Discussion of “Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” by DejanBrkić; and Pavel Praks, Mathematics 2019, 7, 34; doi:10.3390/math7010034

Lotfi Zeghadnia; Bachir Achour; Jean Robert

doi:10.3390/math7030253

Discussion of “Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” by DejanBrkić; and Pavel Praks, Mathematics 2019, 7, 34; doi:10.3390/math7010034

Mathematics ◽

10.3390/math7030253 ◽

2019 ◽

Vol 7 (3) ◽

pp. 253 ◽

Cited By ~ 1

Author(s):

Lotfi Zeghadnia ◽

Bachir Achour ◽

Jean Robert

Keyword(s):

Friction Factor ◽

The Other ◽

Maximum Deviation ◽

Explicit Formulas ◽

Flow Friction ◽

Complex Equation ◽

Other Hand

The Colebrook-White equation is often used for calculation of the friction factor in turbulent regimes; it has succeeded in attracting a great deal of attention from researchers. The Colebrook–White equation is a complex equation where the computation of the friction factor is not direct, and there is a need for trial-error methods or graphical solutions; on the other hand, several researchers have attempted to alter the Colebrook-White equation by explicit formulas with the hope of achieving zero-percent (0%) maximum deviation, among them Dejan Brkić and Pavel Praks. The goal of this paper is to discuss the results proposed by the authors in their paper:” Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” and to propose more accurate formulas.

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solutions of the CW equation for flow friction

10.31219/osf.io/6cnua ◽

2017 ◽

Author(s):

Dejan Brkić

Keyword(s):

Fluid Flow ◽

Friction Factor ◽

Explicit Form ◽

Iterative Procedure ◽

Lambert W Function ◽

Explicit Formulas ◽

Flow Friction ◽

Transcendental Functions ◽

Flow Through

The empirical Colebrook–White (CW) equation belongs to the group of transcendental functions. The CW function is used for the determination of hydraulic resistances associated with fluid flow through pipes, flow of rivers, etc. Since the CW equation is implicit in fluid flow friction factor, it has to be approximately solved using iterative procedure or using some of the approximate explicit formulas developed by many authors. Alternate mathematical equivalents to the original expression of the CW equation, but now in the explicit form developed using the Lambert W-function, are shown (with related solutions). The W-function is also transcendental, but it is used more general compared with the CW function. Hence, the solution to the W-function developed by mathematicians can be used effectively for the CW function which is of interest only for hydraulics.

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An Explicit Approximation of Colebrook's Equation for Fluid Flow Friction Factor

10.31219/osf.io/tjbxk ◽

2017 ◽

Author(s):

D. Brkić

Keyword(s):

Fluid Flow ◽

Friction Factor ◽

Iterative Procedure ◽

Lambert W Function ◽

Explicit Formulas ◽

Flow Friction

The Colebrook equation for determination of hydraulic resistances is implicit in fluid flow friction factor and hence it has to be approximately solved using iterative procedure or using some of the approximate explicit formulas which were developed by many authors. Here will be shown one approximation of the Colebrook equation based on Lambert W-function.

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A study of cometary eruptions through OH radio-lines

International Astronomical Union Colloquium ◽

10.1017/s025292110003150x ◽

1999 ◽

Vol 173 ◽

pp. 249-254

Author(s):

A.M. Silva ◽

R.D. Miró

Keyword(s):

Short Duration ◽

Growth Curves ◽

The Other ◽

Initial Mass ◽

Radio Lines ◽

Other Hand ◽

Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

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Closing the GAP—A 5Å Scanning Microscope

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100061938 ◽

1969 ◽

Vol 27 ◽

pp. 6-7

Author(s):

A. V. Crewe

Keyword(s):

Normal Form ◽

The Other ◽

Resolving Power ◽

Scanning Microscope ◽

Conventional Microscope ◽

Other Hand ◽

Closing The Gap ◽

Thermal Sources ◽

Better Than ◽

Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

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Life Beyond 1MeV

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s1431927600000118 ◽

1980 ◽

Vol 38 ◽

pp. 30-33

Author(s):

K.H. Westmacott

Keyword(s):

Electron Microscopy ◽

Past Experience ◽

The Other ◽

Good Case ◽

Other Hand ◽

The U.S

Life beyond 1MeV – like life after 40 – is not too different unless one takes advantage of past experience and is receptive to new opportunities. At first glance, the returns on performing electron microscopy at voltages greater than 1MeV diminish rather rapidly as the curves which describe the well-known advantages of HVEM often tend towards saturation. However, in a country with a significant HVEM capability, a good case can be made for investing in instruments with a range of maximum accelerating voltages. In this regard, the 1.5MeV KRATOS HVEM being installed in Berkeley will complement the other 650KeV, 1MeV, and 1.2MeV instruments currently operating in the U.S. One other consideration suggests that 1.5MeV is an optimum voltage machine – Its additional advantages may be purchased for not much more than a 1MeV instrument. On the other hand, the 3MeV HVEM's which seem to be operated at 2MeV maximum, are much more expensive.

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Can the Academic Self-Concept be Positive and Realistic?

Zeitschrift für Pädagogische Psychologie ◽

10.1024/1010-0652.19.3.132 ◽

2005 ◽

Vol 19 (3) ◽

pp. 129-132 ◽

Cited By ~ 6

Author(s):

Reimer Kornmann

Keyword(s):

Academic Performance ◽

Opposite Effect ◽

Self Esteem ◽

Point Of View ◽

The Other ◽

Self Concept ◽

High Ability ◽

Self Image ◽

Other Hand

Summary: My comment is basically restricted to the situation in which less-able students find themselves and refers only to literature in German. From this point of view I am basically able to confirm Marsh's results. It must, however, be said that with less-able pupils the opposite effect can be found: Levels of self-esteem in these pupils are raised, at least temporarily, by separate instruction, academic performance however drops; combined instruction, on the other hand, leads to improved academic performance, while levels of self-esteem drop. Apparently, the positive self-image of less-able pupils who receive separate instruction does not bring about the potential enhancement of academic performance one might expect from high-ability pupils receiving separate instruction. To resolve the dilemma, it is proposed that individual progress in learning be accentuated, and that comparisons with others be dispensed with. This fosters a self-image that can in equal measure be realistic and optimistic.

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Stories and the Self

Journal of Media Psychology Theories Methods and Applications ◽

10.1027/1864-1105/a000255 ◽

2020 ◽

Vol 32 (2) ◽

pp. 47-58 ◽

Cited By ~ 1

Author(s):

Stefan Krause ◽

Markus Appel

Keyword(s):

Meta Analysis ◽

The Self ◽

The Other ◽

Lower Degree ◽

Contrast Effects ◽

Self Perception ◽

Self Perceptions ◽

Other Hand ◽

The One ◽

Implicit And Explicit

Abstract. Two experiments examined the influence of stories on recipients’ self-perceptions. Extending prior theory and research, our focus was on assimilation effects (i.e., changes in self-perception in line with a protagonist’s traits) as well as on contrast effects (i.e., changes in self-perception in contrast to a protagonist’s traits). In Experiment 1 ( N = 113), implicit and explicit conscientiousness were assessed after participants read a story about either a diligent or a negligent student. Moderation analyses showed that highly transported participants and participants with lower counterarguing scores assimilate the depicted traits of a story protagonist, as indicated by explicit, self-reported conscientiousness ratings. Participants, who were more critical toward a story (i.e., higher counterarguing) and with a lower degree of transportation, showed contrast effects. In Experiment 2 ( N = 103), we manipulated transportation and counterarguing, but we could not identify an effect on participants’ self-ascribed level of conscientiousness. A mini meta-analysis across both experiments revealed significant positive overall associations between transportation and counterarguing on the one hand and story-consistent self-reported conscientiousness on the other hand.

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Don’t Put Me in This Group

Social Psychology ◽

10.1027/1864-9335/a000363 ◽

2019 ◽

Vol 50 (2) ◽

pp. 80-93

Author(s):

Jort de Vreeze ◽

Christina Matschke

Keyword(s):

Positive Emotions ◽

Negative Emotions ◽

Negative Information ◽

The Self ◽

The Other ◽

Other Hand ◽

Group Memberships

Abstract. Not all group memberships are self-chosen. The current research examines whether assignments to non-preferred groups influence our relationship with the group and our preference for information about the ingroup. It was expected and found that, when people are assigned to non-preferred groups, they perceive the group as different to the self, experience negative emotions about the assignment and in turn disidentify with the group. On the other hand, when people are assigned to preferred groups, they perceive the group as similar to the self, experience positive emotions about the assignment and in turn identify with the group. Finally, disidentification increases a preference for negative information about the ingroup.

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