Fanning coefficient

For Reynolds numbers up to 3 x 10 , Wasp et al. (1977) recommended the use of Nlku-radse equation for the Fanning coefficient ... 

Fanning friction factor /i for inner wall and / 2 for outer wall of annulus /l for ideal tube bank sldn friction drag coefficient Dimensionless Dimensionless... 

The dimensionless relations are usually indicated in either of two forms, each yielding identical resiilts. The preferred form is that suggested by Colburn ran.s. Am. In.st. Chem. Eng., 29, 174—210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cQ, the Prandtl number c Jk, and the Reynolds number DG/[L. For more accurate correlation of data (at Reynolds number <10,000), two additional dimensionless groups are used ratio of length to diameter L/D and ratio of viscosity at wall (or surface) temperature to viscosity at bulk temperature. Colburn showed that the product of the Stanton number and the two-thirds power of the Prandtl number (and, in addition, power functions of L/D and for Reynolds number <10,000) is approximately equal to half of the Fanning friction fac tor//2. This produc t is called the Colburn j factor. Since the Colburn type of equation relates heat transfer and fluid friction, it has greater utility than other expressions for the heat-transfer coefficient. 

Circulation of air at velocities of I to 10 m/s is desirable to improve the surface heat-transfer coefficient and to eliminate stagnant air pockets. Proper air flow in tray dryers depends on sufficient fan capacity, on the design of ductwork to modify sudden changes in direction, and on properly placed baffles. Nonuniform airflow Is one of the most serious problems in the operation of tray di yers. 

The equations have been expressed as proportionals however, they can be used by simply ratioing an old to a new value. To add credibility to fan law adaptation, recall the flow coefficient, Equation 5.19, The term Qj/N is used which shows a direct proportion between volume Qj and speed N. Equation 5.12 indicates the head, Hp, to be a function of the tip speed, squared. The tip speed is, in turn, a direct function of speed making head proportional to speed. Finally, the power, Wp, is a function of head multiplied by flow, from which the deduction of power, proper tional to the speed cubed, may be made. 

Figure 8-33. Correiation of axiai dispersion coefficient for fiow of fiuids through pipes in iaminar fiow region (Noe < 2,000). (Source Wen, C. Y. and Fan, L. T, Modeis for Fiow Systems and Chemicai Reactors, Marcel Dekker Inc., 1975.)...

The wind velocities are local values at the height of the doorway, so no additional wind sheltering coefficients or height corrections are necessary. A solution is sought for which both situations above can be handled with the same air curtain device by just changing the fan speed and the heating power of the air curtain. 

Figures 12-46 illustrates the key styles of wheels for use on the rotating shafts of multistage centrifugal, single-stage compressors and fans, and axial flow compressors (to he discussed later in this chapter). The flow-handling capability of a specific impeller geometry is descrihed hy the flow coefficient, ...

P[3 = P[ = fan input power D = fan size (impeller or wheel diameter) N = fan speed Nj = fan specific speed p = fan air density Q = fan flow rate Kp = compressibility coefficient L, = sound power level Pjt = fan total pressure Pjy = fan velocity pressure Pj-s = fan static pressure... 

Po = fan output power = total output power Q = fan flow rate, cfm Pjt = fan total pressure Kp = compressibility coefficient 7 = isentropic coefficient... 

Tj = air or gas temperature at outlet, °R P, = fan outlet velocity pressure, in. water abs or other absolute units n = polytropic coefficient Cj = fan static efficiency, fraction... 

Air-cooled exchangers consist of banks of finned tubes over which air is blown or drawn by fans mounted below or above the tubes (forced or induced draft). Typical units are shown in Figure 12.68. Air-cooled exchangers are packaged units, and would normally be selected and specified in consultation with the manufacturers. Some typical overall coefficients are given in Table 12.1. These can be used to make an approximate estimate of the area required for a given duty. The equation for finned tubes given in Section 12.14 can also be used. 

Any measure of the coordinate correlation is arbitrary. Here, the linear correlation coefficient r is used, largely because it is familiar. It measures the quality of a least-squares fit of a line to coordinates, with a magnitude that varies from 0 (for uncorrelated random coordinates) to 1 (for fully correlated coordinates lying on the line). For the correlated coordinates in Fig. 3.1 b, d, and f, theoretical relationships for r, that is, r =/(p1 p2) can be derived as shown in Appendix 3B. They show that r lies between the inclusive bounds of 1/2 and 1 for WEG, and between the inclusive bounds, 0 and 1, for FAN and PAR. 

Figure 3.3a-c shows graphs of correlation coefficient r versus p2 f°r different pj in WEG, FAN, and PAR. The curves are limiting values of r evaluated as described in Appendix 3B. The symbols are the average r s from 1000 simulations of 500 random correlated coordinates for different pj and p2. The agreement is excellent, except for r < 0.1. The small deviation probably is caused by minor imperfections in the random number generator. 

FIGURE 3.3 Graph of linear correlation coefficient r versus /J2 f°r various Pi in (a) WEG, (b) FAN, and (c) PAR. Curves are predictions points are simulation averages. 

Because the friction loss and wall stress are related by Eq. (5-47), the loss coefficient for pipe flow is related to the pipe Fanning friction factor as follows ... 

However, as regards the conventional method, a linearity exists only in the case when the fan was off, and the track densities T in the turbulent atmosphere were higher than those in the still atmosphere. The calibration coefficients K and K were calculated with a multi-step method of linear regression analysis (Skinner and Nyberg,... 

The biofilm thickness (Lf) and density (X = 50 g/L) were assumed uniform and the biofilm treated as a continuum. A substrate diffusion-reaction model assuming spherical particle was used. Diffusion coefficient of phenol and oxygen in the biofilm were assessed according to Fan et al. [64] ... 

Kang, Fan and Kim(96) measured coefficients for heat transfer from a cone-shaped heater to beds of glass particles fluidised by water. They also found that the heat transfer coefficient passed through a maximum as the liquid velocity was increased. The heat transfer rate was strongly influenced by the axial dispersion coefficient for the particles, indicating the importance of convective heat transfer by the particles. The region adjacent to the surface of the heater was found to contribute the greater part of the resistance to heat transfer. 

Fan specifically excluded the role of i ct when he made the identification, and his major arguments were based on the summary and interpretation of the previously published data on lithium diffusion coefficients in both the cathode and anode and the fact that the surface area of the cathode is normally only a fraction of the anode. Without data from direct measurement, the above speculation seems to be premature hence, further experimental confirmation is needed. 

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