Constraints for Using Lambert Function-Based Explicit Colebrook–White Equation
Publication: Journal of Hydraulic Engineering
Volume 130, Issue 9
Abstract
We analyze the general applicability of a recent explicit expression of the Colebrook–White equation for turbulent flow friction factor calculation. This explicit expression, which is based on the Lambert function, is characterized by an exponential term which imposes restrictions on its use. These constraints have been expressed in terms of pipe roughness and the Reynolds number R that are required for friction factor calculation. These constraints were determined as and respectively, for machines using single precision and double precision computations. Using the Lambert function, an explicit equation relating R and was derived at the limiting case which allowed for a graphical representation of the applicability of the explicit form of the Colebrook–White equation in the R versus space. Before computing friction factors using the explicit Colebrook–White equation, a quick check must be performed to see if the desired combination of R and values satisfies the applicable constraint mentioned above.
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Copyright © 2004 American Society of Civil Engineers.
History
Received: Jan 24, 2003
Accepted: Feb 10, 2004
Published online: Aug 16, 2004
Published in print: Sep 2004
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