Exact equations for pipe-flow problems/ Des équations exactes pour les problèmes d'écoulement en conduite

Abstract

The three basic and problems encountered in hydraulic engineering practice are the determination of the head loss, pipe diameter, and discharge. Out of these problems Swamee and Jain [J. Hydraul. Engng. ASCE 102 (1976) 657] gave exact solution for the discharge problem. Exact solutions of the remaining two pipe flow problems are not possible because of the implicit form of Colebrook equation that gives the friction factor for commercial pipes. For the friction factor problem a large number of approximate solutions have been proposed from time to time. Reported herein are exact equations for friction factor and pipe diameter. These exact equations can also be utilized with advantage in optimization studies of pipelines and water distribution systems.

Keywords:

• Darcy–Weisbach equation
• discharge
• friction factor
• head loss
• hydraulics
• Lagrange's theorem
• pipe diameter
• pipe flow