Pipe Sizing

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.

For laminar flow (Re < 2,100), the friction factor is a function of Reynolds number only.

In turbulent flow (Re > 4,000), f depends upon Reynolds number and pipe roughness.

Hydraulically smooth pipes. In this case, the friction factor is solely a function of 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.

Commercial pipe. In this case, 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. Hydraulically smooth pipes. Using Equation (1) and the friction factor correlation for smooth pipe, Equation (8) is found.

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

Discharge

To determine discharge, pressure drop and diameter must be known. Hydraulically smooth pipes. Equations (1) and (3) allow us to find an expression for the discharge of a smooth pipe.

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

Pipe Diameter

Rearranging Equation (1) to yield an expression for pipe diameter gives Equation (13).

Smooth pipes. Substituting Equation (5) for f yields a correlation for pipe diameter.

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

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.

Case 1: Extremely smooth pipe. Gu = 0.

Case 2: Extremely rough pipe. Gu = 10 ⁶

Here, we see that even for very rough pipe (ε/ D = 0.01, Re = 10 ⁸), the diameter estimate will be
only 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.