Fanning equation

If the friction factor is assumed to be OcRe ° where a is a constant, and the Fanning equation is solved for physical property terms, the result is... 

For turbulent flow across tube banks, a modified Fanning equation and modified Reynold s number are given. 

This correlation is good for a Reynolds number range of between 2,100 and 10 . The Fanning equation for pressure drop is ... 

In turbulent flow the pressure losses, Ap (psi), can be calculated from the Fanning equation [60]. 

For uniform circular pipe the Fanning equation can be used ... 

By analogy to single-phase flow, the two-phase frictional pressure-drop can be expressed by the conventional Fanning equation, and thereby a friction factor is defined. These friction factors may be based on liquid properties, gas properties, or on a fictitious single fluid of mean properties obtained by some averaging procedure. Typical definitions, such as those shown in equation (32), have been given and discussed recently by Govier and Omer (G4) ... 

The pressure drop AP (Pa) in turbulent flow of an incompressible fluid with density p (kg m ) through a tube of length L (m) and diameter d (m) at an average velocity of v (m s ) is given by Equation 2.10, namely, the Fanning equation ... 

At this point, a review is in order. Please note again Eq. (6.6). The Darcy equation, also known as the Fanning equation, is applicable to any single-phase flowing fluid, liquid or gas. There are seven factors that make up the dimensional analysis of this equation ... 

Integration over the length of the pipe requires an empirical expression for th" friction term dF. This is usually given by the Fanning equation ... 

INTEGRATED FORM OF THE FANNING EQUATION. If the linear velocity, density, and viscosity of the flowing fluid remain constant and the pipe diameter is uniform over a total pipe length L, Eq. (5) can be integrated to give the following result ... 

It is convenient to express the pressure drop for heat exchangers in a form similar to the Fanning equation as presented in Chap. 14. Because the transfer of heat is involved, a factor must be included for the effect of temperature... 

The pressure drop for flow through the gas passages resulting from momentum transfer from the flowing gas to the stationary screen-enclosed catalyst slabs follows from the general Fanning equation... 

The frictional effects of bends and fittings are often expressed in terms of a quantity called the velocity head drop . To introduce this concept, we begin by observing that the specific energy lost to friction, F(J/kg), for incompressible flow follows from an integration of the Fanning equation (4.20) with friction factor and velocity constant over the length of pipe ... 

We begin by observing that the energy lost to friction is found by integrating the Fanning equation (4.20), repeated below ... 

If the Reynolds number indicates viscous flow, equation 27 (where p ,= viscosity at the tube wall, Cp) is used. If the flow is turbulent, equation 26 is used. Both of these equations are based on the Fanning equation. The Motion factor incorporated in the viscous equation is simply f = 16IRe. The friction factor used for turbulent flow is f = 0.048/Rc . A safety factor of 20% is used to take care of fouling and the effect of possible overtolerance of the tube wall. 

This nomograph solves the Fanning equation expressed in the form ... 

Sometimes the pressure drop in the reactor is sufficiently large to be necessary to account for it, instead of using an average value. For an empty tube the Fanning equation may be used in the usual Bernoulli equation ... 

The pressure drop equation Eq. (c) not only accounts for friction losses in the straight portions and in the bends of the coil but also for changes in momentum. The first term in the brackets on the right-hand side arises from the Fanning equation, the second from Nekrasov s equation [20] for the additional pressure drop resulting from the curvature in the bends. Furthermore, since... 

Equations T5.10.18 through T5.10.20 are used for sizing the fan. Equation T5.10.18 calculates the pressure loss of air through the loaded belt. Equation T5.10.19 correlates the airflow with the air velocity. Equation T5.10.20 estimates the required electrical power to operate the fan. 

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