Momentum Transfer and Fluid Flow

by Garrett Craft

Submitted : Fall 2008

This project is, as a whole, an attempt to concisely formulate mathematical formulae both depicting and collaborating empirical observations of viscous flow of Newtonian liquids through a cylindrical pipe of varying diameter under constant temperature and pressure. Deriving an equation which adequately describes shear and velocity profiles of such systems is based on a momentum-balance approach in the form of the shell method where one sets up the following situation: [Rate of momentum entering system] - [rate of momentum leaving system] + [sum of all forces acting upon system] = 0 and substitutes the relevant expressions describing said momentum flux. Further, said momentum fluxes can be considered as stresses, acting perpendicular to the direction of flow (in the case solved here, along the z-axis).

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