Modeling of pipe flows

Lots of technical devices use flows in pipes and channels caused by pressure drop, along with one's axis, which is energy consuming and has to be estimated. For the estimation resistant coefficient, dependent on flow regime and streamlined surface roughness, is required. Turbulence $f$-model applicable for calculation for both laminar and turbulent flow and smooth and rough walls is used for investigation. The problem of incompressible viscous liquid steady flow in a smooth round pipe is considered for different Reynolds numbers. First integrals for velocity profile and turbulence measure are obtained in form of transcendental equations and solved by Newton's method for algebraic equation system. Calculated results are compared with data from alternative theoretical approaches and experiments.