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The objective of the study is to recognise whether epoxy resin or polyurethane internal linings of ductile iron (DI) pipes create visibly smaller head loss in flow than cement mortar linings. Some data reported by the Ductile Iron Pipes Research Association (DIPRA) was used in the calculations. Only the data from hydraulic tests performed no later than 30 years after the placing of the mortar lining were considered. The average values of the Hazen–Williams roughness coefficients C for each of the internal pipe diameters were calculated, and single experimental data neglected. Two different approaches were taken for interpreting the DIPRA experimental results and omitting the fact that the flow rates during these tests are unknown. The Hazen–Williams roughness coefficients C were used in both for computing the friction factor f from the Moody chart for three values of flow rate: being equal to the optimal value for a given diameter, and then by 50% larger and 50% smaller than this value. Next, the computed friction factors were compared with the values predicted from the Moody chart for smooth pipes. In the first approach, the friction factors f were computed using the Epanet2 software, and in the second approach, a general equation for calculating f from known C and flow parameters was applied. Both approaches resulted in friction factors f very close to those for smooth pipes for the whole range of Q. In conclusion, more smooth plastic linings of DI pipes do not result in a significantly more visible saving of energy for pumping.

Pulsatile rough-wall turbulent pipe flow is compared against its non-pulsatile counterpart using data obtained from direct numerical simulation. Results are presented at a mean friction Reynolds number of 540 for a set of three geometrically scaled roughness topographies at a single forcing condition, which, based on existing classifications, falls into the current-dominated very-high-frequency regime. By comparing the pulsatile data against an equivalent non-pulsatile dataset (Chan et al. , J. Fluid Mech. , vol. 854, 2018, pp. 5–33), the key differences (and similarities) between the forced and unforced configurations are identified. A major finding of this study is that the flow in the outer region retains its self-similar functional form under pulsatile rough-wall conditions, and, as a result, Townsend’s outer-layer similarity hypothesis holds for the roughness-forcing combinations considered here. On the other hand, the unsteady cases exhibit a rich array of flow physics in the region beneath the roughness crests not observed in the steady case. These differences are examined using a Moody chart, which encapsulates how the hydraulic properties of pulsatile rough-wall pipe flow differ from their non-pulsatile counterpart.

International audience; This paper presents data reduction of average friction factor of gas flow through adiabatic micro-channels. In the case of micro-channel gas flow at high speed, the large expansion occurs near the outlet and the pressure gradient along the length is not constant with a significant increase near the outlet. This results in flow acceleration and a decease in gas temperature. Therefore the friction factor of micro-channel gas flow should be obtained with measuring both the pressure and temperature. The data reductions on friction factors were carried out under the assumption of isothermal flow for numerous experimental and numerical studies since temperature measurement International Journal of Heat and Mass Transfer 2 of micro-channel gas flow at high speed is quite difficult due to the measurement limitations. In the previous study, it was found that the gas temperature can be determined by the pressure under the assumption of one dimensional flow in an adiabatic channel (Fanno flow). Therefore in the present study data reduction to estimate friction factors between two relatively distant points considering the effect of a decrease in temperature is introduced with the temperature determined by the measured pressure at a specific location. The Friction factors obtained by using the present data reduction are examined with the available literature and the results are compared with empirical correlations on Moody chart.

This paper presents a direct closed form analytical solution for the implicit type equation of Colebrook-White for friction factor calculation. Based on the developed expression, the friction factor can be directly calculated given the fluid flow parameters namely the relative roughness and the Reynolds number. Obtained expression is explicit and it does not require any iterative calculation as it is built reposing on the analytical solution of a cubic equation of real coefficients. The used cubic equation is obtained through a 3rd order Taylor series expansion of the original Colebrook-White equation around an expansion point reasonably defined. The reliability of the proposed expression is proved through comparison with original Moody chart values as well as others results issued from previous approximations found in literature and the exact solution of Colebrook-White equation. The accuracy and the robustness of the established expression over other explicit correlations were emphasized. The presented closed form expression was proved to be simple, robust and accurate. Additionally it has the advantages of covering all the range of applicability of the original Colebrook-White equation.

The evaluation of operation status of thermal power plant plays a important role to measure whether a power plant has a good development. The traditional method of analytic hierarchy process has disadvantage in the assignment of judgment matrix, this paper tried to improve the method and applied the modified method to five thermal power plants based on Moody Chart method, and the score of economic indicators of the five power plants is calculated by both methods. The calculation of the example shows the advantage of simplicity and maneuverability in the improved method, and the case verifies the rationality of it.

Actual fluids have different flow regimes due to viscosity. The regimes include laminar flow and turbulent flow. The regimes, viscosity, and pipe wall surface have influence on flow resistance, which leads to head loss for fluids flow. In this chapter, we will firstly introduce types of head loss (friction loss and minor head loss) and two regimes of fluids flow. Then we will study characteristics of laminar flow and turbulent flow in circular pipe. Furthermore, we will present the definition of friction factor and discuss ways to determine value of friction factor in order to calculate friction loss. Finally, we will give determination of minor head loss.

In this research, we studied the pressure drop affecting on the internal surface roughness and the curvature radius of a U-tube, which is used for the cooling system in PWR(Pressurized Water Reactor). Using ANSYS-FLUENT, a commercial code based on CFD(Computational Fluid Dynamics) technique, we compared a Moody chart with the Darcy friction factor changed by a range of various surface roughness and Reynolds numbers of a straight pipe model. We studied the effect giving variation about a range of various surface roughness and the curvature radius of the full scale U-tube model. The material of the heat transfer tube is Inconel 690 used in the steam generator. We compared the velocity distribution of selected 4 locations, and derived the correlation between the surface roughness and the pressure drop for the U-tube of each representative curvature radius using the linear regression method.

Prediction of frictional pressure drop in rough pipes is a challenging task for process engineers. All the chemical and allied industries have large and complex piping networks made up of varied materials. The pumping system design needs accurate estimation of frictional pressure drop in pipes. This is done using Moody chart which relates friction factor with two key variables, namely Reynolds number and roughness parameter. Obtaining exact mathematical relationship explicit in nature is very difficult and hence use of artificial intelligence using neural network systems can be a promising approach. In this work, the Moody chart has been digitized and an ANN model has been trained and tested. The regression coefficient of 99% was obtained for training and validation steps.

In this chapter, the general principles of airflow in ducts are explained, the fluid being treated as incompressible. The relevant equations are given and the general characteristics of flow described. The methods of calculating pressure losses in straight ducts and in fittings are illustrated, together with the pressure distributions. The concept of resistance is explained, and the chapter concludes by giving some relevant methods for measuring flow rates. An understanding of these topics is important before going on in subsequent chapters to consider the design and sizing of ductwork systems, fan selection, and on-site balancing procedures.

In this research, the surface roughness affecting the pressure drop in a pipe used as the steam generator of a PWR was studied. Based on the CFD (Computational Fluid Dynamics) technique using a commercial code named ANSYS-FLUENT, a straight pipe was modeled to obtain the Darcy frictional coefficient, changed with a range of various surface roughness ratios as well as Reynolds numbers. The result is validated by the comparison with a Moody chart to set the appropriate size of grids at the wall for the correct consideration of surface roughness. The pressure drop in a full-scale U-shaped pipe is measured with the same code, correlated with the surface roughness ratio. In the next stage, we studied a reduced scale model of a U-shaped heat pipe with experiment and analysis of the investigation into fluid-structure interaction (FSI). The material of the pipe was cut from the real heat pipe of a material named Inconel 690 alloy, now used in steam generators. The accelerations at the fixed stations on the outer surface of the pipe model are measured in the series of time history, and Fourier transformed to the frequency domain. The natural frequency of three leading modes were traced from the FFT data, and compared with the result of a numerical analysis for unsteady, incompressible flow. The corresponding mode shapes and maximum displacement are obtained numerically from the FSI simulation with the coupling of the commercial codes, ANSYS-FLUENT and TRANSIENT_STRUCTURAL. The primary frequencies for the model system consist of three parts: structural vibration, BPF(blade pass frequency) of pump, and fluid-structure interaction.

A porous metal was suggested to be used for the anode of a DCFC. Thermo-fluidic characteristics of fuel-electrolyte mixture in the porous metal should be known in order for proper design of the anode. Previous researchers investigated pressure drop and heat transfer performance of fluids flowing through metal foams that have different pore densities and porosities. Various characteristic length scales were used for the Reynolds number and friction factor of metal foams in the previous works. In the present study, we propose a realistic definition of the characteristic length scale that is applicable to pressure drop evaluation in metal foams regardless of pore density and porosity. A series of experiments was conducted to obtain friction factor of metal foam. An equivalent diameter based on permeability and porosity appeared to best fit the experimental data produced using various metal foams. The relationship between the friction factor and Reynolds number through metal foams can be classified into three regimes. In Re 2000, the value of friction factor approaches 0.17. The relationship between friction factor and Reynolds number of foam materials appeared to be similar trend to that of Moody chart.

Flow of CO 2 in the vicinity of its critical point was studied experimentally in two different flow configurations. First, a 60 cm long stainless steel pipe with 2.1 mm inner diameter was used to study near-critical CO 2 pipe flow. In terms of raw flow data, the results indicated high sensitivity of pressure drop to mass flow rate as well as to inlet conditions; i.e. pressure and temperature. Remarkably though, when friction factor and Reynolds number were defined in terms of the inlet conditions, it was established that the classical Moody chart described the flow with satisfactory accuracy. This was rationalized using shadowgraphs that visualized the process of transition from a supercritical state to a two-phase subcritical state. During the transition the two phases were separated due to density mismatch and an interface was established that traveled in the direction of the flow. This interface separated two regions of essentially single-phase flow, which explained the effective validity of the classical Moody chart. Second, Joule–Thomson throttling was studied using a 0.36-mm-diameter orifice. For conditions relevant to carbon capture and sequestration, the fluid underwent Joule–Thompson cooling of approximately 0.5 °C/bar. The temperature difference during the cooling increased with increasing inlet enthalpy. Discrepancies with previous computed and experimentally measured values of Joule–Thompson throttling were discussed in detail.

ASHRAE Handbooks are the worldwide reference books for HVAC engineers. When we tried to develop a duct software, we also followed the steps shown in 2013 ASHRAE Handbook. Accidently we found that some friction loss data of a duct design example seemed contrary to the data obtained from duct friction chart. Then we go back to adopt Darcy’s and Colebrook’s equations that have been used to solve duct/pipe friction loss for decades. However, the calculation process needs to use complicated computer program. After doing huge trial and error processes by computerized program, we obtained one integrated equation that can be used to calculate duct/pipe friction loss by hand calculator. We own an HVAC&R consultancy firm and have the opportunity to contact many real duct/pipe projects. This empirical equation has been successfully applied to dozens of actual duct and pipe design projects. For Reynolds Number (Re) is greater than 10,000 (i.e. turbulent flow), our analysis shows the friction losses obtained from this integrated equation are within ±2.0% of those obtained from Darcy’s and Colebrook’s equations. The accuracy (±2.0%) is good enough for engineers doing realistic duct/pipe designs. Hence, this one-step equation can be the handy alternative for Darcy’s and Colebrook’s equations. For the practical duct/pipe designs, engineers can calculate friction loss easily, no need to use iterative method.

An alternate inner wall variable, for flow over a transitional rough pipe surface, is defined as the ratio of normal coordinate measured above the mean roughness level to the wall roughness scale. The Reynolds equations for mean turbulent flow in a transitional rough pipe, in two layers (inner and outer) are considered. The predictions of the mean velocity and friction factor in fully developed turbulent flow in a rough pipe flow, presented here, covers all types of roughness. The data for a particular case of the machine honed Princeton superpipe roughness, analogous to inflectional type roughness of Nikuradse, is presented, as two expressions using our roughness scale. The velocity profile and friction factor, on a transitional rough wall, are shown to be governed by the new log laws, which are explicitly independent of the transitional wall roughness. Further, the inflectional roughness has also been connected with geometric roughness parameters; like, arithmetic mean roughness, mean peak to valley heights roughness, root mean square (rms), roughness based on texture measure; and the friction factor implicit and approximate explicit formulas have also been proposed. In entire transition region between fully smooth and fully rough wall, monotonic roughness of Colebrook (Moody Chart) over estimaton the friction factor when compared with present inlectional roughness.

Despite the presence of a variety of studies dealing with the magnitude of particle Reynolds number, Re p defining transition from laminar to turbulent regime for flow through packed beds, the manner is still one of the unknowns. An approach based on the experimental data concerning upward airflow through fixed cylindrical packed beds is presented in this paper. The utilized packed beds had the following ranges of; sphericity, Φ , 0.55 ⩽ Φ ⩽ 1.00, packing material diameter to bed length ratio, D p / L , 0.04 ⩽ D p / L ⩽ 0.72, and bed porosity, e , 0.36 ⩽ e ⩽ 0.56. The test cases covered the ranges of particle Reynolds number, Re p 708 ⩽ Re p ⩽ 7772 and particle Froude number; Fr p 2.86 ⩽ Fr p ⩽ 10.39. The measurements of pressure drop through packed bed; Δ P Bed and superficial mean exit velocity; U are used to determine bed frictional effects in reference to the available literature on particle friction factors, f p . The magnitude of Re p defining transition is assumed to be 2000 with particular emphasis to the flow dynamics. The definitions of Bird et al. [R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena , John Wiley and Sons, NY, 1960] are used to calculate f p . The calculated f p for the covered test cases are given as a function of pressure coefficient, Δ P * and Re p, Fr p , Φ , e , D p / L in the approximate ranges of laminar and turbulent flow for Re p p > 2000, respectively. The proposed separate equations of f p = f p (Δ P *, Re p , Fr p , Φ , e , D p / L ) are satisfied for laminar and turbulent flows with corresponding average error margins of ±7.6% and ±18%. Furthermore ranges of transitional and fully rough flow through packed beds are estimated as 2000 ⩽ Re p ⩽ 4000 and Re p > 5000 with an analogy to the well-known Moody Chart in pipe flows.

The "fluid friction factor" (f) should be abandoned because it is a mathematically undesirable parameter that complicates the solution of fluid flow problems. f is the dimensionless group  2 g PD 5 /8LW 2 . This group is mathematically undesirable because it includes  P, W, and D. Therefore if f is used in the solution of a problem, the problem must be solved with  P, W, and D in the same term, even though fluid flow problems are generally much easier to solve if  P, W, and D are in separate terms. (Just as it is generally much easier to solve equations if x and y are in separate terms). The mathematical complication introduced by f is illustrated by the Moody chart (Fig. 1). Because the chart is based on f, it must be read iteratively (or by trial-and-error) to determine W or D. But if the Moody chart is transformed in order to eliminate f, the transformed chart (Fig. 2) is read directly to determine  P, W, or D. The fluid flow methodology described herein altogether abandons f, and allows fluid flow problems to be solved in the simplest possible manner.

In this study, it is shown how the equivalent sand roughness required in the Moody chart can be calculated for arbitrarily shaped wall roughnesses. After a discussion of how to define the wall location and roughness height in the most reasonable way, a numerical approach based on the determination of entropy production in rough pipes and channels is presented. As test cases, three different two-dimensional roughness types have been chosen which are representative of regular roughnesses on machined surfaces. In the turbulent range, skin friction results with these test roughnesses can be linked to Nikuradse's sand roughness results by a constant factor. For laminar flows, a significant effect of wall roughness is identified which in most other studies is neglected completely. The dissipation model of this study is validated with experimental data for laminar and turbulent flows.

A number of correlations for friction factor determinations in smooth pipes have been proposed in the past decades. The accuracy and applicability of these friction factor formulas should be examined. Based on this notion the paper is designed to provide a comparative study of friction factor correlations in smooth pipes for all flow regimes of Bingham fluids. Nine models were chosen. The comparisons of the selected equations with the existing experimental results, which are available in the literature, were expressed through MARE, MRE+, MRE-, RMSE, Ѳ, and S. The statistical comparisons were also carried out using MSC and AIC. The analyses show that the Wilson-Thomas (1985) and Morrison (2013) models are best fit models to the experimental data for the Reynolds number up to 40000. Within this range, both models can be used alternately. But beyond this Re value the discrepancy of the Wilson-Thomas model is higher than the Morrison model. In view of the fact that the Morrison model requires fewer calculations and parameters as well as a single equation is used to compute the friction factor for all flow regimes, it is the authors’ advice to use this model for friction factor estimation for the flow of Bingham fluids in smooth pipes as an alternative to the Moody chart and other implicit formulae.

We describe a mixing-length extension of the lattice Boltzmann approach to the simulation of an incompressible liquid in turbulent flow. The method uses a simple, adaptable, closure algorithm to bound the lattice Boltzmann fluid incorporating a law-of-the-wall. The test application, of an internal, pressure-driven and smooth duct flow, recovers correct velocity profiles for Reynolds number to 1.25 × 105. In addition, the Reynolds number dependence of the friction factor in the smooth-wall branch of the Moody chart is correctly recovered. The method promises a straightforward extension to other curves of the Moody chart and to cylindrical pipe flow.

Having similar densities as liquids but with viscosities up to 20 times lower (higher diffusion coefficients), supercritical CO2 is the ideal (co-)solvent for fast and/or highly efficient separations without mass-transfer limitations or excessive column pressure drops. Whereas in liquid chromatography the flow remains laminar in both the packed bed and tubing, except in extreme cases (e.g. in a 75 mu m tubing, pure acetonitrile at 5 ml/min), a supercritical fluid can experience a transition from laminar to turbulent flow in more typical operation modes. Due to the significant lower viscosity, this transition for example already occurs at 1.3 ml/min for neat CO2 when using connection tubing with an ID of 127 mu m. By calculating the Darcy friction factor, which can be plotted versus the Reynolds number in a so-called Moody chart, typically used in fluid dynamics, higher values are found for stainless steel than PEEK tubing, in agreement with their expected higher surface roughness. As a result turbulent effects are more pronounced when using stainless steel tubing. The higher than expected extra-column pressure drop limits the kinetic performance of supercritical fluid chromatography and complicates the optimization of tubing ID, which is based on a trade-off between extra-column band broadening and pressure drop. One of the most important practical consequences is the non-linear increase in extra-column pressure drop over the tubing downstream of the column which leads to an unexpected increase in average column pressure and mobile phase density, and thus decrease in retention. For close eluting components with a significantly different dependence of retention on density, the selectivity can significantly be affected by this increase in average pressure. In addition, the occurrence of turbulent flow is also observed in the detector cell and connection tubing. This results in a noise-increase by a factor of four when going from laminar to turbulent flow (e.g. going from 0.5 to 2.5 ml/min for neat CO2). (C) 2014 Elsevier B.V. All rights reserved.

The purpose of this paper is to present petroleum and chemical engineers with a simple means of measuring or estimating the absolute surface roughness, ϵ, and relative roughness, ϵ/D, for internally coated pipes. Our research thrust is to develop new relative roughness charts along with corresponding mathematical equations for internally coated pipes. An integral part of the frictional pressure drop due to fluid flow in pipes involves the determination of absolute surface roughness and relative roughness. An accurate determination of the pressure drop due to fluid flow in oil and gas wells is required for optimizing oil and gas production design calculations. Some of these calculations include developing tubing programs to maximize well deliverability, wellbore flow performance, sizing surface flow lines, and designing artificial lift installations. Previous multiphase fluid flow laboratory and field tests, during the past 50 years, provided correlations for calculating pressure gradients in tubulars [Chem. Eng. Prog. 45(1) (1949) 39; Hetsroni, G., 1982. Handbook of Multiphase Systems, Hemisphere/McGraw Hill, 1174 pp.; Brown, K.E., 1984. The Technology of Artificial Methods, vol. 4, Penn Well Publishing, Tulsa, OK, 447 pp.; Tengesdal, J.O., 1998. Predictions of Flow Patterns, Pressure Drop, and Liquid Holdup in Vertical Upward Two-Phase Flow. MSc Thesis, The University of Tulsa, Tulsa, OK; Farshad, F., Garber, J.D., Polaki, V., 2000. Comprehensive model for predicting corrosion rates in gas wells containing CO2. Soc. Pet. Eng. Prod. Facil. 15(3), 183–190]. All the multiphase fluid flow correlations, used in production operations to calculate these pressure gradients and flow regimes, stem from the general energy balance equation and involves the determination of friction pressure losses. Still today, these friction losses only are being evaluated by practicing engineers using the Darcy–Weisbach equation, which involves the Moody friction factor, f [Szilas, A.P., 1975. Production and Transport of Oil and Gas. Elsevier Sci. Publ., Amsterdam, p. 630; Economides, M.J., Hill, D.A., Ehlig-Economides, C., 1994. Petroleum Production Systems, Prentice Hall, Englewood Cliffs, NJ, 611 pp.]. Moody [Trans. AME 66 (1944) 671] prepared a relative roughness chart for a number of common piping materials. This initial relative roughness correlation was based on experiments on pipes artificially roughened with sand grains. At that time, internally coated pipes were not invented. Hence, Moody did not provide the relative roughness for internally coated pipes. In addition, Moody did not perform a regression analysis of the data to generate functional forms of equations by relating roughness, ϵ/D, as a function of internal pipe diameter, D. Currently, internally coated pipes are being utilized worldwide in oil field production systems. Consequently, new absolute surface roughness and relative roughness values of internally coated pipes are needed to properly model the hydrodynamics [Brown, K.E., 1984. The Technology of Artificial Methods, vol. 4, Penn Well Publishing, Tulsa, OK, 447 pp.]. The new relative roughness plots developed for internally coated pipes are presented and show that the correlation fits between the commercial steel and drawn tubing in the Moody chart.

An unrigorous but plausible analysis suggests that the concept of a critical roughness height, below which roughness does not affect a turbulent wall flow, is erroneous. The Oseen approximation implies that the effect of roughness on the additive constant in the logarithmic law of the wall should vary as the square of the roughness Reynolds number (specifically the roughness height in “wall units”). This is an important point in determining whether surfaces used in experiments at high unit Reynolds number can be regarded as hydraulically smooth. Attention is also called to the qualitative difference between Nikuradse’s measurements of friction factor in pipe flow with uniform-size sand-grain roughness in the “transitional” range of Reynolds number and the data correlation in the Moody chart of 1944; the latter was derived from tests on miscellaneous real-life rough surfaces in the 1930s. Nearly all textbooks on elementary fluid dynamics present, but practically none discuss, this difference. Nikuradse’s m...

Foams are considered as highly complex phenomena and their complexity becomes more challenging when they start to flow. An experimental foaming system based on the milk protein foam was developed in order to investigate the foam flow characterization which enabled the foam transport through a horizontal channel. The article presents the macroscopic phenomena, mechanism and flow characterization of milk protein foam during mechanical transport. The protein foam quality was obtained by controlling the gas and liquid flowrate. The pressure gradient was measured as a function of the foam quality and the influence of the gas and liquid flowrate on the pressure drop was studied. The foam flow revealed a uniform profile within a pressure drop deviation of 600–850 Pam-1. The foam rheology was described by the well-known Moody chart for Newtonian fluids and the empirical power-law model. The corresponding friction factor and Reynolds number were obtained from the entire foam qualities exhibited a close agreement with the well-known equation for laminar flow of a single Newtonian fluid in a pipe ( ) with a constant value of 36.723 and an exponent of 1.034. Practical Applications The improvement of foam product qualities in food stuffs is undoubtedly a major concern for food producers. Because proteins are widely used foaming agents in food industry, a comprehensive knowledge of protein foam flow is required. The aim of this study was assigned to offer the first experimental results in terms of the milk protein foam flow dynamics, corresponding pressure gradient and related foam rheology in a horizontal channel flow in order to improve the manufacturing process.

One of the most important resources available in the field of fluid mechanics, the Moody Chart gives Darcy friction factor as a function of Reynolds number and relative roughness. The experimentalists who generated the data correlated in the Moody Chart, however, roughened pipe surfaces by coating their internal surfaces with a monolayer of sand, the pipe wall roughness being defined as the average diameter of the sand grains. Thus, the sand-grain roughness values required for use with the Moody Chart are not derived from any direct measure of roughness using modern surface characterization equipment, such as an optical profilometer. Using direct measurements of surface roughness in fluid flow calculations may therefore result in significant error. In this paper we present a simple algorithm with which various measured surface roughness parameters can be converted to equivalent sand-grain roughness. For nearly every surface roughness value converted to equivalent sand-grain roughness using the algorithm, better agreement with fluid flow experiments is seen over using the raw roughness value.

The effects of rib-patterned surfaces on laminar, transitional to turbulent gas flow in micro-channels were experimentally investigated in the present study. The experiments were performed for two micro-channels having either smooth or rib-patterned surfaces. The micro-channels were etched into silicon wafers and capped with glass substrates. The micro-ribs were patterned on the microchannel surfaces and oriented perpendicular to the flow direction. The pressure was measured at seven locations along the channel length to determine local values of Mach number and friction factor for a wide range of flow regime from laminar to turbulent flow. The friction factors with the hydraulic diameter based on the rib-to-upper-wall height were compared with that for incompressible theory on Moody chart. The values of the product of friction factor and Reynolds number (f·Re) as a function of Mach number were also compared with those of smooth micro-channels and incompressible theory.

This paper presents experimental investigations on turbulent gas flow characteristics of nitrogen gas through a micro-channel. The micro-channels were etched into silicon wafers, capped with glass, and their hydraulic diameter is 147.76 micro meters. The micro-channel was designed with a main flow channel and seven side channels, which lead to the pressure transducers. The stagnation pressure was designated in such a way that the flow is in turbulent flow regime. The outlet of the channel faced to the atmosphere. The pressures of the main channel at seven locations were measured by gauge pressure transducers to determine local values of Mach number. And the pressure differences of each pressure ports were measured by differential pressure transducers to obtain the pressure losses precisely. The pressure distribution of turbulent gas flow through a micro-channel falls steeply and Mach number increases near the outlet with increasing the inlet pressure due to flow acceleration. Both Darcy friction factor and Fanning friction factor were obtained for turbulent flow. The result shows that the obtained both friction factors were evaluated as a function of Reynolds number on the Moody chart. The values of Darcy friction factors differ from Blasius correlation for turbulent flow regime due to the compressibility effects, however the values of Fanning friction factors coincide with Blasius correlation.Copyright © 2011 by ASME

In this paper, we propose a novel explicit equation for friction factor, which is valid for both smooth and rough wall turbulent flows in pipes and channels. The form of the proposed equation is based on a new logarithmic velocity profile and the model constants are obtained by using the experimental data available in the literature. The proposed equation gives the friction factor explicitly as a function of Reynolds number and relative roughness. The results indicate that the present model gives a very good prediction of the friction factor and can reproduce the Colebrook equation and its Moody plot. Therefore, the new approximation for the friction factor provides a rational, accurate, and practically useful method over the entire range of the Moody chart in terms of Reynolds number and relative roughness.

Though predicted by the Moody chart that if lower than 5%, the effect of roughness on laminar flow characteristics can be ignored in macro-scale tubes, the statement is challenged by the recent experimental studies for fluid flow in micro-scale tubes. In this paper, a simplified three-dimensional roughness element model was constructed based on the SEM observation of the inner wall topography of a stainless microtube. Numerical calculations were carried out to study the characteristics of resistance for incompressible laminar flow in the rough tubes. The effect of relative height, relative length, angular width of roughness elements and Reynolds number on flow characteristics were numerically studied by employing the SIMPLE algorithm. The general trend can be observed that bigger sizes of roughness element lead to higher flow resistance. Particularly, the effect of roughness can no longer be ignored at relative roughness height higher than 3%, for the product of friction factor and Reynolds number can be up to 17% higher than the theoretical 64 in a macrotube.

An algorithm for the calculation of the Darcy friction factor, for the estimation of pressure losses in pipe flows, is presented. The algorithm includes the five correlations that generate the Moody chart. The codification of the algorithm in Visual Basic for Applications, for use in the MS Excel spreadsheet, is presented. The Prandtl and Colebrook correlations, which are not explicit in the friction factor, are solved through a Newton numerical method; the derivatives of the functions are obtained through a numerical central perturbation procedure. The algorithm also calculates the values of the friction factor for the critical flow zone, between the zones of laminar and turbulent flow, in order to avoid numeric discontinuities during optimization processes. The results are shown as an Excel-generated Moody chart.Copyright © 2006 by ASME

The characteristics of a gaseous flow of nitrogen in commercial stainless steel microtubes for gas chromatography having a nominal inner diameter of 762, 508, 254 and 127 μm are experimentally investigated. The friction factor is calculated as a function of the Reynolds number and plotted in a Moody chart. A comparison among three different methods to calculate the friction factor is made in order to evidence limitations and advantages of each method. It was observed that in the laminar regime the Poiseuille law correctly predicts the value of the pressure drop. It has been evidenced that in order to make accurate experiments on the frictional characteristics of commercial microtubes the value of the inner diameter given by the manufacturer has to be always verified. The experimental data presented in this work remark how in microtubes the compressibility effects related to the axial variation of the gas density tend to become important at large Reynolds numbers and small diameters even if the average Mach number is low. The effects due to the gas acceleration on the laminar-to-turbulent transition in microtubes are investigated by evidencing the role of the L/D (length to diameter) ratio on the transition to turbulence. No early transition to turbulence has been evidenced in the tests, instead it takes place at Reynolds numbers ranging between 1800 and 2900.

Surface roughness is known to have significant effect on turbulent flow depending on the magnitude of the roughness. Also, a pipe is considered hydrodynamically smooth (for a given surface roughness) below certain value of Re. As the flow becomes laminar, there is little known about the surface roughness effect, particularly for small channel diameters (micro-channels). Data available to date from the literature, on micro-channels, indicate that the friction-Re relationship deviates from the known Moody Chart, for laminar flow. These differences are attributed, sometimes, to the surface roughness. Micro-channels are currently under consideration as a candidate for Stirling Engine Regenerators. In this paper, the effect of surface roughness on the flow and heat transfer characteristics has been studied using the CFD-ACE commercial software. A CFD model is created with small tooth like structures on the inner walls of a pipe with equal height and spacing between them. CFD analysis is done for different roughness values and the variation of heat transfer and fluid characteristics with the increase in roughness is studied. The study is done on a pipe with a hydraulic diameter of 0.62 mm by considering it first as smooth and then with average roughness values of 1.0 and 2.2 microns. The results were compared with the analytical solution (for smooth pipes) and experimental results available from the literature.

Static pressures in non-circular ducts and pipe fittings (globe, ball and butterfly valves) have been measured in a closed circuit water channel at the range of Reynolds number from 20 000 to 80 000, which give rise to fully developed turbulent pipe flow, so as to define the friction coefficient (C-f) and resistance coefficients (K). A new proposed equation for friction factor with two new dimensionless parameters as a function of cross sectional area are successfully adopted to fully developed turbulent flow in all cross sections with a precision of better than +/-4%. Measurements showed that friction factors decreased with increasing eccentricity and were in good agreement with the proposed equation. It was also found out that Reynolds number has no effect on resistance coefficients of butterfly, globe and gate valves, but the closing ratio caused K to increase remarkably, and the K value of bends can easily be obtained by an empirical formula based on Moody chart friction factor. Static pressures on front and back sides of the circular disc of butterfly valve decreased with Reynolds number, remained almost constant in the radial direction and increased particularly at closing angles of bigger than 60 degrees, where flow rate starts to decrease sharply.

Local friction factors for turbulent gas flows in circular microtubes with constant wall heat flux were obtained numerically. The numerical methodology is based on arbitrary-Lagrangian-Eulerian method to solve two-dimensional compressible momentum and energy equations. The Lam-Bremhorst's Low-Reynolds number turbulence model was employed to calculate eddy viscosity coefficient and turbulence energy. The simulations were performed for a wide flow range of Reynolds numbers and Mach numbers with different constant wall heat fluxes. The stagnation pressure was chosen in such a way that the outlet Mach number ranged from 0.07 to 1.0. Both Darcy friction factor and Fanning friction factor were locally obtained. The result shows that the obtained both friction factors were evaluated as a function of Reynolds number on the Moody chart. The values of Darcy friction factor differ from Blasius correlation due to the compressibility effects but the values of Fanning friction factor almost coincide with Blasius correlation. The wall heat flux varied from 100 to 10000 W/m2. The wall and bulk temperatures with positive heat flux are compared with those of incompressible flow. The result shows that the Nusselt number of turbulent gas flow is different from that of incompressible flow.

In support of the High Flux Isotope Reactor program, experimental determinations were made of friction factors, burnout heat fluxes, and average and local nonboiling heattransfer coefficients for forced-convection flow of water through this aluminum and nickel rectangular channels under the following conditions: heat flux = 0.1 x 10/sup 6/ to 7.4 x 10/sup 6/ Btu/hr - ft/sup 2/, velocity = 10 to 85 fps, Reynolds number = 9,000 to 270,000, pressure = 1 to 39 atmospheres absolute, flow gap = 0.043 to 0.057 in., and heated length = 12 and 18 in. A few tests were made to ascertain the effect of an axially oriented cylindrical spacer strip on surface temperature distribution and burnout heat flux. The results of these studies, are in reasonably good agreement with accepted ccrrelations. The friction factors are in satisfactory agreement with the Moody chart for the relative roughness of the test sections used, the burnout heat fluxes are well reproduced by the Soviet Zenkevich-Subbotin correlation, and the local and average heat-transfer coefficients are slightly larger than values predicted by the Hausen and Sieder-Tate equations. Miscellaneous experimental and analytical HFIR heat-transfer studies are included. (auth)