Friction Factor in U-Type Undulated Pipe Flow

Abstract

Measurements of pressure losses in a U-type undulated hydraulically smooth wall pipe, having constant radius curvature, are presented. The effect of the dimensionless curvature radius 2R/d on the Darcy friction factor was investigated in the range of the Reynolds number from about 50 to 10,000 and for the dimensionless pipe curvature radiuses 2R/d=6.62, 7.95, 11.13, 16.03, 22.58, and 27.85. A smooth transition from laminar to turbulent region in the friction factor versus Reynolds number plot, typical for curved pipe flows, was observed. The experimental data were correlated with the relatively simple equation using new Dean number Den=Re * (Den=Re * (d/2R):ln(fw * Re/64)=a+b(ln(Den))2, which is not valid for larger values of Den and 2R/d, e.g., for Den>200 at 2R/d=22.58, and for Den>70 at 2R/d=27.85. The new Dean number, below which the influence of the pipe curvature in comparison to the straight tube was not seen, is Den≤∼3.[S0098-2202(00)02802-9]