## Introduction

• 1
Page: 1258: In friction factor relations 34, 35, 36, and 37, replace $δ$ by $D$ in first location, to read as
$1λ=-2log10[2.51Reλ+h3.7Dexp(-j5.66Reλδh)]$
34
$1λ=-1.93log10[1.90Reλ+h3.7Dexp(-j5.66Reλδh)]$
35
$1λ=-2log10[5.74Re0.9+h3.7Dexp(-j12.91Re0.9δh)]$
36
$1λ=-1.932log10[4.22Re0.9+h3.7Dexp(-j9.50Re0.9δh)]$
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. $Rq$ $1λ=-2log10(Rq0.7D)$ $1λ=-2log10[2.51Reλ+Rq0.7Dexp(-j1.062Reλ δRq)]$ (1a) $hs=5.333Rq$ $1λ=-2log10[5.74Re0.9+Rq0.7Dexp(-j2.58Re0.9 δRq)]$ (1b) $RZ$ $1λ=-2log10(RZ3D)$ $1λ=-2log10[2.51Reλ+RZ3Dexp(-j4.55Reλ δRZ)]$ (2a) $hs=1.244RZ$ $1λ=-2log10[5.74Re0.9+RZ3Dexp(-j10.41Re0.9 δRZ)]$ (2b) $Ra$ $1λ=-2log10(Ra0.57D)$ $1λ=-2log10[2.51Reλ+Ra0.57Dexp(-j0.88Reλ δRa)]$ (3a) $hs=6.45Ra$ $1λ=-2log10[5.74Re0.9+Ra0.57Dexp(-j2.02Re0.9 δRa)]$ (3b) $Rq/H$ $1λ=-2log10(Rq/H0.5D)$ $1λ=-2log10[2.51Reλ+Rq/H0.5Dexp(-j0.754Reλ δRq/H)]$ (4a) $hs=7.71Rq/H$ $1λ=-2log10[5.74Re0.9+Rq/H0.5Dexp(-j1.724Re0.9 δRq/H)]$ (4b) $h$ $1λ=-2log10(h3.7D)$ $1λ=-2log10[2.51Reλ+h3.7Dexp(-j5.66Reλ δh)]$ (5a) $1λ=-2log10[5.74Re0.9+h3.7Dexp(-j12.91Re0.9 δh)]$ (5b) $h$ $1λ=-1.93log10(h3.7D)$ $1λ=-1.93log10[2.51Reλ+h3.7Dexp(-j5.66Reλ δh)]$ (6a) $1λ=-1.93log10[4.22Re0.9+h3.7Dexp(-j9.50Re0.9 δh)]$ (6b)
 Scale Friction factor for fully rough pipes Friction factor for transitional rough pipes implicit and approximate explicit expressions; $(j=11)$1 Eq. $Rq$ $1λ=-2log10(Rq0.7D)$ $1λ=-2log10[2.51Reλ+Rq0.7Dexp(-j1.062Reλ δRq)]$ (1a) $hs=5.333Rq$ $1λ=-2log10[5.74Re0.9+Rq0.7Dexp(-j2.58Re0.9 δRq)]$ (1b) $RZ$ $1λ=-2log10(RZ3D)$ $1λ=-2log10[2.51Reλ+RZ3Dexp(-j4.55Reλ δRZ)]$ (2a) $hs=1.244RZ$ $1λ=-2log10[5.74Re0.9+RZ3Dexp(-j10.41Re0.9 δRZ)]$ (2b) $Ra$ $1λ=-2log10(Ra0.57D)$ $1λ=-2log10[2.51Reλ+Ra0.57Dexp(-j0.88Reλ δRa)]$ (3a) $hs=6.45Ra$ $1λ=-2log10[5.74Re0.9+Ra0.57Dexp(-j2.02Re0.9 δRa)]$ (3b) $Rq/H$ $1λ=-2log10(Rq/H0.5D)$ $1λ=-2log10[2.51Reλ+Rq/H0.5Dexp(-j0.754Reλ δRq/H)]$ (4a) $hs=7.71Rq/H$ $1λ=-2log10[5.74Re0.9+Rq/H0.5Dexp(-j1.724Re0.9 δRq/H)]$ (4b) $h$ $1λ=-2log10(h3.7D)$ $1λ=-2log10[2.51Reλ+h3.7Dexp(-j5.66Reλ δh)]$ (5a) $1λ=-2log10[5.74Re0.9+h3.7Dexp(-j12.91Re0.9 δh)]$ (5b) $h$ $1λ=-1.93log10(h3.7D)$ $1λ=-1.93log10[2.51Reλ+h3.7Dexp(-j5.66Reλ δh)]$ (6a) $1λ=-1.93log10[4.22Re0.9+h3.7Dexp(-j9.50Re0.9 δh)]$ (6b)

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

$h$ = Equivalent sand grain roughness.

$Rq$ = Root mean square (rms) roughness, $RZ$ = Mean peak to valley heights roughness.

$Ra$ = Arithmetic mean roughness, $Rq/H$ = 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).