Development

We apply the Law of Conservation of Energy to a control volume. To do so, we must identify the forms of energy in the control volume. Consider the following system

The forms of energy in this system are:

·         Pressure energy: The pressure in a fluid also does work by generating force on a cross section which then moves through a distance. This is energy since work is energy.

·         Kinetic energy: This is due to the motion of the mass of fluid.

·         Potential energy: This is due to the height above an arbitrary datum

Pressure Energy

Kinetic Energy

From classical physics, the kinetic energy of the mass entering is:

Potential Energy

The potential energy of the mass entering, due to the height above the datum is:

Total Energy

The total energy at the entry to the system is just the sum:

Final Form

It is more usual to consider the energy per unit weight, and so we divide through by