Fanning friction factor difference

The Fanning friction factor differs from the Moody firiction factor by a constant... 

Numerous researchers have studied damage to micro-organisms during flow in pipes, (Fig. 11) [87,88] Most researchers use a Fanning friction factor, f, to calculate the energy dissipation rate for fully developed flow in tubular bioreactors and capillary flow devices. There are minor differences in the equations that are used but they are generally of the following form [89,901 ... 

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).

The subscript s is used in Ap, and to call attention to the fact that in Eqs. (5.7) and (5.7a) these quantities, when they are associated with the Fanning friction factor, relate only to skin friction. If other terms in the Bernoulli equation are present or if form friction is also active, p — p differs from Ap,. If boundary-layer separation occurs, hf is greater than hf. The last term in Eq. (5.7), which includes the friction factor, is written in a manner to show the relation of to the velocity head V j2g. ... 

In the engineering community there are two types of friction factors - Fanning and Darcy. Although basically the same, they differ by a factor of four /nn = 4 ffm. The Darcy factor is used here. 

The friction factor / now remains to be specified. The pressure drop equation, (11.5.1-3), requires special attention, it differs from the Fanning equation, in which the right-hand side is multiplied by 2. When a friction factor is substituted into (11.5.1-3), special care has to be taken to check from which type of pressure drop relation /was derived. Further, the units have to be handled with care. Equation (11.5.1-3) is written for S.i. units, with pt m Pa = N/m/ With other units, the right-hand side has to be multiplied by a conversion factor. When engineering units are used for pt (kg force/m = N x 9.81), the right-hand side has to be divided by g (mVs). 

Friction Loss. Flow, turbulent or streamline, may be represented by a single mathematical formula, except that a different friction factor is used for each region (streamline or turbulent) of flow. Fanning s equation (originally derived for turbulent flow) for flow in a circular conduit is... 

There are numerous sources of frictional losses for the airflow through the hood and ductwork to be overcome by the exhaust fan. The air entering the hood must be accelerated from a minimal velocity in the room to the velocity within the duct. Due to physical factors, there is always some turbulence created during this process, so that the pressure difference created by the fan must be sufficient to provide the desired airspeed in the duct and overcome the losses due to turbulence. In the specifications for a hood, the hood static pressure data provided are a direct measure of the total of the energy needed for acceleration and to overcome turbulence losses. The static pressure will be proportional to the square of the velocity of the air entering the hood face. 

The problan formulation consists of applying the Bernoulli equation to the three different pipes, with diameters dl, d2, and d3, and a global mass balance at the splitter. The fanning factor for the friction loss is calculated using the Colebrook correlation [5] ... 

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