The friction factor in the Darcy-Weissbach equation can be determined by the Moody diagram or the application of the Colebrook-White (CW) equation. The CW equation is a transcendental equation with iterative resolution. Even though few iterations already lead to a result, calculations of pipe networks are compromised. The equation of CW received several approaches in recent decades. Some years ago, an exact solution (but with relative complexity) was proposed: http://www.sciencedirect.com/science/article/pii/S0893965911001121
Does the increase of the processing power of personal computers drastically reduce the usefulness of these alternative expressions?
Mr Liberzon,
I agree with your statements. I question the validity of many efforts to analytically solve the equations of CW.
Thanks for the suggested reading.
However, you say that "the CW equation is a simplification of PKN relations." I believe it is not exactly so. Colebrook and White used results of Nikuradse, Karmann and Prandtl, in addition to their own results to create a new equation.
I have somewhat difficult to understand why would we search for an exact solution of an empirically-derived equation. It's also known that the differences between Swamee or even simple power-law equations (e.g. Hazen Wiliams or Manning) in some specific ranges perform as well as Colebrook White eq.
Does the analytical expression of the solution of CW helps to understand the problem in hand of friction due to turbulence in the pipe, better than a solution that uses purely empirical approaches, such as Moody charts or Swamee formula or even engineering nomograms?
Mr Liberzon,
I agree with your statements. I question the validity of many efforts to analytically solve the equations of CW.
I agree partially with some previous answers. The practical problem of solving implicit equations with respect to its variables was overcome with the arrival of digital calculators and the first personal computers in the decades of 70th and 80th. In the engineering practice, the ancient Colebrook-White Equation works, but for smooth-pipe flow or fully-rough flow regimes some old simple power-laws give generally acceptable results too. It looks much more difficult to improve effectively the existing turbulence models or develop new better ones.
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