Pipe Friction Factor Research Articles

Pipe friction factors for concentrated aqueous solutions of polyacrylamide

Experimental friction factor results are presented for aqueous solutions of polyacrylamide (Separan AP-273) for concentrations of 1500 ppm, 2000 ppm and 2500 ppm in laminar and turbulent flow through tubes of 2.21 cm and 1.30 cm inside diameter. The solutions studied show a highly non-Newtonian behavior with values of the flow behavior index varying from 0.45 to 0.90. The measured friction factors are slightly lower than the maximum drag reduction asymptote proposed by Virk. For the concentrated viscoelastic solutions the generalized Reynolds number provides a better presentation of the data than the Reynolds number based on the apparent viscosity. In such a presentation there is no influence of pipe diameter or solution concentration on the friction factor. A power law approximation for the friction factor in terms of the generalized Reynolds number was determined using present experimental data. This expression may be used to represent the maximum drag reduction asymptote.

Accurate Explicit Equation for Friction Factor

The solution of pipe flow problems encountered in engineering practice requires an intermediate step of computation of friction factor. The friction factor of commercial pipes is described by a semi-empirical equation developed by Colebrook. This equation that expresses the friction factor as a function of relative roughness and Reynolds number is an implicit one requiring a trial-and-error procedure for its determination. Wood has pointed out obvious disadvantages of an implicit relationship and recognizing the necessity of an explicit equation proposed one to replace the implicit equation for friction factor. It has, however, been possible to develop a simple and more accurate explicit equation for friction factor, based on the Colebrook-White formula, and is presented herein.

Further On the Calculation of Friction Factors For Use In Flowing Gas Wells

Abstract A comparison of two computer subroutines to calculate friction factors from the Moody(2) chart has been made. The comparison shows that, contrary to the claim of Dranchuk and Abou-Kassem(1), their method and that of Aziz et al.(5) give identical results in the partially-rough-wall and the fully-rough-wall turbulence regions. The transition from the former to the latter is predicted to occur at slightly different Reynolds numbers in the two methods because of the choice by Dranchuk and Abou-Kassem of an arbitrary transition criterion. Both routines are suitable for computer calculation of friction factors, but the Aziz et al. method is more efficient, requiring fewer iterations. IN A RECENT TECHNICAL NOTE, Dranchuk and Abou Kassem(l) recommend the use of the Moody chart(2) instead of approximate relationships to determine friction factors in pressure-drop calculations for flowing gas wells. Without doubt, fundamental equations with a properly chosen friction factor based on the correct reynolds number and the best estimate of the relative roughness will yield more accurate pressure-drop predictions than equations incorporating approximations for the friction factor(3). (Equation in full paper) Dranchuk and Abou-Kassem compare Darcy-Weisbach friction factors calculated by their own and the Aziz et al. method and arrive at the following conclusions: The Aziz-Govier-Fogarasi method:generates Fanning friction factors;yields values which are higher than Colebrook at low values of Re and lower than Colebrook at high values of Re;yields values which are higher than Moody at low values of Re and lower than Moody at high values of Re when flow is in the transition zone) but higher than Moody at low values of Re and lower than Moody for high values of Re when flow is fully turbulent;cannot generate values for smooth pipe." These conclusions seem unwarranted. Table 1 shows a comparison of Darcy-Weisbach friction factors calculated by the two methods for a wide range of relative roughnesses and Reynolds numbers. The comparison shows that:the friction factors are exactly the same in the PRW and FRW regions, as they should be, because both routines use the same equations;a slight difference (half a per cent or less) at the transition from PRW to FRW turbulence due to the difference in the transition criterion chosen by Dranchuk and Abou-Kassem and the assymptotic approach used in the Aziz et al. routine;the Aziz et al. routine is more efficient, requiring fewer iterations. (Table in full paper) Keeping in mind that Moody indicated that his chart would predict friction factors with no better than 10 per cent accuracy, the small differences are insignificant. The friction factors, for practical purposes, are the same. Finally, the Aziz et al. method was not intended for the calculation of friction factors in smooth pipes. It was designed only to deal with the practical problem of estimating pressure drops in actual gas wells, which may always be expected

Some aspects of fully developed turbulent flow in non-circular ducts

An experimental study of fully developed uniform-density turbulent flow in a circular pipe containing one or two rods located off-centre is described. The friction factor in both cases was found to be approximately 5 % higher than the simple pipe friction factor. The shear stress distribution on the rod surface was determined using calibrated boundary-layer fences. The normalized shear stress distributions were independent of Reynolds number in the range 3·7 × 104to 2·15 × 105. Mean-velocity measurements were obtained to check the validity of the universal law of the wall near the rod surface. Secondary-flow velocities were measured by a hot-wire anemometer and integrated to yield the secondary-flow stream function. Secondary-flow velocities of the order of 1 % of the mean velocity were observed. In the gap between the two pins, however, the secondary-flow velocities were only ½% of the mean velocity. It is demonstrated that the secondary flow cannot be neglected if a force balance is used to determine the shear stress distribution on the rod surface.

Drag reduction in rough pipes

Drag reduction caused by dilute, distilled water solutions of four polyethylene-oxides and one polyacrylamide, molecular weights respectively 0·1 × 106 to 8 × 106 and 13 × 106, was studied experimentally in one smooth and three sand-roughened pipes, relative roughnesses (R/k) 15, 23, 35, all of about 0·34, in inside diameter. The onset of drag reduction in the rough pipes occurred at the same wall shear stress as in smooth; the onset wall shear stress was essentially independent of polymer concentration, varied inversely as the square of polymer radius of gyration and was unaffected by the flow regime, hydraulically smooth, transitional or fully rough, during which onset occurred. Following onset a flow regime was observed wherein the fractional slip, i.e. fractional increase in mean velocity relative to solvent at a given friction velocity, obtained with a given polymer solution in a rough pipe was the same as the fractional slip in the smooth pipe despite marked differences in the respective rough and smooth friction factors. This ‘effectively smooth’ regime prevailed for values of non-dimensional roughness k+* < k+ < k+es from onset, k+*, to an upper limit given by k+es ∼ 50 for all of the present experiments. For k+ < k+es, the fractional slip in the rough pipes was always less than that corresponding to smooth and was a function of relative roughness as well as flow and polymeric parameters. The maximum drag reduction possible in the rough pipes was limited by an asymptote which was independent of polymeric parameters. Under asymptotic conditions, friction factors in all the rough pipes identically obeyed the smooth pipe friction factor relation for k+ < 12; the onset of roughness at k+ ∼ 12 indicated that the maximum viscous sublayer thickness attained during drag reduction was approximately 2½ times Newtonian.

An Accurate Equation for the Computation of the Friction Factor for Smooth Pipes From the Reynolds Number

An Accurate Equation for the Computation of the Friction Factor for Smooth Pipes From the Reynolds Number

Closure to “Discussions of ‘Orifice-Metering Coefficients and Pipe Friction Factors for the Turbulent Flow of Lead-Bismuth Eutectic’” (1957, Trans. ASME, 79, p. 1083)

Closure to “Discussions of ‘Orifice-Metering Coefficients and Pipe Friction Factors for the Turbulent Flow of Lead-Bismuth Eutectic’” (1957, Trans. ASME, 79, p. 1083)

Orifice-Metering Coefficients and Pipe Friction Factors for the Turbulent Flow of Lead-Bismuth Eutectic

Abstract Pipe friction factors and orifice-metering coefficients are reported for the turbulent flow of lead-bismuth eutectic and are found to be in satisfactory agreement with the results for water flow when compared on the usual dimensionless basis.

Displacement Versus Time Characteristics of Hydraulic Actuators

Abstract This paper develops the relation between the displacement and time of a piston in a hydraulic actuator in terms of the load, mass, pressure drop, viscosity, and special operating conditions. It is based upon the Fanning law of friction in pipes and the value of the friction factor in smooth pipes as given by Hagen-Poiseuille and Blasius. The relation developed will cover most conditions met in the design of hydraulic equipment and will suggest a means to analyze those conditions not covered. This method is valid for pressures up to 100 atm and, with modifications, to higher pressures.

Pressure Losses in Tubing, Pipe, and Fittings

Abstract This paper is a continuation of the second half of the problem involved in the writer’s 1933 paper on pipe flow and Prof. Lewis F. Moody’s 1944 paper. The pipe-flow situation is shown to be in satisfactory condition; the main attention is on bends and fittings. It has been customary in the past to rate the losses in bends and fittings as a function of velocity head. Another old method, less used, was to rate the loss in equivalent length of pipe. In the case of bends and fittings two types of loss are superposed, i.e., skin friction or pipe-loss type, and bend loss. The methods of test are less accurate than for pipe as they involve getting the difference between two much larger readings. Consequently the test data are much poorer than for pipe, for several reasons: one given above; another that the pipe fittings are not geometrically similar; and the test data are very much less than those on pipe. It seems clear that a rational formulation, however, could be attempted if we can establish some picture of the factors involved in the losses. Up to the present time bend and fitting losses have been taken from a range of factors unconnected with size, roughness, or velocity of flow. This formulation, on the basis of the tests, endeavors to show that there is a true bend loss for smooth fittings underlying the superposed losses due to roughness and Reynolds number. The final formulation involves an evaluation of the true bend loss and an evaluation of the roughness and Reynolds number effects paralleling the friction factor in pipe. The final conclusion is that the equivalent pipe length is by all means the most reliable and convenient method of tabulating losses in different kinds of fittings and bends. The final formulation is ζ=ζ1+ζ2=0.106(rd)-2.5+2000f2.5. This formulation has been checked against the test results and while it is obvious that the factors will be both plus and minus over a considerable range, the general correlation of the test data appear to be as good as our present test information will permit.

NOTE ON THE ENERGY AND MOMENTUM CORRECTION FACTORS FOR FLOW IN CIRCULAR PIPES

The energy and momentum correction factors are expressed as functions of two integrals depending on the velocity distribution. General relations for any stream cross-section are given for the sign and relative size of the integrals. Using the Karman–Prandtl velocity distribution laws for circular pipes the integrals are evaluated numerically and given as functions of the bulk Reynolds number, the pipe friction factor, and other useful quantities likely to be known in practice.