In this chapter, we continue the study of kinematics by considering in more detail the motion of fluid parcels, by deriving expressions for the areal, volumetric, and mass flow rates across lines and surfaces drawn in a fluid, and by developing numerical methods for evaluating kinematic variables of interest in terms of derivatives and integrals of the velocity field. 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.