Reynold’s Transport Theorem
The basic laws of Physics (i.e. conservation of mass, conservation of energy, and rate of change of momentum) are defined for a fixed particle or system of particles.
When dealing with fluids it is often more tractable to use an Eulerian frame of reference in which the properties of the fluid are defined at a spatial location. The fluid particles at this location change with time. Hence, a method for applying the basic laws of Physics to a continuously changing set of particles is required. The Reynolds Transport Theorem provides such a method.
Learning Objectives:
Describe the need for Reynold’s Transport Theorem
Flow through a SurfaceThe equation for the velocity normal to a surface is developed. 

Volume Crossing a SurfaceThe volume of fluid crossing a control surface 

Rate of Change of an Extensive PropertyFluid Transport, Reynolds Transport Theorem, Extensive Property 