Conservation of Energy
Conservation of Energy is one of the three fundamental equations that govern the flow of fluids. The other two are Conservation of Mass and Rate of Change of Momentum. In addition to these equations material properties and state equations are needed.
The Conservation of Energy equation must account for a wide range of energy sources and mechanisms for adding or removing energy. The relationship between work and energy is very important since energy must be consumed when work is done or energy can be increased when work is done on a body.
The 1st Law of Thermodynamics for a closed system (one in which there is no mass exchange with the surroundings) will be used along with Reynolds Transport Theorem to derive the Conservation of Energy equation for a control volume or open system (one in which there is mass exchange with the surroundings). As a first step we will examine different forms of energy and work.
Learning Objectives:
Define open system, define closed system
Internal EnergyInternal energy, U, is a thermodynamic property that is associated with the microscopic random motion of atoms and molecules that make up a system. 

Kinetic Energy 

Potential EnergyThe potential energy of a fixed system of particles is governed by the equation … 

Flow WorkFlow work is similar to the work done by a force moving through a distance. In the case at hand, pressure times velocity is integrated over a surface to give the rate at which work is done, or, power. 

Conservation of Energy: Closed SystemThe 1st Law of Thermodynamics states that the total change in energy, E, for a closed system is equal to the difference between the heat added to the system and the work done by the system. 

Conservation of Energy – Open SystemThe Conservation of Energy equation for an open system is one of the three equations that govern the flow of fluids. 