Flow Coefficient Reynolds Number

At velocities greater than the critical, the fluid velocity profile in the conduit is uniform across the conduit diameter except for a thin layer of fluid at the conduit wall. This boundary layer continues to move in laminar flow. In connection with flow measurement, most flowmeters have constant coefficients under turbulent flow conditions. Some flowmeters have the advantage of constant coefficients over Reynolds Number ranges encompassing both turbulent and laminar flows. See also Fluid and Fluid Flow and Reynolds Number. 

A qualitative explanation of the above results is based on fluid dynamics and other heat transfer results. First, a relationship of the form h,/h() = [ (Re) (.J (Re)/]Y would be expected. The fact that this exponent X is composed of a constant term plus a term dependent on (Re)y is not surprising, in light of the results of others—for example, Eckert and Drake (2). For axial flow, having no flow separation, the rate of increase of heat transfer coefficient with Reynolds number remains essentially constant for cross flow, at Reynolds numbers such that flow separation occurs, it increases with increasing Reynolds number. The... 

In double-pipe and shell-and-tube heat exchangers, fluids flow through straight, smooth pipes and tubes of circular cross section. Many correlations have been published for the prediction of the inside-wall, convective heat transfer coefficient, /i when no phase change occurs. For turbulent flow, with Reynolds numbers, = D,G/ ji, greater than 10,000, three empirical correlations have been widely quoted and applied. The first is the Dittus-Boelter equation (Dittus and Boelter, 1930) for liquids and gases in fully developed flow (Z>,/L < 60), and with Prandtl numbers, = Cp[iJk, between 0.7 and 100 ... 

The model described has been applied to compressible air flow with Reynolds numbers in the range of 500 to 1,500. These values were obtained using Eq. 5 that is also valid for shockwave propagation in a narrow channel [2]. Further, based on the analysis of gas flow characteristics in silicon microchannels [6], the friction coefficient/has been found to be approximately 0.04 for a Reynolds number of 500, while for Reynolds numbers greater than 1,000, the friction coefficient becomes less than 0.005. 

Vapor Flow Effect For a relatively large conventional heat pipe, the wick structures existing in the heat pipe help to reduce the vapor flow effect on the liquid flow. For a micro/miniature heat pipe, the vapor space in the micro heat pipe is so small and the ratio of the hydraulic diameter of the vapor flow channel to the hydraulic diameter of liquid flow in the comer regions is much larger than a conventional heat pipe. The vapor flow has a larger effect on the heat transport capability than the conventional heat pipe. Ma et al. [5] have conducted a detailed investigation of the vapor flow effect on the liquid flow. The friction coefficient Reynolds number product, i. e., Cfj Rei, for the liquid flow in the comer region must include the vapor flow effect, which depends on the vapor flow rate. 

The gas flow for Reynolds numbers Rey > 2100 is practically turbulent. In this range, the resistance coefficient Jr is only marginally dependent on the Reynolds number Rey. In practical applications, columns equipped with larger-diameter packing elements of d > 0.025 m are always operated in the turbulent range. 

An outstanding advantage of common differential pressure meters is the existence of extensive tables of discharge coefficients ia terms of beta ratio and Reynolds numbers (1,4). These tables, based on historic data, are generally regarded as accurate to within 1—5% depending on the meter type, the beta ratio, the Reynolds number, and the care taken ia manufacture. Improved accuracy can be obtained by miming an actual flow caUbration on the device. 

This equation is appHcable for gases at velocities under 50 m/s. Above this velocity, gas compressibiUty must be considered. The pitot flow coefficient, C, for some designs in gas service, is close to 1.0 for Hquids the flow coefficient is dependent on the velocity profile and Reynolds number at the probe tip. The coefficient drops appreciably below 1.0 at Reynolds numbers (based on the tube diameter) below 500. 

Characterization and influence of electrohydro dynamic secondary flows on convective flows of polar gases is lacking for most simple as well as complex flow geometries. Such investigations should lead to an understanding of flow control, manipulation of separating, and accurate computation of local heat-transfer coefficients in confined, complex geometries. The typical Reynolds number of the bulk flow does not exceed 5000. 

Fig. 17. Heat-transfer coefficient comparisons for the same volumetric flow rates for (A) water, 6.29 kW, and a phase-change-material slurry (O), 10% mixture, 12.30 kW and ( ), 10% mixture, 6.21 kW. The Reynolds number was 13,225 to 17,493 for the case of water.

The minimum velocity requited to maintain fully developed turbulent flow, assumed to occur at Reynolds number (R ) of 8000, is inside a 16-mm inner diameter tube. The physical property contribution to the heat-transfer coefficient inside and outside the tubes are based on the following correlations (39) ... 

The Reynolds number is sufficient as a parameter for describing the internal flow characteristics, such as discharge coefficient, air core ratio, and spray angle at the atomizer exit. 

Transition Region Turbulent-flow equations for predicting heat transfer coefficients are usually vahd only at Reynolds numbers greater than 10,000. The transition region lies in the range 2000 < < 10,000. 

Coils For flow inside helical coils, Reynolds number above 10,000, multiply the value of the film coefficient obtained from the apphcable equation for straight tubes by the term (1 + 3..5 D /DJ. 

Not only is the type of flow related to the impeller Reynolds number, but also such process performance characteristics as mixing time, impeller pumping rate, impeller power consumption, and heat- and mass-transfer coefficients can be correlated with this dimensionless group. 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

For low values of the Reynolds number, such as 10, where sn eamline flow should certainly apply, the Nusselt number has a value of about 2, and a typical value of the average heat transfer coefficient is 10 ". For a Reynolds number of 104, where the gas is certainly in turbulent flow, the value of the Nusselt number is typically 20. Hence there is only a difference of a factor of ten in the heat transfer coefficient between tlrese two extreme cases. 

Coolant flow is set by the designed temperature increase of the fluid and needed mass velocity or Reynolds number to maintain a high heat transfer coefficient on the shell side. Smaller flows combined with more baffles results in higher temperature increase on the shell side. Reacting fluid flows upwards in the tubes. This is usually the best plan to even out temperature bumps in the tube side and to minimize temperature feedback to avoid thermal runaway of exothermic reactions. 

Flow coefficients and pressure coefficients can be used to determine various off-design characteristics. Reynolds number affects the flow calculations for skin friction and velocity distribution. 

Coefficient A and exponent a can be evaluated readily from data on Re and T. The dimensionless groups are presented on a single plot in Figure 15. The plot of the function = f (Re) is constructed from three separate sections. These sections of the curve correspond to the three regimes of flow. The laminar regime is expressed by a section of straight line having a slope P = 135 with respect to the x-axis. This section corresponds to the critical Reynolds number, Re < 0.2. This means that the exponent a in equation 53 is equal to 1. At this a value, the continuous-phase density term, p, in equation 46 vanishes. 

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