter roimd. The solid line (Fig. 3) represents a computed ideal flow solution. The dashed line represents experimental data obtained with nitrogen and water in the cavitation tunnel and from a scaled-up aerodynamic model studied in a large wind tunnel. The experimental results shown are all for a Reynolds number of about 600,000. The data for the various fluids are in good agreement, especially in the critical minimum-pressure region. The experimental pressure distribution shown here is assumed to apply at incipient cavitation, or more exactly, to the single-phase liquid condition just prior to the first visible cavitation. 

Liquid-liquid stratified flow in microchannel is often used in biological analysis, such as during ion exchange or solvent extraction from one phase to another phase [1]. For liquid flow in microfluidics, the Reynolds number is small and the flows are always laminar. Laminar fluid diffusion interfaces (LFDIs) are generated when two or more streams flow in parallel within a single microstructure [2], as shown in Fig. la. 

Whereas in a fixed bed reactor with a single fluid phase there exist only two modes of operation, either downflow (which is used in most cases) or upflow, and only two different flow regimes, either laminar or turbulent flow, which can be observed and characterized by a Reynolds number as the single relevant dimensionless group, the fluiddynamics in multiphase catalytic fixed bed reactors are much more complex. 

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