Pressure losses for fluid flow in curved pipes

Abstract

Tlus paper presents the results of a study of the flow of water in smooth-walled, large-radius curved pipes for the viscous and turbulent regimes over a range of Reynolds numbers from 500 to 60,000. The discussion is based on data obtained with %-inch brass tUbing. Two series of tests were made. In the first series pressure losses were measured on t en bends, and simultaneous measurements were made on the downstream tangents. In the second series pressure losses were measured on four equal segments on each of four bends. The greater part of the paper is devoted to a consideration of the results in the viscous flow regime. In this part of the investigation care was taken to assure parabolic velocity distribution, or nearly so, at the entrance of the bends. Empiri-cal formulas are given for the effective resisbnce coefficient of an entire bend and for the downstream tangent. A method of computing to a first approximation the length of curve required for the establishment of the velocity distribution charac-teristic of a curved pipe is presented. Critical numbers for bends of different curvature ratios when the entering flow is laminar are briefly discussed. Average values for the relative increase in resist-ance in a bend as compared with straight pipe in the regime of turbulent flow are given for the range of R eynolds numbers from 40,000 to 60,000. 1. Resistance in bends, including transition segment_ _ _ _ _ _ _ _ _ _ _ _ _ 97 2. The transition segment of a bend ___________________________ 102 3. Resistance in a straight pipe below a bend_ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ 105 V. Transition from viscous to turbulent flow ___________________________ 109 VI. Experimental results for turbulent flow ____ ________ __________ _______ 114