Describes the time rate of change of a physical quantity of a material element subjected to a velocity field
Link between [[Eulerian Velocity Field|Eulerian]] and [[Lagrangian Velocity Field|Lagrangian]] descriptions of flow fields
Captures changes in momentum of the fluid volume in the flow field due to space and time
A flow can be steady, yet a fluid volume can steadily accelerate over time.
$
\frac{D}{Dt}=\underbrace{\frac{\partial}{\partial t}}_\text{time}+\underbrace{U_x\frac{\partial}{\partial x}+U_y\frac{\partial}{\partial y}+U_z\frac{\partial}{\partial z}}_\text{space}
$
$
\frac{D}{Dt}=\frac{\partial}{\partial t}+\boldsymbol{U}\cdot\nabla
$