Fanning expression

VNBGt)Bi,2,..n Amouiit of biogas produced at time t at standard conditions in blank flasks Fbi, Fb2,—Fan expressed in cm Thbiogasi,2,..n Amount of theoretic biogas calculated by equation 2 in respective test flasks Fti, FT2,.-FTn... 

The relative pressure drop, AP, expression is based on the Fanning pressure-drop equation ... 

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. 

For smooth pipe, the friction factor is a function only of the Reynolds number. In rough pipe, the relative roughness /D also affects the friction factor. Figure 6-9 plots/as a function of Re and /D. Values of for various materials are given in Table 6-1. The Fanning friction factor should not be confused with the Darcy friction fac tor used by Moody Trans. ASME, 66, 671 [1944]), which is four times greater. Using the momentum equation, the stress at the wall of the pipe may be expressed in terms of the friction factor ... 

Two more consequences must be recognized about the very low pressure increases of 1 to 200 mm of water column made by the blowers. One is that those piressure surges, common in turbocompressors generating large pressure increases, are absent in these fans therefore, these can be operated at low flows. The second is that, in calculation of energy consumption and dissipation, the expression for incompressible fluids can be used even for gases. 

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. 

We denoted the mass of dry air in a volume V as that is, p, - w,/Vj, and the mass of water vapor in V as m, that is, pp = mp/Yp. In practical calculations we usually handle volume flow volume flow is known in the suction inlet of a fan when the operating point of the fan is defined. Volume flow q, expressing the total air flow or the combined volume flow of water vapor and dry air, is not constant in various parts of the duct, because the pressure and temperature can vary. Therefore in technical calculations dealing with humid air, materia flows are treated as mass flows. Also, while the humidity can vary, the basic quantity is dry air mass flow w,(kg d.a./s). If, for instance, we know the volume flow q,. of a fan, the dry air mass flow through the fan is... 

Fach-ausdruck, m. technical term or expression, -bildung, /. professional education, technical education, -blatt, n. = Fachzeitschrift. facheln, v.t. fan. 

Sound power is the total energy emitted from a fan that is a function of the fan s speed and point of operation and is independent of the fan s installation and surrounding environment Sound power level is the acoustical power expressed in decibels (dB) radiating from a source. Sound power can be converted into predictable pressure levels (dBA) after the acoustical environment surrounding the fan is defined. Sound pressure for a specific fan varies with... 

To size the fan it is necessary to know the total air volume and the pressures in the system. These are calculated from the losses in the system on the longest or index leg, and begin with the hood. The hood entry loss can be expressed as 0.6 of the velocity head and is accurate enough for first estimates. The losses are then calculated on the velocities in the ducts. Each change of direction means a small loss in each length of duct. Added to the pressure drop loss across the collector and the outlet losses, these give the total static pressure required in the system. 

Macpherson JL, Boyd MP, Amdt AJ, Todd AV, Fanning GC, Ely JA, Elliott F, Knop A, Raponi M, Murray J, Gerlach W, Sun LQ, Penny R, Symonds GP, Carr A, Cooper DA (2005) Long-term survival and concomitant gene expression of ribozyme-transduced CD4 + T-lymphocytes in HIV-infected patients, J Gene Med 7 552-564... 

Luo W, Fan W, Xie H, ling L, Ricicki E, Vouros P, et al. Phenotypic anchoring of global gene expression profiles induced by A -hydroxy-4-acetylaminobiphenyl and benzo[a]pyrene diol epoxide reveals correlations between expression profiles and mechanism of toxicity. Chem Res Toxicol 2005 18 619-29. 

Bubbly flow. In bubbly flow, the holdup is generally known and/or near homogeneous flow condition exists, and the frictional pressure drop can be correlated through similarity analysis (Dukler et al., 1964). The development shows that the frictional loss is expressed by a Fanning-type equation,... 

Huang, C-S, Y-E Fan, C-Y Lin, and M-L Hu. 2007. Lycopene inhbitis matrix metalloproteinase-9 expression and down-regulates the binding activity of nuclear facter-kappa B and stimulatory protein -1.7 Nutr Biochem 18 449 -56. 

Limiting expressions of r for large numbers of coordinates in WEG, FAN, and PAR were calculated from Equation 3.B4 and expressions described in Appendix 3B for a family of (3i and p2 values and were tested by simulation. Specifically, 500 (x, y) random correlated coordinates were distributed over WEG, FAN, and PAR for specific Pi and p2> and rwas calculated from the usual statistics equation (Eq. 3.B 1 in Appendix 3B). The simulation was repeated 1000 times, and the average r was compared to the limiting expressions. 

Yang W, Fan H, Gao X et al (2004) The first fluorescent diboronic acid sensor specific for hepatocellular carcinoma cells expressing sialyl Lewis X. Chem Biol 11 439 148... 

If the wall stress (rw) in Eq. (6-11) is expressed in terms of the Fanning friction factor (i.e., tw = /pF2/2) and the result solved for/, the dimensionless form of the Hagen-Poiseuille equation results ... 

Kobayashi, N. R., Fan, D-P., Giehl, K. M., Bedard, A. M., Wiegand, S. J. and Tetzlaff, W. BDNF and NT-4/5 prevent atrophy of rat rubrospinal neurons after cervical axotomy, stimulate GAP-43 and Tal-tubulin mRNA expression, and promote axonal regeneration. /. Neurosci. 17 9583-9595, 1997. 

Nagai, Y., Tsugane, M., Oka, I.-I. and Kimura, H. Hydrogen sulfide induces calcium waves in astrocytes, The FASEB loumal express article 10.1096/1).03 1052 fje. Published online fan.20,2004. 

White, I. M. Suter, J. D. Oveys, H. Fan, X., Universal coupling between metal clad waveguide and optical ring resonators, Opt. Express 2007, 15, 646 651... 

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