A Novel Explicit Equation for Friction Factor in Smooth and Rough Pipes

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Atakan Avci ◽  
Irfan Karagoz
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Entire Range ◽  
Present Model ◽  
Good Prediction ◽  
Explicit Equation ◽  
Relative Roughness ◽  
Logarithmic Velocity Profile

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.

Comments on Compressor Efficiency Scaling With Reynolds Number and Relative Roughness

1989 ◽  
Author(s):  
Terry Wright
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Friction Factor ◽  
Model Test ◽  
Large Scale ◽  
Recent Literature ◽  
Test Results ◽  
Relative Roughness ◽  
Scaling Algorithms ◽  
Compressor Efficiency

The background and literature on scaling of model test results to predict the performance of large scale turbomachines are presented and discussed in the context of both industry restrictions and recent improvements in analytical rigor and accuracy of scaling algorithms. The variety and disparity of methods developed before about 1970 is illustrated and plausible explanation is offered to account for the broad differences. The more recent literature is considered and the older exponential algorithms for scaling are reconciled with the current methods based on friction factor correlations. A simpler form is developed in terms of either exponential or friction factor formulations which includes the influence of Reynolds Number, relative roughness and fixed, friction-independent losses. This method is compared to the recently developed algorithms and to experimental data taken from the literature.

Friction Factor Directly From Roughness Measurements

2001 ◽  
Author(s):  
Elling Sletfjerding ◽  
Jon Steinar Gudmundsson
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Power Spectrum ◽  
Friction Factor ◽  
High Reynolds Number ◽  
Gas Flow ◽  
Relative Roughness ◽  
High Reynolds ◽  
Friction Factor Correlation ◽  
Roughness Measurements

Abstract Pressure drop experiments on natural gas flow in 150 mm pipes at 80 to 120 bar pressure and high Reynolds number were carried out for pipes smooth to rough surfaces. The roughness was measured with an accurate stylus instrument and analyzed using fractal methods. Using a similar approach to that of Nikuradse the measured friction factor was related to the measured roughness values. Taking the value of the relative roughness and dividing it by the slope of the power spectrum of the measured roughness, a greatly improved fit with the measured friction factor was obtained. Indeed, a new friction factor correlation was obtained, but now formulated in terms of direct measurement of roughness.

scholarly journals Modeling of Laminar Flows in Rough-Wall Microchannels

2005 ◽  
Vol 128 (4) ◽  
pp. 734-741 ◽  
Author(s):  
R. Bavière ◽  
G. Gamrat ◽  
M. Favre-Marinet ◽  
S. Le Person
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Numerical Modeling ◽  
Pressure Drop ◽  
Analytical Model ◽  
Analytical Approach ◽  
Laminar Flows ◽  
Numerical Results ◽  
Rough Wall ◽  
Relative Roughness

Numerical modeling and analytical approach were used to compute laminar flows in rough-wall microchannels. Both models considered the same arrangements of rectangular prism rough elements in periodical arrays. The numerical results confirmed that the flow is independent of the Reynolds number in the range 1–200. The analytical model needs only one constant for most geometrical arrangements. It compares well with the numerical results. Moreover, both models are consistent with experimental data. They show that the rough elements drag is mainly responsible for the pressure drop across the channel in the upper part of the relative roughness range.

An Alternative (Preferable) Friction Factor

2006 ◽  
Author(s):  
Richard A. Gaggioli
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Pipe Flow ◽  
Incompressible Flows ◽  
Flow Regimes ◽  
Relative Roughness ◽  
Curve Fit ◽  
Moody Diagram ◽  
Approximate Formulas

An alternative to the traditional friction factor for pipe flow is presented (φ = [R]f). For incompressible flows, the correlation of this new friction factor with Reynolds Number [R] and Relative Roughness [ε] is presented graphically, and appears much simpler and more intuitive than the Moody Diagram (or other equivalents). Moreover, relatively simple curve-fit formulas for representing φ explicitly as a function of R and ε are presented for various flow regimes, along with measures of error associated with these approximate formulas.

scholarly journals Solution of the Implicit Colebrook Equation for Flow Friction Using Excel

2017 ◽  
Author(s):  
Dejan Brkić
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Hydraulic Resistance ◽  
Iterative Solution ◽  
Pipe Surface ◽  
Implicit Equation ◽  
Flow Friction ◽  
Relative Roughness ◽  
Additional Task ◽  
Accepted Standard

Empirical Colebrook equation implicit in unknown ow friction factor (λ) is an accepted standard for calculation of hydraulic resistance in hydraulically smooth and rough pipes. e Colebrook equation gives friction factor (λ) implicitly as a function of the Reynolds number (Re) and relative roughness (ε/D) of inner pipe surface; i.e. λ0=f(λ0, Re, ε/D). e paper presents a problem that requires iterative methods for the solution. In particular, the implicit method used for calculating the friction factor λ0 is an application of xed- point iterations. e type of problem discussed in this "in the classroom paper" is commonly encountered in uid dynamics, and this paper provides readers with the tools necessary to solve similar problems. Students’ task is to solve the equation using Excel where the procedure for that is explained in this “in the classroom” paper. Also, up to date numerous explicit approximations of the Colebrook equation are available where as an additional task for students can be evaluation of the error introduced by these explicit approximations λ≈f(Re, ε/D) compared with the iterative solution of implicit equation which can be treated as accurate.

scholarly journals Turbulent drag reduction with polymer additive in rough pipes

2009 ◽  
Vol 642 ◽  
pp. 279-294 ◽  
Author(s):  
SHU-QING YANG ◽  
G. DOU
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Drag Reduction ◽  
Turbulent Flows ◽  
Newtonian Fluid ◽  
Effective Viscosity ◽  
Eddy Diffusivity ◽  
Viscous Sublayer ◽  
Friction Factors ◽  
Theoretical Predictions

Friction factor of drag-reducing flow with presence of polymers in a rough pipe has been investigated based on the eddy diffusivity model, which shows that the ratio of effective viscosity caused by polymers to kinematic viscosity of fluid should be proportional to the Reynolds number, i.e. u∗R/ν and the proportionality factor depends on polymer's type and concentration. A formula of flow resistance covering all regions from laminar, transitional and fully turbulent flows has been derived, and it is valid in hydraulically smooth, transitional and fully rough regimes. This new formula has been tested against Nikuradse and Virk's experimental data in both Newtonian and non-Newtonian fluid flows. The agreement between the measured and predicted friction factors is satisfactory, indicating that the addition of polymer into Newtonian fluid flow leads to the non-zero effective viscosity and it also thickens the viscous sublayer, subsequently the drag is reduced. The investigation shows that the effect of polymer also changes the velocity at the top of roughness elements. Both experimental data and theoretical predictions indicate that, if same polymer solution is used, the drag reduction (DR) in roughened pipes becomes smaller relative to smooth pipe flows at the same Reynolds number.

scholarly journals A Comparison of Data Reduction Methods for Average Friction Factor Calculation of Adiabatic Gas Flows in Microchannels

Micromachines ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 171 ◽  
Author(s):  
Danish Rehman ◽  
Gian Morini ◽  
Chungpyo Hong
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Numerical Analysis ◽  
Friction Factor ◽  
Data Reduction ◽  
Hydraulic Diameter ◽  
Accurate Estimation ◽  
Gas Flows ◽  
Adiabatic Wall ◽  
Loss Coefficients

In this paper, a combined numerical and experimental approach for the estimation of the average friction factor along adiabatic microchannels with compressible gas flows is presented. Pressure-drop experiments are performed for a rectangular microchannel with a hydraulic diameter of 295 μ m by varying Reynolds number up to 17,000. In parallel, the calculation of friction factor has been repeated numerically and results are compared with the experimental work. The validated numerical model was also used to gain an insight of flow physics by varying the aspect ratio and hydraulic diameter of rectangular microchannels with respect to the channel tested experimentally. This was done with an aim of verifying the role of minor loss coefficients for the estimation of the average friction factor. To have laminar, transitional, and turbulent regimes captured, numerical analysis has been performed by varying Reynolds number from 200 to 20,000. Comparison of numerically and experimentally calculated gas flow characteristics has shown that adiabatic wall treatment (Fanno flow) results in better agreement of average friction factor values with conventional theory than the isothermal treatment of gas along the microchannel. The use of a constant value for minor loss coefficients available in the literature is not recommended for microflows as they change from one assembly to the other and their accurate estimation for compressible flows requires a coupling of numerical analysis with experimental data reduction. Results presented in this work demonstrate how an adiabatic wall treatment along the length of the channel coupled with the assumption of an isentropic flow from manifold to microchannel inlet results in a self-sustained experimental data reduction method for the accurate estimation of friction factor values even in presence of significant compressibility effects. Results also demonstrate that both the assumption of perfect expansion and consequently wrong estimation of average temperature between inlet and outlet of a microchannel can be responsible for an apparent increase in experimental average friction factor in choked flow regime.

scholarly journals Intelligent Flow Friction Estimation

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Dejan Brkić ◽  
Žarko Ćojbašić
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Reynolds Number ◽  
Friction Factor ◽  
High Accuracy ◽  
Ann Model ◽  
Flow Friction ◽  
Relative Roughness ◽  
Friction Estimation ◽  
Artificial Neural Network Ann

Nowadays, the Colebrook equation is used as a mostly accepted relation for the calculation of fluid flow friction factor. However, the Colebrook equation is implicit with respect to the friction factor (λ). In the present study, a noniterative approach using Artificial Neural Network (ANN) was developed to calculate the friction factor. To configure the ANN model, the input parameters of the Reynolds Number (Re) and the relative roughness of pipe (ε/D) were transformed to logarithmic scales. The 90,000 sets of data were fed to the ANN model involving three layers: input, hidden, and output layers with, 2, 50, and 1 neurons, respectively. This configuration was capable of predicting the values of friction factor in the Colebrook equation for any given values of the Reynolds number (Re) and the relative roughness (ε/D) ranging between 5000 and 108and between 10−7and 0.1, respectively. The proposed ANN demonstrates the relative error up to 0.07% which had the high accuracy compared with the vast majority of the precise explicit approximations of the Colebrook equation.

Local Friction Factor of Compressible Laminar or Turbulent Flow in Micro-Tubes

2011 ◽  
Author(s):  
Shintaro Murakami ◽  
Yutaka Asako
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Numerical Procedure ◽  
Choked Flow ◽  
Curvilinear Grid ◽  
Wide Range ◽  
Darcy Friction Factor ◽  
Fanning Friction Factor

Laminar/turbulent flows of compressible fluid in microtubes were simulated numerically to obtain the effect of compressibility on the local pipe friction factors. For gaseous flows, the effect of compressibility had not been clarified except for laminar flow whose Mach number is less than 0.45, so the present work extended this to handle higher speed flows including choked ones and turbulent flows. The numerical procedure based on arbitrary-Lagrangian-Eulerian method solves two-dimensional compressible momentum and energy equations. The Lam-Bremhorst Low-Reynolds number turbulence model was adopted to calculate eddy viscosity coefficient and turbulence energy. The physical domain of simulation with the back region downstream from the outlet of the micro-tube was used to be able to calculate the case of under-expansion flow in the tube. The orthogonal curvilinear grid was used for the computational mesh to obtain accurate results. The computations were performed for a wide range of Reynolds number and Mach number including laminar/turbulent choked flows. It was found that in laminar regimes the ratio of the Darcy friction factor to its conventional (incompressible flow’s) value is a function of Mach number and the same goes for the Fanning friction factor. On the other hand, in turbulent regimes, the ratio is still a function of Mach number for the Darcy friction factor but is equal to about unity for the Fanning friction factor. Namely, the Fanning friction factor of gaseous flow in micro-tubes coincides with Blasius formula, even when Mach number is not small and compressibility effect appears. This fact can be seen in choked flow.

The Influence of Surface Roughness on Resistance to Flow Through Packed Beds

1986 ◽  
Vol 108 (3) ◽  
pp. 343-347 ◽  
Author(s):  
C. W. Crawford ◽  
O. A. Plumb
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Entire Range ◽  
Reynolds Numbers ◽  
Packed Beds ◽  
Sphere Diameter ◽  
Relative Roughness ◽  
Roughness Elements ◽  
Flow Through ◽  
High Reynolds

Experiments were performed to determine the effect of roughness on flow through randomly packed beds of spheres. Three different packings were investigated, one of smooth spheres, and two others composed of spheres with roughness elements added to the surface. The relative roughness, defined as the height of the added elements divided by the diameter of the smooth spheres, was .012 and .026 for these two cases. The experiments covered a range of Reynolds numbers based on the sphere diameter from near unity where the flow is dominated by viscosity to 1600 where the flow is dominated by inertia. It was found that the pressure drop is substantially increased by the presence of surface roughness over the entire range of Reynolds numbers studied. The observed behavior is quite different from that which has been proposed previously by drawing analogy with flow in rough pipes, since the flow at low Reynolds number as well as high Reynolds number was affected by roughness.

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