Fluid flow Colebrook equation

Chemical engineers are familiar with the Fanning (or Darcy) friction factor,/, the Moody chart of/vs. Reynolds number, Rg, and how all of this fits together to calculate pressure drop for a given fluid flow in a given sized pipe. The friction factor is calculated from the Colebrook equation ... 

Solving problems in chemical engineering and science often requires finding the real root of a single nonlinear equation. Examples of such computations are in fluid flow, where pressure loss of an incompressible turbulent fluid is evaluated. The Colebrook [8] implicit equation for the Darcy friction factor, f, for turbulent flow is expressed... 

The Colebrook equation is convenient for determining the flow rate from the allowable friction loss (e.g., driving force), tube size, and fluid properties. Published plots of/vs. and e/D (i.e., the Moody diagram) are usually generated from the Colebrook equation. 

The friction factor/for turbulent flow of an incompressible fluid in a pipe is given by the nonlinear Colebrook equation... 

Example 1.1 Solution of the Colebrook Equation by Successive Substitution, Linear Interpolation, and Newton Raph on Methods. Develop MATLAB functions to solve nonlinear equations by the successive substitution method, the linear interpolation, and the Newton-Raphson root-finding techniques. Use these functions to calculate the friction factor from the Colebrook equation [Eq. (1.4)] for flow of a fluid in a pipe with e/Z> =10 and Njf, = 10. Compare these methods with each other. 

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 ... 

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