File:RTT x.png

An illustration, for an explanation of Reynolds Transport Theorem, describing the changes undergone by a single control volume at location ${\displaystyle {\boldsymbol {x}}}$. Several different fluid particles, with initial locations ${\displaystyle {\boldsymbol {\xi }}_{1},{\boldsymbol {\xi }}_{2},{\boldsymbol {\xi }}_{3},{\boldsymbol {\xi }}_{4}}$, pass through the given control volume at times ${\displaystyle t_{1},t_{2},t_{3},t_{4}}$. The rate of change of the property of the fluid ${\displaystyle F}$ in this control volume is the partial derivative ${\displaystyle {\frac {\partial F}{\partial t}}}$, where ${\displaystyle {\boldsymbol {x}}}$ is held constant.