More on Kinematics

We continue the study of kinematics by considering in more detail the be- havior of fluid parcels, by deriving expressions for the volumetric and mass flow rate across surfaces drawn in a fluid, and by developing numerical meth- ods for evaluating kinematic variables of interest in terms of derivatives and integrals of the velocity. Mass conservation and physical conditions imposed at boundaries introduce mathematical constraints that motivate the description of a flow in terms of ancillary functions that expedite the mathematical analysis and considerably simplify the numerical computation.