Chapter 3 - Flow in Pipes and in Conduits of Non-circular Cross-sections

Abstract

This chapter discusses the various engineering relationships that describe flow in a variety of geometries and particularly focuses on the so-called purely viscous or time-independent type of fluids for which the viscosity model describing the flow curve is already known. Various formulae presented in the chapter relate the frictional pressure drop (Δp) to the volumetric flow rate (Q), and the major application of this relationship is in the mechanical energy balance which is written to calculate the total head loss in a pipe network, which in turn allows the estimation of the required power to be delivered by a pump. The isothermal, steady, and fully developed flow of power-law and Bingham plastic fluids in concentric annulus are analyzed, and appropriate expressions and/or charts that permit the calculation of pressure gradient for a given application are presented. General features of a range of pumps commonly used in industry, particularly the positive-displacement, centrifugal, and screw pumps are briefly described here. Gear pumps, in which one of the gear wheels is driven and the other turns as the teeth engage, are one of the most common forms of the pumps and are extensively used for both high-viscosity Newtonian liquids and non-Newtonian fluids. The most common type of pump used in the chemical industry is the centrifugal pump, whose performance deteriorates rapidly with increasing viscosity of fluids, even with Newtonian fluids. Screw extruders, which are used in the polymer processing and food industries, form the most important class of pumps handling highly viscous non-Newtonian materials and their basic function is to shear the fluid in the channel between the screw and the wall of the barrel.