Fluid Kinematics

Fluid kinematics describes the motion of fluids, liquids and gases, without reference to the forces or energy that cause that motion.  It is concerned strictly with how fluid particles move in space and time, providing a geometric and mathematical description of flow.  In this context, a fluid particle is treated as a small, continuously deformable element of the fluid, and its motion is analyzed using fields such as velocity and acceleration that vary with position and time.  These fields form the basis for describing flow patterns in a rigorous and continuous manner.

A central aspect of fluid kinematics is the distinction between different descriptions of motion, most notably the Eulerian and Lagrangian.  In Eulerian, properties like velocity are expressed as functions of spatial coordinates and time, focusing on specific points in the flow field.  In Lagrangian, individual fluid particles are tracked as they move through space.   Fluid kinematics also defines key concepts such as streamlines, pathlines, and streaklines, which represent different ways of visualizing fluid motion, as well as deformation measures like strain rates and rotation, which quantify how fluid elements change shape and orientation during flow.

Fluid kinematics does not address why the motion occurs, that is the domain of fluid dynamics, where forces, pressure, viscosity, and energy interactions are analyzed.  Instead, fluid kinematics provides the foundational language and mathematical structure needed to describe motion itself.