A Generalized Pipeline Design Correlation For Pseudoplastic Fluids
Authors: Desouky Saad El-Din M. , El-Emam Nour A. 
Published: March 2010

Abstract
An equation relating the pressure loss within a pipeline to he flow rate for all pseudoplastic fluids under turbulent conditions was developed. The Gates four-point method was modified to convert the basic shear data of pseudoplastic fluids to flow shear data. The equations proposed were programmed to stimulate the pipeline design calculations under turbulent conditions.
To assess the validity of the present analysis a comparison was made between the friction factors calculated from the proposed equation and published experimental data. The field measurements obtained from Mobil and Hargarian Agyo pipelines were reused to determine the accuracy of the program calculations.

Introduction
The precision of the pipeline design calculation depends upon the accuracy of the correlation selected to determine the pressure loss. In view of several correlations developed for calculating pressure loss in pipelines, there are two groups empirical and semi-theoretical. Shaver and Merill(1), Eissenberg and Bogue(2) Well(3) and Boque (4) measured the time mean velocity and/or the friction factors of different pseudoplastic fluids. The measured data were then statistically analyzed to derive the required empirical correlations. As for the semi-theoretical group, the researchers derived different forms for velocity distribution and/or friction factor equations, and then used experimental data to determine the constants in the derived equations. Different theoretical equations were developed by Metzner and Reed(5). Dodge and Metzner(6), Bogue and Metzner(7), Zandi and Rust (8), Hall (9) and Murthy and Zandi(10).
The correlations proposed by both groups were only limited to one type of pseudoplastic fluids(11–15). The rheological characteristics of this type o fluids can be described by Qstwald's rheological model(16).This rheological model is one of the twenty known rheological models of pseudoplastic fluids given in Table 1. Thus, the correlations developed by previous investigators cannot be used to predict the pressure loss in pipelines for all pseudoplastic fluids. Therefore, the present analysis was carried out to develop a general equation for all pseudoplastic fluids. The rheological characteristics of all pseudoplastic fluids and be expressed In term s of the apparent viscosity (µapp) as follows(4).
Equation (Available In Full Paper)
It is evident that through the use of the use of the term (µapp) it is possible to obtain a general rheological model for all pseudoplastic fluids.
Since the application of the developed equation requires the determination of Metzner and Reed parameters (n and k) a modified numerical integration method was proposed to convert the basic shear data (Equation Available In Full Paper) to flow shear date (Equation Available In Full Paper). Finally, a computer program was developed to be used in the pipeline design calculations.

Theoretical Analysis
An equation for designing a pipeline handling any type of pseudoplastic fluids under turbulent conditions was derived.
The derivation consisted of three major steps:The velocity distribution equation was derived from the momentum and continuity equations(17)The friction factor equation was obtained from integrating the velocity distribution equation over the cross-sectional area of the pipeline10