Pipe Sizing

## Friction Factor

Fluid flowing through pipes experiences resistance due to viscosity, turbulence and roughness of the pipe surface. The Darcy-Weisbach Equation (1) is commonly used for the analysis of steady-state, Newtonian-fluid flow inside pipes. It summarizes the relations between frictional head loss, fluid properties, pipe geometry and discharge.

In turbulent flow (Re > 4,000),

*f*depends upon Reynolds number and pipe roughness.**. In this case, the friction factor is solely a function of**

*Hydraulically smooth pipes**Re*. For the determination of friction factor, Von Kármán and Prandtl developed Equation (3).

This correlation must be solved by iterative procedures, but simpler correlations given by Colebrook and Blasius are written as Equations (4) and (5), respectively.

**. In this case,**

*Commercial pipe**f*is governed by both Re and relative roughness, expressed as ε /

*D*. The Colebrook-White’s Equation (6) is used to calculate

*f*.

As this equation requires trial-and-error solution, Altshul has developed Equation (7), a computationally simpler choice.

## Pressure Drop

To determine pressure drop, discharge and diameter must be known.

**. Using Equation (1) and the friction factor correlation for smooth pipe, Equation (8) is found.***Hydraulically smooth pipes***. Using Equation (1) and the friction factor correlation for smooth pipe, Equation (9) is found.**

*Commercial pipes*## Discharge

To determine discharge, pressure drop and diameter must be known.

**. Equations (1) and (3) allow us to find an expression for the discharge of a smooth pipe.***Hydraulically smooth pipes***. Equations (1) and (6) allow us to find an expression for the discharge of a commercial pipe.**

*Commercial pipes*## Pipe Diameter

**. Determining the diameter of a rough pipe requires the use of Gu, the dynamic roughness.**

*Commercial pipes*Manipulating Equation (7) to reflect Gu and substituting into the expression for pipe diameter gives Equation (17), commercial pipe diameter. Several design parameters can be condensed into a constant, named λ.

The range of Gu is: 0 <>6, based on the known ranges of Re and ε/

*D*for all pipe and flow conditions. Substituting these two extreme values of Gu into Equation (15) gives the following extreme cases, which a pipe diameter must fall between.Here, we see that even for very rough pipe (ε/

only about five thirds of that for smooth pipe.

*D*= 0.01, Re = 10^{8}), the diameter estimate will beonly about five thirds of that for smooth pipe.

## Graphical Sizing Method

To avoid lengthy calculations, a graphical method can be used to approximate pipe diameter. Dividing Equation (17) by Equation (18), we get the diameter multiplier, Ψ.

A graphical method using Ψ can help to quickly estimate the degree of roughness the chosen pipe can withstand.

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