Newtonian and Non-Newtonian Fluids: Velocity Profiles, Viscosity Data, and Laminar Flow Friction Factor Equations for Flow in a Circular Duct

Abstract

Newtonian fluid flow in a duct has been studied extensively, and velocity profiles for both laminar and turbulent flows can be found in countless references. Non-Newtonian fluids have also been studied extensively, however, but are not given the same attention in the Mechanical Engineering curriculum. Because of a perceived need for the study of such fluids, data were collected and analyzed for various common non-Newtonian fluids in order to make the topic more compelling for study. The viscosity and apparent viscosity of non-Newtonian fluids are both defined in this paper. A comparison is made between these fluids and Newtonian fluids. Velocity profiles for Newtonian and non-Newtonian fluid flow in a circular duct are described and sketched. Included are profiles for dilatant, pseudoplastic and Bingham fluids. Only laminar flow is considered, because the differences for turbulent flow are less distinct. Also included is a procedure for determining the laminar flow friction factor which allows for calculating pressure drop. The laminar flow friction factor in classical non-Newtonian fluid studies is the Fanning friction factor. The equations developed in this study involve the Darcy-Weisbach friction factor which is preferred for Newtonian fluids. Also presented in this paper are viscosity data of Heinz Ketchup, Kroger Honey, Jif Creamy Peanut Butter, and Kraft Mayonnaise. These data were obtained with a TA viscometer. The results of this study will thus provide the student with the following for non-Newtonian fluids: • Viscosity data and how it is measured for several common non-Newtonian fluids; • A knowledge of velocity profiles for laminar flow in a circular duct for both Newtonian and non-Newtonian fluids; • A procedure for determining friction factor and calculating pressure drop for non-Newtonian flow in a duct.