Applications in Pipeline Flow

A number of kinds of emulsions, foams and suspensions may be made to flow in tubes or pipes, at scales ranging from the laboratory (e.g. capillary viscometers. Section 6.3.1) to full-scale industry (e.g. transportation pipelines. Sections 10.2 and 11.3.4). The pressure drop and pumping requirements are functions of the type of flow and of the rheological properties of the dispersion. If the flow rate in a pipeline falls below the critical deposit velocity (also termed the stationary deposit velocity), then particles or emulsion droplets will either sediment or cream to form a layer on the bottom or top wall, respectively, of the pipe. Some correlations that have been developed for the prediction of critical deposit velocity are discussed by Nasr-El-Din [103] and Shook et /. [104]. 

For Newtonian fluids flowing in smooth pipes, the friction losses can be estimated for laminar flow (l e 2100) using the Fanning friction factor,/. The Reynolds number. Re, is given by 

For turbulent flow of Newtonian fluids in smooth pipes, two common correlations are those of Blasius [105] for 3000 Re 100 000  

The shear rate at the wall for a power law fluid in a smooth pipe is given by 

A number of kinds of emulsions, foams, and suspensions may be made to flow in tubes or pipes, at scales ranging from the laboratory (e.g., capillary viscometers, Section 6.2.1) to full-scale industry (e.g., transportation pipelines, Sections 10.2 and 

Equations for a number of non-Newtonian fluid types are available in the literature [213,359]. They tend to be somewhat unwieldy and require a knowledge of the fluid rheology. For power-law fluids in smooth pipes, the friction factor can be estimated by using a modified Reynolds number in Eq. (6.57). The Metzner-Reed modified Reynolds number, Re, is given by  

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