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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fanning friction factor ： ウィキペディア英語版 Fanning friction factor The Fanning friction factor, named after John Thomas Fanning (1837–1911), is a dimensionless number used in fluid flow calculations. It is related to the shear stress at the wall as: :$$ \tau = \frac where: *$\backslash tau$ is the shear stress at the wall *$f$ is the Fanning friction factor of the pipe *$v$ is the fluid velocity in the pipe *$\backslash rho$ is the density of the fluid The wall shear stress can, in turn, be related to the pressure loss by multiplying the wall shear stress by the wall area ($2\; \backslash pi\; R\; L$ for a pipe) and dividing by the cross-sectional flow area ($\backslash pi\; R^2$ for a pipe). Thus $f\; =\; \backslash frac\; \backslash frac$ The friction head can be related to the pressure loss due to friction by dividing the pressure loss by the product of the acceleration due to gravity and the density of the fluid. Accordingly, the relationship between the friction head and the Fanning friction factor is: :$$ h_f = \frac where: *$h\_f$ is the friction loss (in head) of the pipe. *$f$ is the Fanning friction factor of the pipe. *$v$ is the fluid velocity in the pipe. *$L$ is the length of pipe. *$g$ is the local acceleration of gravity. *$D$ is the pipe diameter. == Fanning friction factor formula == This friction factor is one-fourth of the Darcy friction factor, so attention must be paid to note which one of these is meant in the "friction factor" chart or equation consulted. Of the two, the Fanning friction factor is the more commonly used by chemical engineers and those following the British convention. The formulae below may be used to obtain the Fanning friction factor for common applications. The friction factor for laminar flow in round tubes is often taken to be: $f=\; \backslash frac$ where Re is the Reynolds number of the flow. For a square channel the value used is: $f\; =\; \backslash frac$ The Darcy friction factor can also be expressed as〔Yunus, Cengel. Heat and Mass Transfer. New York: Mc Graw Hull, 2007.〕 $f\; =\; \backslash frac$ where: * $\backslash tau\_w$ is the shear stress at the wall * $\backslash rho$ is the density of the fluid * $V\_$ is the average fluid velocity For the turbulent flow regime, the relationship between the Fanning friction factor and the Reynolds number is more complex and is governed by the Colebrook equation 〔Colebrook, C.F. and White, C.M. 1937, "Experiments with Fluid friction roughened pipes.", ''Proc. R.Soc.(A)'', 161〕 which is implicit in $f$: :$=\; -4.0\; \backslash log\_\; \backslash left(\backslash frac\}\; +\; \}\; \}\; \}\; \backslash right)\; ,\; \backslash text$ Various explicit approximations of the related Darcy friction factor have been developed for turbulent flow. Stuart W. Churchill〔Churchill, S.W., 1977, "Friction factor equation spans all fluid-flow regimes", ''Chem. Eng.'', 91〕 developed a formula that covers the friction factor for both laminar and turbulent flow. This was originally produced to describe the Moody chart, which plots the Darcy-Weisbach Friction factor against Reynolds number. The Darcy Weisbach Formula $f\_D$ is 4 times the Fanning friction factor $f$ and so a factor of $\backslash frac$ has been applied to produce the formula given below. * Re, Reynolds number (unitless); * ε, roughness of the inner surface of the pipe (dimension of length); * ''D'', inner pipe diameter; :$f\; =\; 2\; \backslash left($ \left( \frac \right) ^ + \left( A+B \right) ^ \right) ^ } :$A\; =\; \backslash left(\; 2.457\; \backslash ln\; \backslash left(\; \backslash left(\; \backslash left(\; \backslash frac\; \backslash right)\; ^\; +\; 0.27\; \backslash frac\; \backslash right)^\; \backslash right)\; \backslash right)\; ^$ :$B\; =\; \backslash left(\; \backslash frac\; \backslash right)\; ^$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fanning friction factor」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.