# Conservation of Energy – Open System

The Conservation of Energy equation for an open system is one of the three equations that govern the flow of fluids. It is obtained by combining the 1st Law of Thermodynamics for a closed system and the Reynolds Transport Theorem.

The Reynolds Transport Theorem can be used to transform the 1st Law of Thermodynamics for a closed system to the 1st Law of Thermodynamics for an open system. The total energy is an extensive property that depends on the amount of mass present. An intensive property can be obtained by dividing the total energy by the mass of the system.

Applying Reynolds Transport Theorem yields the equation

Combining this equation with the 1st Law of Thermodynamics for a Closed System yields the 1st Law of Thermodynamics for an Open System

Using the equation for flow work allows the Conservation of Energy Equation to be written in as

Steady State Form of Equation

Under steady state conditions, nothing changes with time, and the equation reduces to

When average properties are used with a specific number of inlets and outlets, the equation can be written as

## Example Problem

## Learning Objectives:

Apply the 1st Law of Thermodynamics for an Open System