**Turbulent fluid flows in pipes and open channels play an important role in hydraulics, chemical engineering, transportation of hydrocarbon, air duct design, etc.**

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*h*

*f*) due to friction undergone by a fluid motion in a pipe is usually calculated through the Darcy-Weisbach relation.

_{loss}= f (L/D) u

^{2}/2g

^{2}/2g is known as "Velocity Head" where

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^{2}, where, τ is the shear stress, ρ is the density of the liquid that flows in the pipe and ū the mean velocity of the flow.

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*R*≤ 2100), the friction factor is linearly dependent on

*R*, and calculated from the well-known Hagen-Poiseuille equation:

*64 /R*

*R*, the Reynolds number, is defined as

*ū*

*D*/ ν where ν is the kinematic viscosity = m/r, the ratio of viscosity and density.

^{7}, due to the low viscosity and the relative high density of natural gas at typical operating pressures (100-180 bar). For normal liquid lines, the Reynolds number is normally in the range of 5x10

^{4}to 1x10

^{6}

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*R*≥ 4000), the friction factor, f depends upon the Reynolds number (

*R*) and on the relative roughness of the pipe,

*e*/

*D*, where, e

*is the average roughness height of the pipe*

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*k*is very small compared to the pipe diameter D i.e.

*e*/

*D*→0, and f depends only on

*R*.

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*k*/

*D*is of a significant value, at low

*R*, the flow can be considered as in smooth regime (there is no effect of roughness). In a smooth pipe flow, the viscous sub layer completely submerges the effect of

*e*

*R*and is independent of the effect of e

*on the flow.*

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*R*increases, the flow becomes transitionally rough, called as transition regime in which the friction factor rises above the smooth value and is a function of both

*k*and

*R.*

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*k*/

*D*and is independent of

*R*. The following form of the equation is first derived by Von Karman (Schlichting, 1979) and later supported by Nikuradse’s experiments

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*R*and

*e*/

*D*, the equation universally adopted is due to Colebrook and White (1937) proposed the following equation

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*e*→ 0, this reduces to equation for

**smooth pipes**and as R→∞, it forms equation for

**rough pipes**.

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*k*on the flow. In this case, the friction factor f is a function of

*R*and is independent of the effect of

*k*on the flow.

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*k*/

*D*and is independent of

*R*.

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^{6}, and it is very inaccurate around Re = 10

^{4}

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*e*/

*D*, COLEBROOK equation has become the

**universally**

**accepted standard**for calculating the friction factors for rough pipes.

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^{1}.

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^{2}.

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*Idelchik, I.E., M.O. Steinberg, G.R. Malyavskaya, and O.G. Martynenko.*

*1994. Handbook of hydraulic resistance, 3rd ed. CRC Press*

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**“Energy Efficient Pipe Sizing and Piping Optimization”**– A book by the same author. Visit www.ColebrookEquation.com for more details