Dimensionless Fanning friction factor

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... 

Friction Factor and Reynolds Number For a Newtonian fluid in a smooth pipe, dimensional analysis relates the frictional pressure drop per unit length AP/L to the pipe diameter D, density p, and average velocity V through two dimensionless groups, the Fanning friction factor/and the Reynolds number Re. 

D = inlet diameter, feed pipe ft f = fanning friction factor dimensionless tj) = average value of tj)... 

As can be determined from Eqs. (5-47) and (5-49), the pipe wall stress can also be made dimensionless by dividing by the kinetic energy per unit volume of fluid. The result is known as the pipe Fanning friction factor, f ... 

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 ... 

Equation (11) states that the conventional Fanning friction factor, which may be used through Eq. (10) to calculate pipe-line pressure drops, is a unique function of two dimensionless groups for Bingham-plastic fluids. Newtonian fluids represent that special case for which r , and hence the second dimensionless group, is equal to zero. 

Table I. Asymptotic dimensionless laminar flow heat or mass transfer coefficients Nu = a dh/V, (constant wall conditions) and Fanning friction factor / for pressure drop Ap = 2f r 7.ijd ) g for ducts of different cross section [10).

E = efficiency of motor and pump expressed as a fraction f = Fanning friction factor, dimensionless, or function for dynamic programming in Eq. (91) indicating optimum return depends on that input... 

The dimensionless relations are usually indicated in either of two forms, each yielding identical results. The preferred form is that suggested by Colburn [Trarrs. Am. Inst. Chem. Eng., 29,17T-210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cG, the Prandtl number c[ /k, and the Reymolds number DG/p. 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 IC/p for Reynolds number <10,000) is approximately equal to half of the Fanning friction factor 2. This product 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. 

Fanning friction factor, dimensionless f number of sites... 

Initial particle (when dissolving starts) diameter, ft Mass mean particle diameter, ft Impeller diameter, ft Fanning friction factor, dimensionless Distance between feedpipe end and impeller disk or impeller blade, ft... 

Pipe flow analyses may require the determination of either the driving force, flow rate, or pipe diameter. The procedures for these analyses for Newtonian and non-Newtonian fluids are similar, utilizing the engineering Bernoulli equation and the dimensionless expressions for the Fanning friction factor. For these purposes, the engineering Bernoulli equation can be written as... 

F Force, N or lb/, F, gravity force F, shear force / Fanning friction factor, dimensionless... 

Faraday constant, 96,500 C/g equivalent Fanning friction factor, dimensionless Mass velocity, kg/m -s or Ib/ft -h... 

The dimensionless fully developed pressure drop is given by the Fanning friction factor / defined by the relation... 

The Fanning friction factor/and the dimensionless heat transfer coefficient jH for the polyacrylamide 1000-wppm solution measured at an xId of 430 and at the Reynolds number equal to 20,000 [37] are presented in Fig. 10.33 as a function of hours of circulation. The dimensionless jH factor is seen to remain relatively constant at its minimum asymptotic value until some 3 hours have passed. On the other hand, the friction factor does not depart from its asymptotic value until some 30 hours of circulation have occurred. Estimates of the critical Weissenberg number based on the Powell-Eyring model yield values that are in good agreement with those given for the once-through system ... 

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