The potential antifungal effects of Thymus vulgaris L., Thymus tosevii L., Mentha spicata L., and Mentha piperita L. (Labiatae) essential oils and their components against 17 micromycetal food poisoning, plant, animal and human pathogens are presented. The essential oils were obtained by hydrodestillation of dried plant material. Their composition was determined by GC-MS. Identification of individual constituents was made by comparison with analytical standards, and by computer matching mass spectral data with those of the Wiley/NBS Library of Mass Spectra. MIC’s and MFC’s of the oils and their components were determined by dilution assays. Thymol (48.9%) and p-cymene (19.0%) were the main components of T. vulgaris, while carvacrol (12.8%), α-terpinyl acetate (12.3%), cis-myrtanol (11.2%) and thymol (10.4%) were dominant in T. tosevii. Both Thymus species showed very strong antifungal activities. In M. piperita oil menthol (37.4%), menthyl acetate (17.4%) and menthone (12.7%) were the main components, whereas those of M. spicata oil were carvone (69.5%) and menthone (21.9%). Mentha sp. showed strong antifungal activities, however lower than Thymus sp. The commercial fungicide, bifonazole, used as a control, had much lower antifungal activity than the oils and components investigated. It is concluded that essential oils of Thymus and Mentha species possess great antifungal potential and could be used as natural preservatives and fungicides.

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Review of explicit approximations to the Colebrook relation for flow frictionDejan Brkić
To cite this version:Dejan Brkić. (2010) and Vatankhah and Kouchakzadeh (2008, 2009). They are very accurate. Therefore, I have added these two approximations...3. I agree with you that problem of range of applicability of certain approximation is very important. This problem is very complex. So to avoid any further speculations I have added diagram of accuracy of each approximation over the entire practical range of Reynolds number and relative roughness. According to these diagrams, one can choose will he/she use in certain case this particular approximation or not.4. Detailed discussion with results is now presented in more appropriate way.
Conclusion is now rearranged after your suggestions.

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.

Hardy Cross method is common for calculation of loops-like gas distribution networks with known node gas consumptions. This method is given in two forms: original Hardy Cross methodsuccessive substitution methods and improved-simultaneous solution method (Newton-Raphson group of methods). Problem of gas flow in looped network is nonlinear problem; i.e. relation between flow and pressure drop is not linear while relation between electric current and voltage is.
Improvement of original method is done by introduction of influence of adjacent contours inYacobian matrix which is used in calculation and which is in original method strictly diagonal with all zeros in non-diagonal terms. In that way necessary number of iteration in calculations is decreased.If during the design of gas network with loops is anticipated that some of conduits are crossing each other without connection, this sort of network became, so there has to be introduced corrections of third or higher order. 2. Note your eq (10) and (16) Answer: English expression is now probably improved and the text is shorter for about 1000 words, one table is deleted, and one figure is deleted. Shorter abstract is included. Readers will have access to online base e.g. science direct, so there will be available version in colour.
* Detailed Response to ReviewersEditor:1. The length of the manuscript is over the required 10 printing pages by Applied Energy.Authors shall shorten to make it much concise. Suggestion accepted in full: Text is shorter for about 1000 words, one table is deleted, and one figure is deleted. Many equations are deleted, only necessary equations are now in the text. References are checked, and only essential references are still in the text. In the text is something above 5000 words including title, abstract, references… 2. Authors shall discuss how to apply the results in real applications to give readers who might be interesting to use the results from this paper.

This paper presents evolutionary optimization of explicit approximations of the empirical Colebrook's equation that is used for the calculation of the turbulent friction factor (λ), i.e., for the calculation of turbulent hydraulic resistance in hydraulically smooth and rough pipes including the transient zone between them. The empirical Colebrook's equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of the inner pipe surface (ε/D). It is implicit in the unknown friction factor (λ). The implicit Colebrook's equation cannot be rearranged to derive the friction factor (λ) directly, and therefore, it can be solved only iteratively [λ = f(λ, R, ε/D)] or using its explicit approximations [λ ≈ f(R, ε/D)], which introduce certain error compared with the iterative solution. The optimization of explicit approximations of Colebrook's equation is performed with the aim to improve their accuracy, and the proposed optimization strategy is demonstrated on a large number of explicit approximations published up to date where numerical values of the parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After that improvement, the computational burden stays unchanged while the accuracy of approximations increases in some of the cases very significantly.

The eighty years old empirical Colebrook function widely used as an informal standard for hydraulic resistance relates implicitly the unknown flow friction factor , with the known Reynolds number and the known relative roughness of a pipe inner surface ;. It is based on logarithmic law in the form that captures the unknown flow friction factor in a way from which it cannot be extracted analytically. As an alternative to the explicit approximations or to the iterative procedures that require at least a few evaluations of computationally expensive logarithmic function or non-integer powers, this paper offers an accurate and computationally cheap iterative algorithm based on Padé polynomials with only one -call in total for the whole procedure (expensive -calls are substituted with Padé polynomials in each iteration with the exception of the first). The proposed modification is computationally less demanding compared with the standard approaches of engineering practice, but does not influence the accuracy or the number of iterations required to reach the final balanced solution.

Empirical Colebrook equation implicit in unknown flow friction factor (λ) is an accepted standard for calculation of hydraulic resistance in hydraulically smooth and rough pipes. The 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. λ 0 =f(λ 0 , Re, ε/D). The paper presents a problem that requires iterative methods for the solution. In particular, the implicit method used for calculating the friction factor λ 0 is an application of fixedpoint iterations. The type of problem discussed in this "in the classroom paper" is commonly encountered in fluid 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.

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