47,517 research outputs found
Accurate and efficient explicit approximations of the Colebrook flow friction equation based on the Wright omega-function
The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor, f. To date, the captured flow friction factor, f, can be extracted from the logarithmic form analytically only in the term of the Lambert W-function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W-function also known as the Wright omega-function. The Wright omega-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term, y = W (e(x)), of the Lambert W-function to series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W-function is identical to the original expression in terms of accuracy, a further evaluation of the Lambert W-function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contain only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with a relative error of no more than 0.0096%. The presented approximations are in a form suitable for everyday engineering use, and are both accurate and computationally efficient.Web of Science71art. no. 3
Accurate and efficient explicit approximations of the Colebrook flow friction equation based on the Wright ω-function: Reply to Discussion
This reply gives two corrections of typographical errors in respect to the commented article, and then provides few comments in respect to the discussion and one improved version of the approximation of the Colebrook equation for flow friction, based on the Wright ω-function. Finally, this reply gives an exact explicit version of the Colebrook equation expressed through the Wright ω-function, which does not introduce any additional errors in respect to the original equation. All mentioned approximations are computationally efficient and also very accurate. Results are verified using more than 2 million of Quasi Monte-Carlo samples
Accurate and efficient explicit approximations of the Colebrook flow friction equation based on the Wright ω-function
The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor, f . To date, the captured flow friction factor, f , can be extracted from the logarithmic form analytically only in the term of the Lambert W-function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W-function also known as the Wright ω-function. The Wright ω-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term, y=W(ex), of the Lambert W-function to series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W-function is identical to the original expression in terms of accuracy, a further evaluation of the Lambert W-function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contain only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with a relative error of no more than 0.0096%. The presented approximations are in a form suitable for everyday engineering use, and are both accurate and computationally efficient
Integrating multicriteria decision analysis and scenario planning : review and extension
Scenario planning and multiple criteria decision analysis (MCDA) are two key management science tools used in strategic planning. In this paper, we explore the integration of these two approaches in a coherent manner, recognizing that each adds value to the implementation of the other. Various approaches that have been adopted for such integration are reviewed, with a primary focus on the process of constructing preferences both within and between scenarios. Biases that may be introduced by inappropriate assumptions during such processes are identified, and used to motivate a framework for integrating MCDA and scenario thinking, based on applying MCDA concepts across a range of "metacriteria" (combinations of scenarios and primary criteria). Within this framework, preferences according to each primary criterion can be expressed in the context of different scenarios. The paper concludes with a hypothetical but non-trivial example of agricultural policy planning in a developing country
Air-Forced Flow in Proton Exchange Membrane Fuel Cells: Calculation of Fan-Induced Friction in Open-Cathode Conduits with Virtual Roughness
Measurements of pressure drop during experiments with fan-induced air flow in the open-cathode proton exchange membrane fuel cells (PEMFCs) show that flow friction in its opencathode side follows logarithmic law similar to Colebrook’s model for flow through pipes. The stable symbolic regression model for both laminar and turbulent flow presented in this article correlates air flow and pressure drop as a function of the variable flow friction factor which further depends on the Reynolds number and the virtual roughness. To follow the measured data, virtual inner roughness related to the mesh of conduits of fuel cell used in the mentioned experiment is 0.03086, whereas for pipes, real physical roughness of their inner pipe surface goes practically from 0 to 0.05. Numerical experiments indicate that the novel approximation of the Wright-ω function reduced the computational time from half of a minute to fragments of a second. The relative error of the estimated friction flow factor is less than 0.5%
Siewert solutions of transcendental equations, generalized Lambert functions and physical applications
We review the exact solutions of several transcendental equations, obtained
by Siewert and his co-workers, in the '70s. Some of them are expressed in terms
of the generalized Lambert functions, recently studied by Mez\"o, Baricz and
Mugnaini. For some others, precise analytical approximations are obtained. In
two cases, the asymptotic form of Siewert's solutions are written as Wright
omega functions.Comment: 17 pages, 5 figure
Rational approximation for solving an implicitly given Colebrook flow friction equation
The empirical logarithmic Colebrook equation for hydraulic resistance in pipes implicitly considers the unknown flow friction factor. Its explicit approximations, used to avoid iterative computations, should be accurate but also computationally efficient. We present a rational approximate procedure that completely avoids the use of transcendental functions, such as logarithm or non-integer power, which require execution of the additional number of floating-point operations in computer processor units. Instead of these, we use only rational expressions that are executed directly in the processor unit. The rational approximation was found using a combination of a Pade approximant and artificial intelligence (symbolic regression). Numerical experiments in Matlab using 2 million quasi-Monte Carlo samples indicate that the relative error of this new rational approximation does not exceed 0.866%. Moreover, these numerical experiments show that the novel rational approximation is approximately two times faster than the exact solution given by the Wright omega function.Web of Science81art. no. 2
Coherent Photoproduction of Eta-Mesons on Spin-Zero Nuclei in a Relativistic, Non-local Model
The coherent photoproduction of -mesons on spin-zero nuclei is studied
in a relativistic, non-local model, which we have previously applied to the
coherent photoproduction of pions. We find that different off-shell
extrapolations of the elementary production operator lead to large effects in
the cross section. We also show that the almost complete suppression of the
N(1535) seen in earlier studies on this reaction is a result of the local or
factorization approximation used in these works. Non-local effects can lead to
a considerable contribution from this resonance. The relative size of the
N(1535) contribution depends on the structure of the nucleus under
consideration. We give an estimate for the contribution of the N(1520)
resonance and discuss the effect of an -nucleus optical potentialComment: 29 pages, 14 figures; slight changes in presentation, extended
discussion, one new figur
The ECHELON Trail: An Illegal Vision
This article tells the story behind the uncovering of the US operated global telecommunications interceptions system now known as ECHELON. It begins with the use of fieldwork techniques in the early 1970's exploring the configuration of Britain's Post Office Towers – these were ostensibly the microwave links through which Britain's long distance telephone calls were made. This modelling process revealed a system within the system of microwave towers linked to the American Base of Menwith Hill in the North York Moors. All the key researchers were then promptly arrested, a raid by Special Branch on the author's university at Lancaster ensued and later a show trail for the other main researchers, most notably Duncan Campbell. Eventually in 1988, Duncan wrote up the ECHELON story, which for its time was an incredible piece of detective work using materials lifted from waste bins by the women activists campaigning around the Menwith Hill Base. Little notice was taken until 1997 when an obscure book by Nicky Hager, Secret Power explained the role and function of ECHELON in more depth. The author represented these findings in a policy report to the European Parliament on the technology of political control that led to a process of political debate and disagreement of the ethics of such a system which continues even today
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