Fluid kinematics

Fluid kinematics is a field of physics and mechanics concerned with the movement of fluids.^[1] Fluids tend to flow easily, which causes a net motion of molecules from one point in space to another point as a function of time. These fluids may be liquids or may be materials with fluid properties, including crowds of people^[2] or volumes of grains.^[3]

Using the continuum hypothesis, fluids are classified into fluid particles, which are composed of numerous fluid molecules. These particles interact with one another and with the surroundings they are in. Using a Eulerian model (the continuum hypothesis), fluid motion can be described in terms of acceleration or velocity.

Unsteady and convective effects

The composition of the material contains two types of terms: those involving the time derivative and those involving spatial derivatives. The time derivative portion is denoted as the local derivative, and represents the effects of unsteady flow. The local derivative occurs during unsteady flow, and becomes zero for steady flow.

The portion of the material derivative represented by the spatial derivatives is called the convective derivative. It accounts for the variation in fluid property, be it velocity or temperature for example, due to the motion of a fluid particle in space where its values are different.

Acceleration field

The acceleration of a particle is the time rate of change of its velocity. Using an Eulerian description for velocity, the velocity field V = V(x,y,z,t), and deriving it with respect to time, we obtain the acceleration field.

References