Erratum: “Friction factor directly from transitional roughness in a turbulent pipe flow” [ASME Trans. J. Fluid Eng., 2007, 129, pp. 1255–1267]

Afzal, Noor

doi:10.1115/1.4004961

Introduction

1
Page: 1258: In friction factor relations 34, 35, 36, and 37, replace $δ$ by $D$ in first location, to read as
$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{h}{3.7 D} \exp (- j \frac{5.66}{Re \sqrt{λ}} \frac{δ}{h})]$
34
$\frac{1}{\sqrt{λ}} = - 1.93 \log_{10} [\frac{1.90}{Re \sqrt{λ}} + \frac{h}{3.7 D} \exp (- j \frac{5.66}{Re \sqrt{λ}} \frac{δ}{h})]$
35
$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{5.74}{{Re}^{0.9}} + \frac{h}{3.7 D} \exp (- j \frac{12.91}{{Re}^{0.9}} \frac{δ}{h})]$
36
$\frac{1}{\sqrt{λ}} = - 1.932 \log_{10} [\frac{4.22}{{Re}^{0.9}} + \frac{h}{3.7 D} \exp (- j \frac{9.50}{{Re}^{0.9}} \frac{δ}{h})]$
37
2
Page 1259: In Table 1, replace $δ$ by $D$ in the second column, and its corresponding term in the third column. Also in the third column of Eqs. (3a) and (3b), the numerical values $0.754$ and $1.724$ are replaced by $0.88$ and $2.02$ ⁠, respectively. The corrected Table 1 is given below.

Table 1

Roughness scale and friction factors in fully rough and transitional rough pipes

Scale	Friction factor for fully rough pipes	Friction factor for transitional rough pipes implicit and approximate explicit expressions; $(j = 11)$ ¹	Eq.
$R_{q}$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} (\frac{R_{q}}{0.7 D})$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{R_{q}}{0.7 D} \exp (- j \frac{1.062}{Re \sqrt{λ}} \frac{δ}{R_{q}})]$	(1a)
$h_{s} = 5.333 R_{q}$		$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{5.74}{{Re}^{0.9}} + \frac{R_{q}}{0.7 D} \exp (- j \frac{2.58}{{Re}^{0.9}} \frac{δ}{R_{q}})]$	(1b)
$R_{Z}$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} (\frac{R_{Z}}{3 D})$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{R_{Z}}{3 D} \exp (- j \frac{4.55}{Re \sqrt{λ}} \frac{δ}{R_{Z}})]$	(2a)
$h_{s} = 1.244 R_{Z}$		$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{5.74}{{Re}^{0.9}} + \frac{R_{Z}}{3 D} \exp (- j \frac{10.41}{{Re}^{0.9}} \frac{δ}{R_{Z}})]$	(2b)
$R_{a}$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} (\frac{R_{a}}{0.57 D})$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{R_{a}}{0.57 D} \exp (- j \frac{0.88}{Re \sqrt{λ}} \frac{δ}{R_{a}})]$	(3a)
$h_{s} = 6.45 R_{a}$		$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{5.74}{{Re}^{0.9}} + \frac{R_{a}}{0.57 D} \exp (- j \frac{2.02}{{Re}^{0.9}} \frac{δ}{R_{a}})]$	(3b)
$R_{q} / H$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} (\frac{R_{q} / H}{0.5 D})$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{R_{q} / H}{0.5 D} \exp (- j \frac{0.754}{Re \sqrt{λ}} \frac{δ}{R_{q} / H})]$	(4a)
$h_{s} = 7.71 R_{q} / H$		$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{5.74}{{Re}^{0.9}} + \frac{R_{q} / H}{0.5 D} \exp (- j \frac{1.724}{{Re}^{0.9}} \frac{δ}{R_{q} / H})]$	(4b)
$h$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} (\frac{h}{3.7 D})$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{h}{3.7 D} \exp (- j \frac{5.66}{Re \sqrt{λ}} \frac{δ}{h})]$	(5a)
		$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{5.74}{{Re}^{0.9}} + \frac{h}{3.7 D} \exp (- j \frac{12.91}{{Re}^{0.9}} \frac{δ}{h})]$	(5b)
$h$	$\frac{1}{\sqrt{λ}} = - 1.93 \log_{10} (\frac{h}{3.7 D})$	$\frac{1}{\sqrt{λ}} = - 1.93 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{h}{3.7 D} \exp (- j \frac{5.66}{Re \sqrt{λ}} \frac{δ}{h})]$	(6a)
		$\frac{1}{\sqrt{λ}} = - 1.93 \log_{10} [\frac{4.22}{{Re}^{0.9}} + \frac{h}{3.7 D} \exp (- j \frac{9.50}{{Re}^{0.9}} \frac{δ}{h})]$	(6b)

Scale	Friction factor for fully rough pipes	Friction factor for transitional rough pipes implicit and approximate explicit expressions; $(j = 11)$ ¹	Eq.
$R_{q}$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} (\frac{R_{q}}{0.7 D})$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{R_{q}}{0.7 D} \exp (- j \frac{1.062}{Re \sqrt{λ}} \frac{δ}{R_{q}})]$	(1a)
$h_{s} = 5.333 R_{q}$		$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{5.74}{{Re}^{0.9}} + \frac{R_{q}}{0.7 D} \exp (- j \frac{2.58}{{Re}^{0.9}} \frac{δ}{R_{q}})]$	(1b)
$R_{Z}$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} (\frac{R_{Z}}{3 D})$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{R_{Z}}{3 D} \exp (- j \frac{4.55}{Re \sqrt{λ}} \frac{δ}{R_{Z}})]$	(2a)
$h_{s} = 1.244 R_{Z}$		$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{5.74}{{Re}^{0.9}} + \frac{R_{Z}}{3 D} \exp (- j \frac{10.41}{{Re}^{0.9}} \frac{δ}{R_{Z}})]$	(2b)
$R_{a}$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} (\frac{R_{a}}{0.57 D})$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{R_{a}}{0.57 D} \exp (- j \frac{0.88}{Re \sqrt{λ}} \frac{δ}{R_{a}})]$	(3a)
$h_{s} = 6.45 R_{a}$		$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{5.74}{{Re}^{0.9}} + \frac{R_{a}}{0.57 D} \exp (- j \frac{2.02}{{Re}^{0.9}} \frac{δ}{R_{a}})]$	(3b)
$R_{q} / H$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} (\frac{R_{q} / H}{0.5 D})$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{R_{q} / H}{0.5 D} \exp (- j \frac{0.754}{Re \sqrt{λ}} \frac{δ}{R_{q} / H})]$	(4a)
$h_{s} = 7.71 R_{q} / H$		$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{5.74}{{Re}^{0.9}} + \frac{R_{q} / H}{0.5 D} \exp (- j \frac{1.724}{{Re}^{0.9}} \frac{δ}{R_{q} / H})]$	(4b)
$h$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} (\frac{h}{3.7 D})$	$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{h}{3.7 D} \exp (- j \frac{5.66}{Re \sqrt{λ}} \frac{δ}{h})]$	(5a)
		$\frac{1}{\sqrt{λ}} = - 2 \log_{10} [\frac{5.74}{{Re}^{0.9}} + \frac{h}{3.7 D} \exp (- j \frac{12.91}{{Re}^{0.9}} \frac{δ}{h})]$	(5b)
$h$	$\frac{1}{\sqrt{λ}} = - 1.93 \log_{10} (\frac{h}{3.7 D})$	$\frac{1}{\sqrt{λ}} = - 1.93 \log_{10} [\frac{2.51}{Re \sqrt{λ}} + \frac{h}{3.7 D} \exp (- j \frac{5.66}{Re \sqrt{λ}} \frac{δ}{h})]$	(6a)
		$\frac{1}{\sqrt{λ}} = - 1.93 \log_{10} [\frac{4.22}{{Re}^{0.9}} + \frac{h}{3.7 D} \exp (- j \frac{9.50}{{Re}^{0.9}} \frac{δ}{h})]$	(6b)

Note: $δ = a = D / 2$ = pipe radius or semi-depth of channel.

$h$ = Equivalent sand grain roughness.

$R_{q}$ = Root mean square (rms) roughness, $R_{Z}$ = Mean peak to valley heights roughness.

$R_{a}$ = Arithmetic mean roughness, $R_{q} / H$ = Height-Texture (HT) roughness.

a

Explicit approximate friction factor Eqs. (1b)–(5b) with $A = 2$ based on approximate smooth pipe Eq. 38), and approximate explicit friction factor Eq. (6b) with $A = 1.93$ based on Eq. (39).

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Erratum: “Friction factor directly from transitional roughness in a turbulent pipe flow” [ASME Trans. J. Fluid Eng., 2007, 129, pp. 1255–1267]

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Erratum: “Friction factor directly from transitional roughness in a turbulent pipe flow” [ASME Trans. J. Fluid Eng., 2007, 129, pp. 1255–1267]

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