Fluid Motion: More on Kinematics

Abstract

We continue the study of kinematics by considering, in more detail, the behavior of fluid parcels, by deriving expressions for the volumetric and mass flow rate across surfaces drawn in a fluid, and by developing numerical methods for evaluating kinematical variables defined in terms of derivatives or integrals of the velocity. Conservation of mass required by thermodynamics, and physical conditions imposed at boundaries introduce mathematical constraints that motivate the description of a flow in terms of ancillary functions that expedite analysis and numerical computation.