Reynold’s Transport Theorem

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Reynold’s Transport Theorem provides a method for applying the basic laws of Physics to fluids in motion.  The control volume is a fundamental concept used in the derivation of this important theorem.

By Turbojet (Own work) [GFDL or CC-BY-SA-3.0-2.5-2.0-1.0], via Wikimedia Commons

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 Surface

Flow through a Surface

The equation for the velocity normal to a surface is developed.

Volume Crossing a Surface

The volume of fluid crossing a control surface

Rate of Change of an Extensive Property

Rate of Change of an Extensive Property

Fluid Transport, Reynolds Transport Theorem, Extensive Property