Churchill equation

All the relevant variables and parameters are uniquely related through the three dimensionless variables / /VRe, and e/D by the Moody diagram or the Churchill equation. Furthermore, the unknown (DF = ef) appears in only one of these groups (/). The procedure is thus straightforward ... 

The model for turbulent drag reduction developed by Darby and Chang (1984) and later modified by Darby and Pivsa-Art (1991) shows that for smooth tubes the friction factor versus Reynolds number relationship for Newtonian fluids (e.g., the Colebrook or Churchill equation) may also be used for drag-reducing flows, provided (1) the Reynolds number is defined with respect to the properties (e.g., viscosity) of the Newtonian solvent and (3) the Fanning friction factor is modified as follows ... 

Equation (7-25) is implicit for Dec, because the friction factor (/) depends upon Dec through the Reynolds number and the relative roughness of the pipe. It can be solved by iteration in a straightforward manner, however, by the procedure used for the unknown diameter problem in Chapter 6. That is, first assume a value for/ (say, 0.005), calculate Z>ec from Eq. (7-25), and use this diameter to compute the Reynolds number and relative roughness then use these values to find / (from the Moody diagram or Churchill equation). If this value is not the same as the originally assumed value, used it in place of the assumed value and repeat the process until the values of / agree. 

First, assume / = 0.005 and use this to get NRe from Nc=fN 9. From NRe we find Z)ec, and thus s/Dtc. Then, using the Churchill equation or Moody diagram, we find a valyue for / and compare it with the assumed value. This is repeated until convergence is achieved ... 

The driving force (DF) is given by Eq. (7-45), in which the K- s are related to the other variables by the Moody diagram (or Churchill equation) for each pipe segment (Kpipe), and by the 3-K method for each valve and fitting (Kfit), as a function of the Reynolds number ... 

For each pipe segment of diameter Z) , get f from the Churchill equation or Moody diagram using NRei and i/Dh and calculate plpe = 4 (fL/D. ... 

Using this Reynolds number, determine the revised pipe friction factor (and hence ATpipe = AfL/D) from the Moody diagram (or Churchill equation), and the Kfit values from the 3-K equation. 

This value is used to determine/, Dh, A, Wp, and R by iteration using Eqs. (7-64) (7-65) and the Churchill equation, as follows. Assuming a value of x/R permits calculation of A and Wp from Eqs. (7-64) and (7-65), which also gives Dh=4A/Wp. The Reynolds number is then determined from NRe = DbQp/A/i, which is used to determine f from the Churchill equation. These values are combined to calculate the value of //DhA2, and the process is repeated until this value equals 2.13 x 10 9 cm-3. The results are... 

Calculate, VRe = DG//i and use this to find f from the Moody diagram or the Churchill equation. 

Evaluation of each term in Eq. (15-51) is straightforward, except for the friction factor. One approach is to treat the two-phase mixture as a pseudo-single phase fluid, with appropriate properties. The friction factor is then found from the usual Newtonian methods (Moody diagram, Churchill equation, etc.) using an appropriate Reynolds number ... 

The factor K is considered to be 0.5 for this type of distributors (Feintuch, 1977). The Fanning friction factor/for Ren > 4000 is calculated using the Churchill equation (Perry and Green, 1999) ... 

No special hydraulic resistance correlations have been applied in the TRACE reactor hydraulics. Instead, the standard TRACE modified Churchill equation is used with a surface roughness of 2 OE-6 meters. Hydraulic resistance flow factors are added to model non-recoverable form losses and to match the expected overall reactor pressure drop of 2.5% (aP / P inlet) defined in the heat balance. 

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