Friction factor in U-type undulated pipe flow

Measurements of pressure losses in a U-type undulated hydraulically smooth wall pipe, having constant radius curvature, are presented. The effect of t he dimensionless curvature radius 2R/d on the Darcy friction factor was inv estigated in the range of the Reynolds number from about 50 to 10,000 and f or the dimensionless pipe curvature radiuses 2R/d = 6.62, 7.95, 11.13, 16.0 3, 22.58, and 27.85. A smooth transition from laminar to turbulent region i n the friction factor versus Reynolds number plot, typical for curved pipe flows, was observe. The experimental data were correlated with the relative ly simple equation using new Dean number De(n) = Re* (De(n) = Re*(d/2R): ln (f(w)* Re/64) = a + b(ln (De(n)))(2), which is not valid for larger values of De(n) and 2R/d, e.g., for De(n)>200 at 2R/d = 22.58, and for De(n)>70 at 2R/d = 27.85. The new Dean number, below which the influence of the pipe c urvature in comparison to the straight tube was not seen, is De(n)less than or equal to similar to3. [S0098-2202(00)02802-9].