Explicit determinations of the Colebrook equation
for the flow friction factor by statistical analysis.
To evaluate flow resistance in turbulent flow through rough or smooth pipes, the empirical Colebrook equation is in common use :
In the Colebrook equation, [lambda] represents Darcy flow friction factor, Re Reynolds number, and [epsilon]/D relative roughness of inner pipe surfaces (all three quantities are dimensionless).
These quantities are related by the Colebrook equation
The relative roughness was determined iteratively by fitting the experimentally determined friction factors to the Colebrook equation, using the least squares method.
In some cases, a solution of the Colebrook Equation
The relative roughness was determined iteratively by fitting the experimentally determined friction factors to the Colebrook equation using the least squares method: this approach is described in more detail in Idem et al.
Hence if the determination of relative roughness by means of a solution to the Colebrook equation is based on measurements of pressure loss in a developing flow, it is evident that calculated values of [epsilon]/[D.sub.h] will be erroneous, since the Colebrook equation applies only to fully developed flow.
This article presents an automated quick and simple equal friction solution to calculating duct diameter and pressure loss, using an iterative solution to the Colebrook equation. An initial duct diameter is calculated for duct segment airflows at a [DELTA]p/100 ft ([DELTA]p/30 m) to be input by the designer.
The heart of the method presented here is an iterative solution to the Colebrook equation, which draws on that proposed in a previous ASHRAE Journal article.
The Colebrook equation
was used to solve iteratively for the friction factor by means of a standard root-solving procedure.
As proposed by Colebrook (1939), these quantities are related by the Colebrook equation